HK1218024B - Excitation and use of guided surface wave modes on lossy media - Google Patents

Description

Excitation and use of guided surface wave modes on lossy media

The patent Cooperation treaty application claims priority AND benefit OF U.S. patent application Ser. No. 13/789,525 entitled "EXCITATION ANDUSE OF GUIDED SURFACace WAVE MODES ON LOSSY MEDIA" filed ON 7.3.2013 AND U.S. patent application Ser. No. 13/789,538 entitled "EXCITATION AND USE OF GUIDED SURFACace WAVE MODES LOSSY MEDIA" filed ON 7.3.2013, the contents OF both OF which are incorporated herein by reference in their entirety.

Background

For centuries, the signals carried by the radio waves involved radiated fields emitted using conventional antenna structures. Unlike radio science, electrical power distribution systems in the last century involved the transfer of energy directed along electrical conductors. This understanding of the difference between Radio Frequency (RF) and power transfer has existed since the beginning of the 20 th century.

Drawings

Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the figures, like reference numerals designate corresponding parts throughout the several views.

Fig. 1 is a graph illustrating field strength as a function of distance of a guiding electromagnetic field and a radiating electromagnetic field.

Fig. 2 is an illustration of a propagation interface having two regions employed to convey a guided surface wave in accordance with an embodiment of the disclosure.

FIG. 3 is a diagram illustrating placement of a polyphase waveguide probe relative to the propagation interface of FIG. 2 in accordance with an embodiment of the disclosure.

Fig. 4 is a diagram providing one exemplary illustration of phase shifts in ground current to facilitate launching a guided surface waveguide mode on a lossy conducting medium in the propagation interface of fig. 3, according to an embodiment of the disclosure.

FIG. 5 is a complex angle illustrating insertion of electric fields synthesized by a polyphase waveguide probe according to various embodiments of the disclosure.

FIG. 6 is a schematic diagram of a polyphase waveguide probe according to an embodiment of the disclosure.

Fig. 7A-J are schematic diagrams of specific examples of the polyphase waveguide probe of fig. 6 according to various embodiments of the disclosure.

Figures 8A-C are graphs illustrating field strengths of guided surface waves generated at a selected transmit frequency according to different embodiments of a polyphase waveguide probe according to different embodiments of the present disclosure.

Figure 9 illustrates one example of a graph of experimental measurements of field strength of a guided surface wave at 59 megahertz as a function of distance generated by a polyphase waveguide probe in accordance with an embodiment of the present disclosure.

Fig. 10 illustrates a graph of experimental measurements of phase as a function of distance for the guided surface wave of fig. 9 in accordance with an embodiment of the present disclosure.

Figure 11 illustrates another example of a graph of experimental measurements of field strength as a function of distance of a guided surface wave generated by a multi-phase waveguide probe at 1.85 megahertz, in accordance with an embodiment of the present disclosure.

12A-B illustrate examples of receivers that may be employed to receive energy transmitted in the form of a guided surface wave launched by a multi-phase waveguide probe according to various embodiments of the present disclosure.

Fig. 13 illustrates an example of additional receivers that may be employed to receive energy transmitted in the form of a guided surface wave launched by a polyphase waveguide probe in accordance with various embodiments of the present disclosure.

Fig. 14A illustrates a schematic diagram representing the Thevenin-equivalent (Thevenin-equivalent) of the receiver illustrated in fig. 12A-B, according to an embodiment of the present disclosure.

Fig. 14B illustrates a schematic diagram representing a receiver Norton-equivalent (Norton-equivalent) illustrated in fig. 13, in accordance with an embodiment of the present disclosure.

Detailed Description

First, with reference to FIG. 1, certain terms will be established to provide clarity in discussing the concepts to be followed. First, as contemplated herein, a formal distinction is made between a radiating electromagnetic field and a guiding electromagnetic field.

As contemplated herein, the radiated electromagnetic field contains electromagnetic energy emanating from the source structure in the form of waves that are not bound to the waveguide. For example, a radiated electromagnetic field is generally a field that exits an electronic structure such as an antenna and propagates through the atmosphere or other medium and is not bound to any waveguide structure. When radiated electromagnetic waves leave an electronic structure such as an antenna, they continue to propagate in a propagation medium (such as air) independent of their source until they are consumed, regardless of whether the source continues to operate. When electromagnetic waves are radiated, they are not recoverable unless intercepted, and if not intercepted, the energy inherent in the radiated electromagnetic waves is permanently lost. Electronic structures such as antennas are designed to radiate electromagnetic fields by maximizing the ratio of radiation resistance to the structure's loss impedance. The radiated energy spreads out in space and will be lost whether or not a receiver is present. Due to the geometrical extension, the energy density of the radiation field is a function of the distance. Accordingly, all forms of the term "radiation" are used herein to refer to this form of electromagnetic propagation.

A guided electromagnetic field is a propagating electromagnetic wave with energy concentrated within or near the boundary between media having different electromagnetic properties. In this sense, a guided electromagnetic field is an electromagnetic field that is bound to a waveguide and can be characterized as being carried by current flowing in the waveguide. If no load receives and/or consumes energy carried in the guided electromagnetic wave, no energy is lost other than that consumed in the conduction of the guided medium. In other words, if there is no load to guide the electromagnetic wave, energy is not consumed. Thus, a generator or other source that generates the guided electromagnetic field does not deliver real power unless an impedance load is present. To this end, such generators or other sources essentially stall until there is a load. This is similar to running the generator to generate 60 hertz of electromagnetic waves transmitted through a power line without an electrical load. It should be noted that the guided electromagnetic field or wave is equivalently referred to as the "transmission line mode". This is different from a radiated electromagnetic wave that supplies real power at all times to generate a radiated wave. Unlike radiated electromagnetic waves, guided electromagnetic energy does not continue to propagate along the wired length waveguide after the energy source is turned off. Accordingly, all forms of the term "guided" are used herein to refer to such modes of transmission of electromagnetic propagation.

To further illustrate the difference between radiated and guided electromagnetic fields, referring to FIG. 1, FIG. 1 illustrates a graph 100 of field strength in decibels (dB) per meter over an arbitrary reference in volts as a function of distance in kilometers on a log-dB plot. The graph 100 of fig. 1 illustrates a guiding field strength curve 103 showing the field strength of a guiding electromagnetic field as a function of distance. The guiding field intensity curve 103 is substantially identical to the transport line pattern. In addition, the graph 100 of fig. 1 illustrates a radiation field strength curve 106 showing the field strength of a radiated electromagnetic field as a function of distance.

Of interestIs the shape of the curves 103/106 of radiation and guided wave propagation. The radiation field intensity curve 106 is geometrically decreasing (1/d, where d is the distance) and is a straight line on a log-log scale. On the other hand, the guidance field intensity curve 103 hasAnd exhibits different inflection points (knee) 109. Thus, as shown, the field strength of the electromagnetic field is directed toWherein the field strength of the radiated electromagnetic field decreases at a ratio of 1/d, where d is the distance. Due to the fact that the guiding field strength curve 103 decreases exponentially, the guiding field strength curve 103 is characterized by the above-mentioned inflection point 109. The guiding field intensity curve 103 and the radiation field intensity curve 106 intersect at an intersection point 113, which occurs at an intersection distance. At distances smaller than the crossing distance, the field strength of the guiding electromagnetic field is at most locations significantly larger than the field strength of the radiating electromagnetic field. At distances greater than the crossing distance, the opposite is true. Thus, the guiding and radiating field strength curves 103 and 106 also illustrate the fundamental propagation differences between the guiding and radiating electromagnetic fields. For an informal discussion of the difference between the guided and radiated electromagnetic fields, reference is made to Milligan, TModern Antenna Design(McGraw-Hill, first edition, 1985, pages 8-9), the entire contents of which are incorporated herein by reference.

The distinction made above between radiating and guiding electromagnetic waves is easily formalized and placed on a strict basis. Those two different solutions can come from the same linear partial differential equation, the wave equation being analytically derived from the boundary conditions imposed on the problem. The Green function of the wave equation itself contains the distinction between the properties of the radiated and guided waves.

In empty space, the wave equation is a differential operator where the eigenfunction possesses a continuum of eigenvalues across the complex wavenumber plane. This Transverse Electromagnetic (TEM) field is called radiationThe fields, and those propagating fields are referred to as "hertzian waves". However, in the presence of a conduction boundary, the wave equation plus the boundary condition mathematically results in a spectral representation of the wavenumber, which contains the sum of the continuous spectrum plus the discrete spectrum. For this, reference is made to Sommerfeld, A. "Uber dieAusbrietting der Wellen in der Drahtlosen Telegraphie" (Annalen der Physik, Vol.28, 1909, p.665-736). See also "Problems of radiation" by Sommerfeld, A. (published as partial differentiation Equipment in Physics-principles on Theoretical Physics: Chapter 6 in Volume VI, Academic Press, 1949, pages 236-289, 295-296), Collin, R.E. "Hertzian diode radiation Over a ease Earth or Sea: Sommearly and Late 20^thCentury controls "(IEEE Antennas and Propagation magazines, volume 46, No. 2, 4 months 2004, pages 64-79) and Reich, h.j., orndnng, P.F, Krauss, h.l., and Skalnik, j.g.," microwave tools and Techniques "(Van nostrandand, 1953, pages 291-293), the entire contents of each of these references being incorporated herein by reference.

To summarize the above, first, the continuum of the wavenumber-characteristic spectrum corresponding to branch-cut integrations (branch-cut integrations) produces a radiation field, and second, the sum of the discrete spectrum and the corresponding residual error produced by the poles of the integrated profile envelope yields a non-TEM travelling surface wave that decays exponentially for directions transverse to propagation. Such surface waves are guided transmission line modes. For further explanation, reference is made to Friedman, B, "Principles and Techniques of applied Mathesics" (Wiley, 1956, pages 214, 283-286, 290, 298-300).

In free space, the antenna excites a continuum of eigenvalues (continuous eigenvalues) of the wave equation as the radiation field, with E_zAndthe out-propagating RF energy in phase is lost forever. On the other hand, waveguide detectors excite discrete eigenvalues, which result in transmission line propagation. See Collin, R.E. "Field Theory of guided Waves "(McGraw-Hill, 1960, pp 453, 474-477). While such theoretical analysis suggests the possibility of the assumption of launching an open surface guided wave on a lost planar or spherical surface, for over a century there has not been a known structure in the engineering field to achieve this with any practical efficiency. Unfortunately, because of its appearance in the early 20 th century, the theoretical analysis described above remains substantially at a theoretical level, and there are no known structures for realistically achieving the emission of open surface guided waves on planar or spherical surfaces of lossy, heterogeneous media.

In accordance with various embodiments of the present disclosure, a variety of polyphase waveguide detectors are described that are configured to excite a radiating surface current with a resultant field in the form of a composite surface waveguide mode along a surface of a lossy conducting medium. Such a guided electromagnetic field is sufficiently mode-matched in amplitude and phase to a guided surface wave mode on the surface of the lossy conducting medium. Such guided surface wave modes may also be referred to as zernike surface wave modes. Due to the fact that the resultant field excited by the multi-phase waveguide probe described herein is sufficiently mode-matched to a Zenneck surface wave (Zenneck surface wave) mode on the surface of the lossy conducting medium, a guided electromagnetic field in the form of a Zenneck surface wave is launched along the surface of the lossy conducting medium. According to one embodiment, the lossy conducting medium comprises a terrestrial medium such as the earth.

Referring to FIG. 2, there is shown a Propagation interface for examining the boundary value solution of Maxwell's equation in their paper "on the Propagation of Plane Electromagnetic Waves Along a Flat connection surface and the relationship to Wireless Telegraphy" (Zenneck, J, Annalen der Physik, No. 4, Vol.23, p.9-20, p.1907, p.846-866) by Jonathan Zenneck in 1907. Fig. 2 illustrates the cylindrical coordinates of a wave propagating radiatively along the interface between a lossy conducting medium designated as region 1 and an insulator designated as region 2. The region 1 may for example comprise any lossy conducting medium. In one example, such a lossy conducting medium may comprise a terrestrial medium such as the earth or other medium. Zone 2 is a second medium that shares a boundary interface with zone 1 and has different composition parameters relative to zone 1. The region 2 may for example contain any insulator such as the atmosphere or other medium. The reflection coefficient of such a boundary interface is 0 only for incidence at a complex brewster angle. See Electromagnetic therapy of Stratton, j.a. (McGraw-Hill, 1941, page 516).

According to various embodiments, the present disclosure sets forth various polyphase waveguide probes that generate electromagnetic fields that are sufficiently mode-matched to Zernike surface wave modes on a surface of a lossy conducting medium containing region 1. According to various embodiments, such electromagnetic fields are sufficiently synthesized to result in a wavefront of zero reflection at a complex brewster angle of incidence for the lossy conducting medium.

For further explanation, in region 2, where e is assumed^jωtThe field variation and ρ ≠ 0 and z ≧ 0(z is the vertical coordinate orthogonal to the surface of zone 1, ρ is the radial dimension in cylindrical coordinates), the closed-form exact solution of zernike that satisfies the interface conditions along the interface is represented by the following electric and magnetic field components:

and (2)

In region 1, where e is assumed^jωtThe field variables and ρ ≠ 0 and z ≧ 0, the closed-form exact solution of Zernike of Maxwell's equations that satisfies the boundary conditions along the interface is represented by the following electric and magnetic field components:

and (5)

In the context of these expressions,is a complex parametric Hankel function of order n, class two, u₁Is the propagation constant in the positive vertical direction in region 1, u₂Is a propagation constant, σ, in the vertical direction in region 2₁Is the conductivity in region 1, ω being equal to 2 π f, where f is the excitation frequency, ε₀Is the dielectric constant of free space, epsilon₁Is the dielectric constant of region 1, a is the source constant imposed by the source, z is the vertical coordinate orthogonal to region 1, γ is the surface wave radial propagation constant, and ρ is the radial coordinate.

The propagation constants in the ± z-direction are determined by splitting the wave equation above and below the interface between regions 1 and 2 and imposing boundary conditions. In region 2, the training is given

And in region 1, given

u₁＝-u₂(ε_r-jx). (8)

The radial propagation constant γ is given by

Which is a complex expression. In all of the equations above, the equation above,

and (10)

Wherein u is₀Magnetic permeability containing free space, epsilon_rIncluding the relative dielectric constant of region 1. Thus, the generated surface wave propagates parallel to the interface and decays exponentially perpendicular to the interface. This is called oblivious.

Thus, equations (1) - (3) can be viewed as cylindrically symmetric, radially propagating waveguide modes. See Barlow, H.M. and Brown, J. "Radio Surface Waves" (Oxford University Press, 1962, pages 10-12, 29-33). The present disclosure details the structure that excites such "open boundary" waveguide modes. In particular, according to various embodiments, the polyphase waveguide probe is equipped with appropriately sized charge terminals placed with respect to each other and fed with voltages and/or currents so as to excite a relative phasing of the fields of the surface waveguide modes to be emitted along the boundary interface between region 2 and region 1.

Continuing further, the Leontovich impedance boundary condition between region 1 and region 2 is noted as

Wherein the content of the first and second substances,is the unit normal in the positive vertical (+ z) direction, andis the magnetic field strength in the region 2 represented by the above equation (1). Equation (12) indicates that the fields specified in equations (1) - (3) can be obtained by driving the radial surface current density along the boundary interface, such as the radial surface current density specified by:

where A is a constant yet to be determined. In addition, it should be noted that in the vicinity of the polyphase waveguide probe (ρ < λ), equation (13) above has the following behavior:

one may notice the negative sign. This means that when the source current flows vertically upwards, the required "near zone" ground current flows radially inwards. By being atThe matched field on the "near zone", we find that in equations (1) - (6) and (13),

therefore, equation (13) can be restated as

Referring then to FIG. 3, which shows an example of a polyphase waveguide probe 200, polyphase waveguide probe 200 includes charge terminals T arranged along a vertical axis z₁And a charge terminal T₂. According to the present disclosureIn an embodiment, polyphase waveguide probe 200 is disposed over lossy conducting medium 203. According to one embodiment, lossy conducting medium 203 constitutes region 1 (fig. 2). In addition, the second dielectric 206 shares a boundary interface with the lossy conducting medium 203, and constitutes region 2 (fig. 2). The polyphase waveguide probe 200 includes a probe coupling circuit 209 that couples an excitation source 213 to a charge terminal T₁And T₂This will be discussed in more detail with reference to the following figures.

Charge terminal T₁And T₂Over the lossy conducting medium 203. Can connect the charge terminal T₁Considered a capacitor, and as described herein, a charge terminal T₂A counterbalance or a lower capacitor may be included. According to one embodiment, the charge terminal T₁At a height H₁And a charge terminal T₂At a height H along a vertical axis z₂T of (C)₁Is right below, wherein H₂Is less than H₁. Polyphase waveguide probe 200 exhibits a transmission structure with a height H ═ H₁-H₂. Given the foregoing discussion, the lossy conducting medium J can be_ρThe asymptote of the radial Zernike surface current on the surface of (ρ) is determined as J₁(ρ) near zone and J₂(p) a far zone, wherein

Near zone (ρ < λ/8):and (17)

Remote zone (ρ > λ/8):

wherein, I₁Is fed to the first charge terminal T₁Charge Q on₁Conducting current of I₂Is fed to the second charge terminal T₂Charge Q on₂Is conducted. Upper charge terminal T₁Charge Q on₁By Q₁＝C₁V₁Is determined whereinC₁Is a charge terminal T₁The isolation capacitor of (2). Note that for J as set forth above₁Exist ofA third component which follows the Leontovich boundary conditions and is caused by the rising oscillating charge Q on the first charge terminal₁The quasi-static field of (a) into the lossy conducting medium 203. Measurement ofIs the radial impedance of a lossy conducting medium, where gamma_e＝(jωμ₁σ₁-ω²μ₁ε₁)^1/2。

The asymptotes representing the radial current near and far zones as set forth by equations (17) and (18) are complex quantities. According to various embodiments, the physical surface current J (r) is synthesized to match the current asymptote approximately, possibly closely, in magnitude and phase. That is, the near-zone (close-in) | J (r) | is | J₁Is tangent, and the far zone (far-out) | J (r) | is | J₂Tangent of l. Additionally, according to various embodiments, J (r) corresponds to J₁Phase transition to J in the near zone₂Phase of the distal region.

According to one embodiment, if any of the different embodiments of the polyphase waveguide probe described herein is appropriately adjusted, the configuration will give at least an approximate magnitude sum match for the zernike modes and launch a zernike surface wave. It should be noted that the remote phase region φ₂And corresponds to e^-jβρIs due to the fact thatIs/are as followsProportional to the fixed "phase lifting" caused by the phase(s),

where γ is expressed in equation (9) above and depends on ε at the location of the transmitted field on the lossy conducting medium_rThe value of sum σ and the operating frequency f, having two complex rootsTypically on the order of approximately 45 or 225. In other words, to match the zernike surface wave mode at the transmitted field to launch a zernike surface wave, the surface current | J₂Corresponding terms of the | far zone correspond toIs different from the surface current | J by adding a constant of approximately 45 degrees or 225 degrees to₁I phase of the near zone. This is because there areOne near pi/4 and one near 5 pi/4. The properly adjusted resultant radial surface current is

Such a J (p) surface current automatically creates a field that conforms to the following equation according to Maxwell's equations

And (22)

Thus, the surface current | J of the matched Zernike surface wave mode₂Distance zone and surface current | J₁The phase difference between the near zones is due to the inherent characteristics of the hankel functions in equations (20) - (23) set forth above. It is clearly recognized that the fields represented by equations (1) - (6) and (20) have the properties of a transmission line mode bound to a lossy interface rather than a radiated field such as that associated with ground wave propagation. See Barlow, H.M. and Brown, J. "Radiosurface Waves" (Oxford University Press, 1962, pages 1-5). These fields automatically meet the complex brewster angle requirement for zero reflection, which means that the radiation is negligible while dynamically enhancing the surface guided wave propagation, which is validated and supported by the experimental results provided below.

In this regard, review of the nature of the hankerr function used in equations (20) - (23) is provided by emphasizing the special properties of these solutions of the wave equation. It may be observed that the one-and two-class hankers of order n are defined as complex combinations of one-and two-class standard bessel functions

And (24)

These functions represent the radially propagating cylindrical waves inward (superscript (1)) and outward (superscript (2)), respectively. Definition analogous to relationship e^±jxCos x ± j sin x. See, for example, Harrington, R.F. "Time-Harmonic Fields" (McGraw-Hill, 1961, pages 460-463).

TheIs an output wave based on a direct drive from J_n(X) and N_n(X) ofIts large parametric asymptotic behaviour, directly obtained by sequence definition, is easily identified

Which is multiplied by e^jωtWhen of the form e with a spatial variation of 1/√ ρ^j(ωt-kρ)Outwards propagating cylindrical waves. The phase of the exponential component is ψ ═ ω t-k ρ. It is also apparent that

And, another useful attribute of the hankerr function is expressed as

It is described by Jahnke, e, and f.emde, "Tables of Functions" (Dover, 1945, page 145).

In addition, the asymptotes of the small and large parameters of the outward propagation hankel function are as follows:

note that these asymptote expressions are complex quantities. In addition, unlike the ordinary sinusoidal function, the behavior of the complex hankerr function differs from the origin at the near and far regions. When x is a real quantity, equations (29) and (30) are in phaseBut instead it corresponds to an additional phase advance or "phase boost" of 45 deg., or equivalently, λ/8.

Referring to FIG. 4, illustrated J is further illustrated₁(FIG. 3) and J₂The phase transition between (FIG. 3) is the surface current J relative to the position of the polyphase waveguide probe 200 (FIG. 3)₁Near zone and J₂Illustration of the phase of the distal region. As shown in FIG. 4, there are three different observation points P₀、P₁And P₂. The transition region being located at the observation point P₁And observation point P₂In the meantime. Observation point P₀At the location of the polyphase waveguide probe 200. Observation point P₁At a point of observation P₁Placed in the transition region 216 and the observation point P₀From the viewpoint P₀Distance R₁The "near zone" of (c). Observation point P₂Located beyond the transition region 216 as shown, away from the observation point P₀Distance R₂The "far zone" of (c).

At observation point P₀The amplitude and phase of the radial current J are represented asAt observation point P₁The amplitude and phase of the radial current J are represented aswherein, β R₁Is attributable to the observation point P₀And P₁A distance R therebetween₁. At observation point P₂The amplitude and phase of the radial current J are represented asWherein the content of the first and second substances,is attributable to the observation point P₀And P₂A distance R therebetween₂And additional phase shifts present in the transition region 216. Additional phase shiftThe attribute appears as a hankel function as described above.

The foregoing reflects the fact that: multiphase waveguide probe 200 generates surface current J₁Near zone, then transition to J₂And a current far zone. In the transition region 216, the phases of the Zernike surface waveguide modes follow approximately 45 degrees orTo make a transition. This transition or phase shift may be considered "phase-lifting" because the phases of the zernike surface waveguide mode are raised by 45 degrees in the transition region 216. The transition region 216 appears to occur somewhere less than 1/10 th of the wavelength of the operating frequency.

Referring back to FIG. 3, according to one embodiment, a multi-phase waveguide probe may be created that will emit the appropriate radial surface current distribution. According to one embodiment, a zernike waveguide mode is created in the radiation direction. If J (r) given by equation (20) can be created, it will automatically launch a zernike surface wave.

In addition, charge terminal T for one example polyphase waveguide probe shown in FIG. 3₁And T₂Charge Q on₁And Q₂Charge image Q of₁' and Q₂' further discussion is provided. Analysis of lossy conducting medium assumes that the charge reservoir T as described herein is compatible with₁And T₂Charge Q on₁And Q₂Presence of induced effective image charge Q under coherent polyphase waveguide detector₁' and Q₂'. Such image charge Q must also be considered in the analysis₁' and Q₂'. These image charges Q₁' and Q₂' not only with the charge reservoir T₁And T₂Main source charge Q of₁And Q₂180 deg. out of phase as in the case of an ideal conductor. Lossy propagation media, such as, for example, terrestrial media, exhibit phase-shifted imagery. That is to sayNamely, the image charge Q₁' and Q₂' at complex depth (complex depth). For a discussion of plural images, reference is made to "complete image theory-viewed" (IEEE antibodies and presentation Magazine, Vol. 33, No. 4, 8.1991, pp. 27-29) of Wait, J.R., the entire contents of which are incorporated herein by reference.

Instead of being at equal charge Q₁And Q₂Depth of height (i.e., z)_n′＝-h_n) Image charge Q of₁' and Q₂' at a depth z-d/2, a conductive mirror 215 is placed, and the image itself appears at z_n′＝-D_n＝-(d+h_n)≠-h_nAt a given "complex distance" (i.e., "distance" has both amplitude and phase), where n is 1,2, and for vertically polarized sources,

wherein

And (32)

Further, the image charge Q₁' and Q₂The complex spacing of' indicates that the external field will experience an additional phase shift that is not encountered when the interface is a lossless insulator or perfect conductor. The essence of lossy insulator image theory is to replace the earth of limited conduction (or lossy insulator) with a perfect conductor at a complex depth z-d/2. Next, the source image is placed at a plurality of depths D_n＝d/2+d/2+h_n＝d+h_nWhere n is 1, 2. The overlap of the physical charge (at z + h) plus its image (at z' -D) can then be used to calculate the ground levelUpper field (z ≧ 0). Charge image Q at complex depths₁' and Q₂' actually participates in obtaining the desired current phase specified in equations (20) and (21) above.

From equations (2) and (3) above, it is noted that in region 2To pairIs given by

In addition, it should be noted that asymptotically

Thus, it follows directly from equations (2) and (3)

Wherein psi_i，BIs the complex brewster angle. By adjusting the source distribution and synthesizing complex brewster angle illumination at the surface of the lossy conducting medium 203, a zernike surface wave can be excited.

Referring to fig. 5, an incident field E is shown polarized parallel to the plane of incidence. The electric field vector E will be synthesized as an incoming inhomogeneous plane wave, polarized parallel to the plane of incidence. The electric field vector E can be created from separate horizontal and vertical components as:

geometrically, the illustration in fig. 5 shows:

E_ρ(ρ，z)＝E(ρ，z)cosψ_oand (38a)

This means that the field ratio is

Recall, however, that according to equation (36),

so that for Zernike surface waves, psi is desired_o＝θ_i，BWhich result in

These equations imply that if the magnitude of the complex field ratio and the incident vertical and horizontal components E in a plane parallel to the plane of incidence are controlled_zAnd E_ρThe relative phases in between, then the resultant E-field vector will be effectively incident at the complex brewster angle. Such a situation will synthetically excite the zernike surface wave above the interface between region 1 and region 2.

Referring to fig. 6, another view of a polyphase waveguide probe 200 disposed over a lossy conducting medium 203 in accordance with an embodiment of the disclosure is shown. According to one embodiment, lossy conducting medium 203 constitutes region 1 (fig. 2). In addition, the second dielectric 206 shares a boundary interface with the lossy conducting medium 203, and constitutes region 2 (fig. 2).

According to one embodiment, the lossy conducting medium 203 comprises a terrestrial medium such as a planetary earth. To this end, such a ground medium is intended to include all structures or formations (whether natural or man-made) therein. For example, such ground media may contain natural elements such as rocks, soil, sand, fresh water, sea water, trees, vegetation, and all other natural elements that make up our planet. In addition, such ground media may contain man-made elements such as concrete, asphalt, building materials, and other man-made materials. In other embodiments, the lossy conducting medium 203 may comprise some medium other than the earth, whether naturally occurring or man-made. In other embodiments, the lossy conducting medium 203 may comprise other media, such as man-made surfaces and structures, e.g., automobiles, aircraft, man-made materials (such as plywood, plastic sheeting, or other materials), or other media.

Where the lossy conducting medium 203 comprises a terrestrial medium or the earth, the second medium 206 may comprise the atmosphere above the ground. Thus, the atmosphere may be referred to as the "atmospheric medium" which contains air as well as other elements that make up the earth's atmosphere. In addition, it is also possible that the second medium 206 may comprise other media related to the lossy conducting medium 203.

Polyphase waveguide probe 200 includes a pair of charge terminals T₁And T₂. Although two charge terminals T are shown₁And T₂However, it is to be understood that there may be more than two charge terminals T₁And T₂. According to one embodiment, the charge terminal T₁And T₂Over the lossy conducting medium 203 along a vertical axis z orthogonal to the plane represented by the lossy conducting medium 203. At this point, the charge terminal T₁Directly placed at the charge terminal T₂Although two or more charge terminals T may be used_NSome other arrangement of (2). According to various embodiments, the charge Q₁And Q₂Applied to respective charge terminals T₁And T₂。

Charge terminal T₁And/or T₂Any conductive body (conductive mass) that can hold an electronic charge may be included. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. Charge terminal T₁And/or T₂Any shape may be included, such as spherical, disk, cylindrical, conical, toroidal, random, or any other shape. It is also noted that the charge terminal T₁And T₂Need not be identical, but may each be of separate size and shape and comprise different conductive materials. According to one embodiment, the charge terminal T₁Is specified to hold as much charge as practical. Basically, the field strength of the Zernike surface wave launched by the polyphase waveguide probe 200 is directly related to the terminal T₁The amount of charge on is proportional.

If the charge terminal T₁And/or T₂Is a ball or a disk, the corresponding self-capacitance C can be calculated₁And C₂. For example, the self-capacitance of the individual conductive ball is C ═ 4 pi ∈₀r, where r comprises the radius of the sphere in meters. The self-capacitance of the individual disc is C-8 epsilon₀r, where r comprises the radius of the disc in meters.

Thus, a charge reservoir T is given₁Self-capacitance C₁And is applied to the charge terminal T₁Is stored at the charge terminal T₁Charge Q on₁Can be calculated as Q₁＝C₁V。

With further reference to FIG. 6, in accordance with one embodiment, a polyphase waveguide probe 200 includes a coupling to a charge terminal T₁And T₂The detector coupling circuit 209. Detector coupling circuit 209 facilitates coupling excitation source 213 to charge terminal T₁And T₂And facilitates generation of a voltage at the charge terminal T for a given frequency of operation₁And T₂The corresponding voltage amplitude and phase. If two are adoptedMore than one charge terminal T_NThe detector coupling circuit 209 would be configured to facilitate connection at the corresponding charge terminal T_NWhich generate different voltage amplitudes and phases with respect to each other. In the embodiment of the polyphase waveguide probe 200, the probe coupling circuit 209 comprises different circuit configurations to be described.

In one embodiment, the detector coupling circuit 209 is designated to electronically half-wave resonate the polyphase waveguide detector 200. This is at terminal T at any given time₁Or T₂Imposes a voltage + V on the first one of and at the charge terminal T₁Or T₂imposes-V on the second one of. In such a case, it can be appreciated that at the respective charge terminal T₁And T₂The voltages on are 180 degrees out of phase. At the corresponding charge terminal T₁And T₂At a charge terminal T, 180 degrees out of phase₁And T₂The maximum voltage amplitude difference is experienced. Alternatively, the detector coupling circuit 209 may be configured such that the charge terminal T is₁And T₂The phase difference between them is different from 180 degrees. To this end, the detector coupling circuit 209 may be adjusted to vary the voltage amplitude and phase during the adjustment of the polyphase waveguide detector 200.

Due to the charge terminal T₁Directly placed at the charge terminal T₂Above, at the charge terminal T₁And T₂Between them, a mutual capacitance C is created_M. In addition, as described above, the charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. Dependent on the charge terminal T₁And T₂At the respective height of the charge terminal T₁And the lossy conducting medium 203, and a binding capacitance may also exist and be at the charge terminal T₂And the lossy conducting medium 203. Mutual capacitance C_MDependent on the charge terminal T₁And T₂The distance between them.

Finally, the field strength generated by the polyphase waveguide probe 200 will be directly imposed on the upper terminal T₁Charge Q on₁In proportion to the amount of the compound. Further, the charge Q₁And a charge terminal T₁Associated self-capacitance C₁In proportion because of Q₁＝C₁V, where V is imposed at the charge terminal T₁The voltage of (c).

According to one embodiment, an excitation source 213 is coupled to the detector coupling circuit 209 for applying signals to the polyphase waveguide detector 200. The excitation source 213 may be any suitable power source, such as a voltage or current source capable of generating a voltage or current that is applied to the operating frequency of the polyphase waveguide probe 200. To this end, the excitation source 213 may comprise, for example, a generator, a function generator, a transmitter, or other power source.

In one embodiment, excitation source 213 may be coupled to polyphase waveguide probe 200 by magnetic coupling, capacitive coupling, or conductive (direct tap) coupling as will be described. In some embodiments, the probe coupling circuit 209 may be coupled to the lossy conducting medium 203. Additionally, as will be described, in various embodiments, the excitation source 213 may be coupled to the lossy conducting medium 203.

In addition, it should be noted that, according to one embodiment, the polyphase waveguide probe 200 described herein has the following characteristics: its radiation resistance R_rVery small or even negligible. It should be remembered that the radiation resistance R_rIs the equivalent impedance that will dissipate the same amount of power that will ultimately be radiated from the antenna. According to various embodiments, the polyphase waveguide probe 200 emits a Zernike surface wave as a guided electromagnetic wave. According to various embodiments, the polyphase waveguide detector described herein has a very small radiation resistance R_rSince the height of such polyphase waveguide detectors is usually small relative to their operating wavelength. In other words, according to one embodiment, the polyphase waveguide probe described herein is "electronically small". As contemplated herein, the expression "electronically small" is defined as a structure such as the various embodiments of the multi-phase waveguide probe described herein, which may bePhysically bound by a sphere having a radius equal to λ/2 π, where λ is the free space wavelength. See "smallnantennas" by Fujimoto, k., Henderson, k.ahiraawa and j.r.jame (Wiley, 1987, page 4).

For further discussion, the radiation resistance R of a short monopole antenna_rIs shown as

Wherein the short monopole antenna has a height h of uniform current distribution and wherein λ is the wavelength of the frequency of operation. See Stutzman, W.L. et al, "Antenna Theory and Design" (Wiley & Sons, 1981, page 93).

Given radiation resistance R_rIs determined asThen it follows: if the height h of the structure is small relative to the wavelength of the operating signal of the operating frequency, the radiation resistance R_rWill also be small. As an example, if the height h of the transmission structure is 10% of the wavelength of the operating signal of the operating frequency, thenThe resulting value of (a) will be (.1)²01. It will follow: radiation resistance R_rCorrespondingly small.

Thus, according to various embodiments, if the effective height h of the transfer structure is less than or equal toWhere λ is the wavelength of the operating frequency, the radiation resistance R_rWill be relatively small. For the different embodiments of the polyphase waveguide probe 200 described below, the height H of the transfer structure can be calculated as H ═ H₁-H₂Wherein H is₁Is a charge terminal T₁Height of (H)₂Is a charge terminal T₂Of (c) is measured. It should be appreciated that the height h of the transfer structure of each embodiment of the polyphase waveguide probe 200 described herein may be determined in a similar manner.

Although it is used forIs provided as a reference, but it is understood that the ratio of the height of the transmission structure to the wavelength of the operating signal at the operating frequency may be any value. However, it will be appreciated that at a given operating frequency, as the height of a given transmission structure increases, the radiation resistance R_rWill increase accordingly.

Depending on the actual value of the wavelength of the operating signal of the height h and operating frequency, the radiation resistance R_rCan be a value such that a certain amount of radiation can appear with the launch of the zernike surface wave. To this end, the polyphase waveguide probe 200 can be constructed with a small height relative to the wavelength of the operating frequency in order to ensure that little or substantially 0 energy is lost in the form of radiation.

In addition, the charge reservoir T is placed along the vertical axis z₁And T₂Symmetry in the zernike surface waves launched by the polyphase waveguide probe 200 as described by the hankel functions in equations (20) - (23) set forth above is provided. Albeit with two charge reservoirs T along a vertical axis z orthogonal to the plane constituting the surface of the lossy conducting medium 203₁And T₂A polyphase waveguide probe 200 is shown, but it is understood that other configurations may be employed that would also provide the desired symmetry. For example, a further charge reservoir T may be placed along the vertical axis z_NOr some other arrangement may be employed. In some embodiments, symmetry of the transmission may not be desired. In such a case, the charge reservoirs T may be arranged in a configuration other than along the vertical axis z_NTo provide an alternative transfer profile pattern.

When properly tuned to operate at a predefined operating frequency, the polyphase waveguide probe 200 generates a zernike surface wave along the surface of the lossy conducting medium 203. To this end, an excitation source 213 may be employed to generate electrical energy of a predetermined frequency that is applied to the polyphase waveguide probe 200 to excite the structure. Energy from the excitation source 213 is transmitted through the polyphase waveguide probe 200 in the form of a zernike surface wave to one or more receivers that are also coupled to the lossy conducting medium 203 or that are within the effective transmission range of the polyphase waveguide probe 200. Energy is thus carried in the form of zernike surface waves as surface waveguide modes or guided electromagnetic fields. In the context of modern power grids using high voltage lines, the zernike surface waves contain a transmission line mode.

Thus, the Zernike surface waves generated by the polyphase waveguide probe 200 are not radiation waves, but guided waves, the meaning of these terms being described above. The zernike surface waves are launched due to the fact that: the polyphase waveguide probe 200 creates an electromagnetic field that is sufficiently mode-matched to a zernike surface wave mode on the surface of the lossy conducting medium 203. When the electromagnetic fields generated by the polyphase waveguide probe 200 are also sufficiently mode-matched, the electromagnetic fields are sufficiently synthesized to result in a complex brewster angle incident wavefront of the lossy conducting medium 203 with little or no reflection. Note that if the polyphase waveguide probe 200 is not sufficiently mode-matched to the zernike surface waves, the zernike surface waves will not be launched because the complex brewster angle of the lossy conducting medium 203 is not obtained.

In the case where the lossy conducting medium 203 comprises a ground medium such as the earth, as indicated above in equations (1) - (11), the Zernike surface wave modes will depend on the dielectric constant ε of the insulator at the location of the polyphase waveguide probe 200_rAnd a conductivity σ. Therefore, the phases of the hankerr functions in equations (20) - (23) above depend on these constituent parameters at the transmit location and the frequency of operation.

To excite the field associated with the zernike surface wave modes, according to one embodiment, the polyphase waveguide probe 200 sufficiently synthesizes the radial surface current density on the lossy conducting medium of the zernike surface wave modes as represented by equation (20) set forth above. When this occurs, then the electromagnetic field is sufficiently or approximately mode-matched to the zernike surface wave modes on the surface of the lossy conducting medium 203. For this reason, the matches should be as close as possible. According to one embodiment, the Zernike surface wave modes that are substantially matched to the electromagnetic field are represented by equations (21) - (23) set forth above.

To synthesize radial surface current density in a lossy conducting medium of Zernike surface wave modes, the electronic characteristics of the polyphase waveguide probe 200 should be adjusted to provide a charge terminal T for a given operating frequency and given electronic characteristics of the transport sites₁And T₂Appropriate voltage amplitudes and phases are imposed. If more than two charge terminals T are used_NThen it will need to be at the corresponding charge terminal T_NAppropriate voltage amplitudes and phases are imposed on, where N can even be a very large number effectively containing a closed set of charge terminals.

To obtain the appropriate voltage amplitude and phase for a given design of the polyphase waveguide probe 200 at a given location, an iterative approach may be used. In particular, the terminal T may be considered₁And T₂Given excitation and configuration of current-fed polyphase waveguide probe 200, charge terminal T₁And T₂The charges thereon and their images in the lossy conducting medium 203 are analyzed to determine the resulting radial surface current density. The process may be performed iteratively until an optimal configuration and excitation for a given polyphase waveguide probe 200 is determined based on the desired parameters. To help determine whether a given polyphase waveguide probe 200 is operating at an optimal level, the conductivity (σ) of region 1 at the location of polyphase waveguide probe 200 can be based₁) And the dielectric constant (. epsilon.) of region 1₁) Using equations (1) - (11) above, to generate the guidance field strength curve 103 (fig. 1). Such a pilot field strength curve 103 will provide a reference for the operation such that the measured field strength can be compared to the amplitude indicated by the pilot field strength curve 103The degrees are compared to determine if the best transmission has been achieved.

Various parameters associated with polyphase waveguide probe 200 may be adjusted in order to achieve an optimal polyphase waveguide probe 200. In other words, different parameters associated with polyphase waveguide probe 200 can be varied to adjust phase waveguide probe 200 to a desired operating configuration.

One parameter that may be varied to adjust polyphase waveguide probe 200 is charge terminal T₁And/or T₂Relative to the height of the surface of the lossy conducting medium 203. In addition, the charge terminal T can also be adjusted₁And T₂The distance or spacing therebetween. To this end, it can be appreciated that the mutual capacitance C can be minimized or otherwise varied_MOr a charge terminal T₁And T₂Any binding capacitance with the lossy conducting medium 203.

Alternatively, a further parameter which may be adjusted is the respective charge terminal T₁And/or T₂The size of (2). It will be appreciated that by varying the charge terminal T₁And/or T₂Will change the corresponding self-capacitance C₁And/or C₂And mutual capacitance C_M. In addition, the presence of changes at the charge terminal T will be changed₁And T₂Any binding capacitance with the lossy conducting medium 203. For this purpose, the charge terminal T is changed₁And T₂The magnitude and phase of the voltage on.

Additionally, another parameter that may be adjusted is the detector coupling circuitry 209 associated with the polyphase waveguide detector 200. This may be accomplished by adjusting the magnitude of the inductive and/or capacitive reactance of the matched detector coupling circuit 209. For example, in the case where such an inductive reactance comprises a coil, the number of turns of such a coil may be adjusted. Finally, the detector coupling circuit 209 may be adjusted to change the electrical length of the detector coupling circuit 209 to affect the charge terminal T₁And T₂The magnitude and phase of the voltage on.

It is also the case that the frequency of the excitation source 213 applied to the polyphase waveguide probe 200 can be adjusted to optimize the transmission of the zernike surface waves. However, if transmission at a given frequency is desired, other parameters need to be adjusted to optimize the transmission.

Note that it is appreciated that the iteration of the transfer performed by making different adjustments may be accomplished by using a computer model or by adjusting the physical structure. In one approach, a field meter tuned to the transmit frequency may be placed at an appropriate distance from the polyphase waveguide probe 200, and the above adjustments may be made until a maximum or any other desired field strength of the resulting zernike surface wave is detected. For this purpose, the field strength can be matched to the field strength at the terminal T₁And T₂The desired operating frequency and the voltage generated pilot field strength curve 103 (fig. 1) are compared. According to one approach, the appropriate distance to place such a field meter may be specified to be greater than the surface current J₂The transition region 216 in the dominant "far zone" region described above.

By making the above adjustments, a corresponding "near zone" surface current J (r) may be created that approximates the same current J (r) for the Zernike surface wave modes specified in equations (17) and (18) above₁And "far zone" surface current J₂. In doing so, the resulting electromagnetic field will substantially or approximately match the zernike surface wave modes on the surface of the lossy conducting medium 203.

Referring next to fig. 7A-7J, additional examples of a polyphase waveguide probe 200, referred to herein as polyphase waveguide probes 200a-J, are shown according to various embodiments of the present disclosure. According to various embodiments, each of the polyphase waveguide detectors 200a-j includes a different detector coupling circuit 209, which is referred to herein as a detector coupling 209 a-j. Although several examples of detector coupling circuits 209a-j are described, it is understood that these embodiments are merely examples, and that there may be many other circuits not set forth herein that may be employed in accordance with the teachings set forth hereinThe principle described above to provide the charge terminal T₁And T₂To a desired voltage amplitude and phase to facilitate launching the probe coupling circuit 209 of the zernike surface wave.

Additionally, each of the detector coupling circuits 209a-j may employ (but is not limited to) an inductive impedance comprising a coil. Although coils are used, it is understood that other circuit elements (whether lumped or distributed) may be employed as the reactances. Additionally, other circuit elements may be included in the detector coupling circuits 209a-j in addition to those described herein. Additionally, it is noted that the different polyphase waveguide detectors 200a-j with their respective detector coupling circuits 209a-j are described herein merely to provide examples. To this end, there may be many other multi-phase waveguide probes 200 that employ different probe coupling circuits 209 and other circuits that may be used to launch zernike surface waves in accordance with the various principles set forth herein.

Referring now to FIG. 7A, a first example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200a, is shown in accordance with one embodiment. Polyphase waveguide probe 200a includes a charge terminal T disposed along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200a includes a probe coupling circuit 209a, the probe coupling circuit 209a including a coupling circuit having a coupling terminal coupled to a charge terminal T₁And T₂A pair of lead wire coils L of a corresponding one of_1aThe inductive impedance of (2). In one embodiment, coil L_1aIs designated as having an electrical length that is one-half (1/2) of the wavelength of the operating frequency of the polyphase waveguide probe 200 a.

Albeit coil L_1aIs specified to be approximately half (1/2) the wavelength of the operating frequency, but it is understood that the coil L_1aOther values of electrical length may be specified. According to one embodiment, the coil L_1aThe fact that the electrical length is approximately half of the wavelength of the operating frequency is provided at the charge terminal T₁And T₂The advantage of creating a maximum voltage differential. However, when the polyphase waveguide probe 200a is adjusted to obtain the optimum excitation of the Zernike surface wave mode, the coil L_1aMay be increased or decreased in length or diameter. Alternatively, the following may be the case: the inductive impedance is specified to have an electrical length significantly less than or greater than 1/2 of the wavelength of the operating frequency of the polyphase waveguide probe 200 a.

According to one embodiment, the excitation source 213 is coupled to the detector coupling circuit 209 by magnetic coupling. In particular, the excitation source 213 is coupled to a coil L inductively coupled thereto_1aCoil L of_P. This may be accomplished by link coupling, tapped coils, variable reactance, or other coupling methods as may be appreciated. To this end, it can be appreciated that the coil L_PServing as a primary, and a coil L_1aUsed as a secondary.

To condition the polyphase waveguide probe 200a to deliver a desired Zernike surface wave, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1aCan be adjusted by adding or removing turns or by changing the coil L_1aToAnd some other dimensions.

Based on experimentation with multiphase waveguide detector 200a, this appears to be the easiest way to adjust and operate in multiphase waveguide detectors 200a-j to achieve the desired efficiency.

Referring now to FIG. 7B, an example of a polyphase waveguide probe 200 (FIG. 6), referred to herein as polyphase waveguide probe 200B, is shown in accordance with one embodiment. Polyphase waveguide probe 200b includes a charge terminal T disposed along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁And T₂Positioned along the vertical axis z to provide cylindrical symmetry in the resulting zernike surface wave as described above. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

Polyphase waveguide probe 200b further includes a probe coupling circuit 209b, probe coupling circuit 209b including a first coil L_1bAnd a second coil L_2b. As shown, the first coil L_1bCoupled to charge terminal T₁And T₂Each of which. Second coil L_2bCoupled to charge terminal T₂And a lossy conducting medium 203.

Excitation source 213 is magnetically coupled to detector coupling circuit 209 in a similar manner as described above with respect to multi-phase waveguide detector 200a (FIG. 7A) described aboveb. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_1b. Alternatively, the coil L_2bMay also be used as a secondary.

To condition the polyphase waveguide probe 200b to deliver the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1bAnd L_2bMay be formed by adding or removing turns or by changing the respective coil L_1bOr L_2bAnd some other dimensions.

Referring now to FIG. 7C, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200C, is shown in accordance with one embodiment. Polyphase waveguide probe 200c includes a charge terminal T disposed along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200c further includes a probe coupling circuit 209c, the probe coupling circuit 209c including a coil L_1c. As shown, coil L_1cIs coupled to the charge terminal T₁. CoilL_1cIs coupled to the lossy conducting medium 203. Along the coil L_1cIs placed coupled to the charge terminal T₂Is tapped.

The excitation source 213 is magnetically coupled to the detector coupling circuit 209c in a similar manner as described above with respect to the polyphase waveguide detector 200a (FIG. 7A) described above. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_1c. Coil L_PCan be located along the coil L_1cAt any position of (a).

To condition the polyphase waveguide probe 200b for exciting and propagating a desired Zernike surface wave, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1cCan be adjusted by adding or removing turns or by changing the coil L_1cAnd some other dimensions. In addition, the coil L above or below the tap_1cThe inductance presented by the section(s) can be adjusted by moving the position of the tap.

Referring now to FIG. 7D, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200D, is shown in accordance with one embodiment. Polyphase waveguide probe 200d includes charge terminal T positioned along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And is provided withBetween the conductive media 203 depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200d further includes a probe coupling circuit 209d, the probe coupling circuit 209d including a first coil L_1dAnd a second coil L_2d. First coil L_1dIs coupled to the charge terminal T₁First coil L_1dIs coupled to the lossy conducting medium 203. Second coil L_2dIs coupled to the charge terminal T₂Second coil L_2dIs coupled to the lossy conducting medium 203.

The excitation source 213 is magnetically coupled to the detector coupling circuit 209d in a similar manner as described above with respect to the polyphase waveguide detector 200a (FIG. 7A) described above. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_2d. Alternatively, the coil L_1dMay also be used as a secondary.

To condition the polyphase waveguide probe 200b for exciting and propagating a desired Zernike surface wave, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1dAnd L_2dMay be formed by adding or removing turns or by changing the respective coil L_1dOr L_2dAnd some other dimensions.

Referring now to FIG. 7E, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200E, is shown in accordance with one embodiment. Polyphase waveguide probe 200e includes a charge terminal T disposed along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁And T₂Placed along a vertical axis z to provideCylindrical symmetry in the zernike surface waves obtained as described above. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200e further comprises a probe coupling circuit 209e, the probe coupling circuit 209e comprising a first coil L_1eAnd a resistor R₂. First coil L_1eIs coupled to the charge terminal T₁First coil L_1eIs coupled to the lossy conducting medium 203. Resistor R₂Is coupled to the charge terminal T₂An electrical resistor R₂Is coupled to the lossy conducting medium 203.

The excitation source 213 is magnetically coupled to the detector coupling circuit 209e in a similar manner as described above with respect to the polyphase waveguide detector 200a (FIG. 7A) described above. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_1e。

To condition the polyphase waveguide probe 200b to deliver the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1eCan be adjusted by adding or removing turns or by changing the coil L_1eAnd some other dimensions. In addition, the resistance R₂Can also adjust the amount ofAnd (4) saving.

Referring now to FIG. 7F, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200F, is shown in accordance with one embodiment. Polyphase waveguide probe 200f includes a charge terminal T₁And a ground net G as a second charge terminal. Charge terminal T₁And the counterpoise G is positioned along a vertical axis z that is substantially orthogonal to the plane presented by the lossy conducting medium 203. The second medium 206 is over the lossy conducting medium 203. Note that the slave charge terminal T₁Height H of₁Minus the height H of the counterpoise G₂The height h of the transfer structure is calculated.

Charge terminal T₁With self-capacitance C₁And the ground grid G has a self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And the voltage of the ground grid G, respectively at the charge terminal T₁Imposing a charge Q on the counterpoise G₁And Q₂. At the charge terminal T₁And the earth grid G, there may be mutual capacitances C depending on the distance between them_M. In addition, at the charge terminal T₁And between the ground grid G and the lossy conducting medium 203, depending on the charge terminal T₁And the height of the counterpoise G relative to the lossy conducting medium 203, there may be a bound capacitance. Generally, a bound capacitance will exist between the counterpoise G and the lossy conducting medium 203 due to its proximity to the lossy conducting medium 203.

The polyphase waveguide probe 200f includes a probe coupling circuit 209f, the probe coupling circuit 209f including a coupling circuit having a coupling to a charge terminal T₁And a coil L of a pair of leads of the ground net G_1fThe inductance impedance of (1). In one embodiment, coil L_1fIs designated as having an electrical length of one-half (1/2) of the wavelength as the operating frequency of the polyphase waveguide probe 200 f.

Albeit coil L_1fIs specified to be approximately half (1/2) the wavelength of the operating frequency, but it is understood that the coil L_1fOther values of electrical length may be specified. According to one embodimentLoop L of_1fThe fact that the electrical length is approximately half of the wavelength of the operating frequency is provided at the charge terminal T₁And the advantage of creating a maximum voltage differential on the earth grid G. However, when the polyphase waveguide probe 200f is tuned for optimal transfer of Zernike surface wave modes, the coil L_1fMay be increased or decreased in length or diameter. Alternatively, the following may be the case: the inductive impedance is specified to have an electrical length significantly less than or greater than 1/2 of the wavelength of the operating frequency of the polyphase waveguide probe 200 f.

According to one embodiment, the excitation source 213 is coupled to the detector coupling circuit 209f by magnetic coupling. In particular, the excitation source 213 is coupled to a coil L inductively coupled thereto_1fCoil L of_P. This may be accomplished by link coupling, phasor/coupling networks or other coupling methods as may be appreciated. To this end, it can be appreciated that the coil L_PServing as a primary, and a coil L_1fUsed as a secondary.

To condition the polyphase waveguide probe 200a to reflect and transmit the desired Zernike surface waves, the corresponding charge terminal T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1fCan be adjusted by adding or removing turns or by changing the coil L_1fAnd some other dimensions.

Referring now to FIG. 7G, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200G, is shown in accordance with one embodiment. Polyphase waveguide probe 200g includes charge terminal T positioned along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁And T₂Placed along the vertical axis z to provide cylindrical symmetry in the resulting zernike surface wave as described above. Charge terminal T₁With self-capacitance C₁And is andcharge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200g further includes a probe coupling circuit 209g, the probe coupling circuit 209g including a first coil L_1gAnd a second coil L_2gAnd a variable capacitor C_V. As shown, the first coil L_1gCoupled to charge terminal T₁And T₂Each of which. Second coil L_2gWith coupling to a variable capacitor C_VAnd a second lead coupled to the lossy conducting medium 203. Further, a variable capacitor C_VCoupled to charge terminal T₂And a first coil L_1g。

The excitation source 213 is magnetically coupled to the detector coupling circuit 209g in a similar manner as described above with respect to the polyphase waveguide detector 200a (FIG. 7A) described above. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_1gOr coil L_2gAny one of (1).

To condition the polyphase waveguide probe 200g to launch and deliver the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1gAnd L_2gMay be formed by adding or removing turns or by changing the respective coil L_1gOr L_2gSome other scales ofCun should be changed. In addition, the variable capacitance C can be adjusted_V。

Referring now to FIG. 7H, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200H, is shown in accordance with one embodiment. Polyphase waveguide probe 200h includes a charge terminal T disposed along a vertical axis z substantially orthogonal to a plane presented by lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200h further comprises a probe coupling circuit 209h, the probe coupling circuit 209h comprising a first coil L_1hAnd L_2h. First coil L_1hIs coupled to the charge terminal T₁And a first coil L_1hIs coupled to the charge terminal T₂. Second coil L_2hIs coupled to terminal T_TAnd a second coil L_2hIs coupled to the lossy conducting medium 203. Terminal T_TRelative to the charge terminal T₂Is placed so as to be at the charge terminal T₂And terminal T_TThere is a coupling capacitance C between_C。

The excitation source 213 is magnetically coupled to the detector coupling circuit 209h in a similar manner as described above with respect to the polyphase waveguide detector 200a (FIG. 7A) described above. To this end, the excitation source 213 is coupled to a coil serving as a primaryL_pAnd a coil L serving as a secondary_2h. Alternatively, the coil L_1hMay also be used as a secondary.

To condition the polyphase waveguide probe 200h for launching and delivering the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1hAnd L_2hMay be determined by adding or removing turns or by changing the respective coil L_1hOr L_2hAnd some other dimensions. It will be appreciated that the charge terminal T may also be varied₂And terminal T_TThereby modifying the coupling capacitance C_C。

Referring now to FIG. 7I, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200I, is shown in accordance with one embodiment. Polyphase waveguide probe 200i is very similar to polyphase waveguide probe 200H (FIG. 7H) except for the fact that excitation source 213 is coupled in series to probe coupling circuit 209i as will be described.

To this end, the polyphase waveguide probe 200i comprises a charge terminal T placed along a vertical axis z substantially orthogonal to the plane presented by the lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide probe 200i further comprises a probe coupling circuit 209i, the probe coupling circuit 209i comprising a first coil L_1iAnd a second coil L_2i. First coil L_1iIs coupled to the charge terminal T₁And a first coil L_1iIs coupled to a second charge terminal T₂. Second coil L_2iIs coupled to terminal T_TAnd a second coil L_2iIs coupled to the output of the excitation source 213. In addition, the ground lead of the excitation source 213 is coupled to the lossy conducting medium 203. Terminal T_TRelative to the charge terminal T₂Is placed so as to be at the charge terminal T₂And terminal T_TThere is a coupling capacitance C between_C。

Polyphase waveguide probe 200i provides one example of a case where excitation source 213 is coupled in series to probe coupling circuit 209i as described above. Specifically, the excitation source 213 is coupled to the coil L_2iAnd a lossy conducting medium 203.

To condition the polyphase waveguide probe 200i to launch and deliver the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1iAnd L_2iMay be formed by adding or removing turns or by changing the respective coil L_1iOr L_2iAnd some other dimensions. In addition, it will be appreciated that the charge terminal T may be varied₂And terminal T_TThereby modifying the coupling capacitance C_C。

Referring now to FIG. 7J, a further example of a polyphase waveguide probe 200 (FIG. 6), herein designated as polyphase waveguide probe 200J, is shown in accordance with one embodiment. Polyphase waveguide probe 200j includes a rimCharge terminals T disposed along a vertical axis z substantially orthogonal to the plane presented by the lossy conducting medium 203₁And T₂. The second medium 206 is over the lossy conducting medium 203. In this embodiment, the charge terminal T₁Comprising a ball and a charge terminal T₂Including a disc. In this regard, the polyphase waveguide probe 200j provides a charge terminal T_NAny shape illustration may be included.

Charge terminal T₁With self-capacitance C₁And a charge terminal T₂With self-capacitance C₂. In operation, according to the application to the charge terminal T at any given moment₁And T₂At the charge terminals T, respectively₁And T₂Imposing a charge Q on₁And Q₂. At the charge terminal T₁And T₂Depending on the distance between them, there may be a mutual capacitance C_M. In addition, at the corresponding charge terminal T₁And T₂And the lossy conducting medium 203, depending on the corresponding charge terminal T₁And T₂There may be a bound capacitance with respect to the height of the lossy conducting medium 203.

The polyphase waveguide detector 200j includes a detector coupling circuit 209j, the detector coupling circuit 209j including a coupling circuit having a coupling to a charge terminal T₁And T₂A pair of lead wire coils L of a corresponding one of_1jThe inductive impedance of (2). In one embodiment, coil L_1jIs designated as having an electrical length of one-half (1/2) of the wavelength as the operating frequency of the polyphase waveguide probe 200 j. Albeit coil L_1jIs specified to be approximately half (1/2) the wavelength of the operating frequency, but it is understood that the coil L_1jOther values of electrical length may be assigned, as discussed with reference to polyphase waveguide probe 200a (FIG. 7A) above. In addition, the detector coupling circuit 209j includes a coil L coupled to the lossy conducting medium 203_1jAn upper tap 223.

Excitation source 213 is magnetically coupled to probe in a similar manner as described above with respect to multi-phase waveguide probe 200a (FIG. 7A) described aboveThe detector coupling circuit 209 j. For this purpose, the excitation source 213 is coupled to a coil L serving as a primary_PAnd a coil L serving as a secondary_1j. Coil L_PCan be located along the coil L_1jAt any position of (a). In addition, a coil L_PMay be located above or below tap 223.

To condition the polyphase waveguide probe 200j to launch and deliver the desired Zernike surface waves, respective charge terminals T₁And T₂May vary in height relative to the lossy conducting medium 203 and relative to each other. In addition, a charge terminal T₁And T₂May vary in size. In addition, a coil L_1jCan be adjusted by adding or removing turns or by changing the coil L_1jAnd some other dimensions. In addition, the coil L can be adjusted_1jThe position of upper tap 223.

Referring to the various embodiments of polyphase waveguide detectors 200a-J in figures 7A-J, each of polyphase waveguide detectors 200a-J may be excited to transmit energy carried in the form of a guided wave or in a waveguide mode along the surface of lossy conducting medium 203. To facilitate such transfer, the elements in each of polyphase waveguide detectors 200a-j may be adjusted to provide a corresponding charge terminal T when the corresponding polyphase waveguide detector 200a-j is excited₁And T₂Imposing the desired voltage amplitude and phase. Such excitation may be performed by applying energy from an excitation source 213 to the respective polyphase waveguide detectors 200a-j as described above.

Can be adjusted at the charge terminal T₁And T₂The voltage amplitude and phase imposed so as to give, at a given local dielectric constant ε_rThe fields that are sufficiently mode-matched to the guided or zernike surface waveguide modes of the lossy conducting medium 203 are sufficiently synthesized at the site of transmission of the conductivity σ and possibly other parameters of the lossy conducting medium 203. The waveguide mode of the surface guided wave is expressed in equations (21), (22) and (23) described above. The surface waveguide mode has a diameter in units of amperes per meter expressed in equation (20)Current density to the surface.

It is to be understood that it may be difficult to synthesize a field that exactly matches the surface waveguide mode represented in equations (21), (22), and (23) above. However, if such a field at least approximates a surface waveguide mode, a guided surface wave can be launched. According to various embodiments, the field is synthesized to match a surface waveguide mode within acceptable engineering tolerances for launching the guided surface wave.

Likewise, it may be difficult to synthesize a radial surface current density that exactly matches the radial surface current density of the zernike surface waveguide mode, where the synthesized radial surface current density is derived from the synthesized field described above. According to various embodiments, the polyphase waveguide probe 200 can be tuned to match the radial surface current density of the guided surface waveguide mode within acceptable engineering tolerances to launch zernike surface wave modes. By creating specific charge distributions and their images at complex distances, the different multi-phase waveguide probes 200a-j described above excite surface currents whose fields are designed to approximately match the propagating zernike surface wave modes and launch zernike surface waves. Due to this complex imaging technique inherent in the different polyphase waveguide detectors 200a-j described above, it is possible to sufficiently mode-match the surface waveguide modes that the guiding interface is intended to support at the location of the transmission. The guide interface is the interface between zone 1 (fig. 2) and zone 2 (fig. 2) as described above. According to one embodiment, the guide interface is an interface between the lossy conducting medium 203 presented by the earth and the atmospheric medium described above.

At the charge terminal T₁And T₂The imposed voltage amplitudes and phases are adjusted so that they, and their effective image at complex depths, rely on the Leontovich boundary conditions to excite complex surface currents, the occasion of which is to sufficiently match the field of the zernike surface waveguide mode of the lossy conducting medium 203 at the site of transmission, at which time such fields will automatically sufficiently synthesize a wavefront incident at the complex brewster angle of the lossy conducting medium 203, which will result in zero reflection. This is at the boundaryAnd (4) processing wave matching conditions.

Referring next to fig. 8A, 8B, and 8C, examples of graphs 300a, 300B, and 300C illustrating field strength in volts per meter as a function of distance in kilometers are shown for comparison between a zernike surface wave and a conventional radiation field. In addition, the different graphs 300a, 300b, and 300c illustrate how the distance of transmission of a zernike surface wave varies with the frequency of transmission.

Each graph 300a, 300b, and 300c illustrates a corresponding guidance field intensity curve 303a, 303b, and 303c and a corresponding radiation field intensity curve 306a, 306b, and 306 c. The guidance field strength curves 303a, 300b, and 300c are generated assuming different parameters. Specifically, graphs 300a, 300b, and 300c are applied to upper terminal T at frequencies of 10MHz, 1MHz, and 0.1MHz, respectively₁Constant charge Q (FIG. 3)₁(fig. 3). For calculation purposes, let ε be assumed_rDielectric constants of 15 and 0.008mhos/m, which are obtained according to the R-3 map in the middle of ohio, proposed by the Federal Communications Commission (FCC). The following table provides hypothetical polyphase waveguide probe operating parameters for generating each of the guided field strength curves 303a, 303b, and 303 c.

To have physically realizable operation, terminal T is set for f 0.1MHz and 1.0MHz₁Is designated as H_T18 meters and shortened to 0.8 meters for 10MHz in order to keep the current distribution uniform. In addition, for the operation of f ═ 0.1MHz and 1.0MHz, the terminal T is set₁Self-capacitance C₁Set to 100 pF. The capacitance is too large for use at 10MHz, so the self-capacitance C is reduced for this case₁. However, the resulting terminal charge Q, which controls the parameters of the field strength_T1The curves 303a, 303b and 303c remain at the same value for all three guidance field strengths.

It can be seen from the graph that the lower the frequency, the less the propagation attenuation and the more the field extends a greater distance. However, consistent with conservation of energy, the energy density decreases with distance. In other words, the higher the frequency, the smaller the area over which the energy spreads and, therefore, the greater the energy density. Thus, the "knee" of the zernike surface wave narrows in range as the frequency increases. Alternatively, the lower the frequency, the smaller the propagation attenuation and the greater the field strength of the zernike surface waves at a very large distance from the site of transmission using the polyphase waveguide probe 200 (fig. 6).

The zernike surface waves for each case are identified as guided field strength curves 303a, 303b, and 303c, respectively. The norton ground wave field strength in volts per meter for a short vertical monopole antenna, having a hypothetical ground loss of 10 ohms and the same height as the corresponding polyphase waveguide probe 200, is represented by radiation field strength curves 306a, 306b and 306c, respectively. Asserting this is a reasonable, real assumption for monopole antenna structures operating at these frequencies. The critical point is that the properly mode-matched polyphase waveguide probe launches a guided surface wave that significantly outperforms the radiation field of any monopole at a distance just beyond the "knee" in the guided field strength curve 303a-c of the corresponding zernike surface wave.

Given the foregoing, according to one embodiment, the propagation distance of the guided surface wave varies according to the frequency of transmission. Specifically, the lower the transmit frequency, the less the guided surface wave will exponentially decay, and thus the guided surface wave will propagate further. As described above, the field strength of the surface wave is guided toWhile the field strength of the radiated electromagnetic field decreases geometrically in proportion to 1/d, where d is a distance in kilometers. Thus, each of the guidance field strength curves 303a, 303b, and 303c is characterized by an inflection point as described above. As the transmission frequency of the polyphase waveguide probe described herein decreases, the corresponding guide field intensity curve 30The inflection points of 3a, 303b and 303c will advance to the right in the graph.

Fig. 8A shows a pilot field intensity curve 303a and a radiation field intensity curve 306a generated at a frequency of 10 mhz. As shown, the guided surface wave drops below 10 kilometers. In fig. 8B, the pilot field intensity curve 303B and the radiation field intensity curve 306B are generated at a frequency of 1 mhz. The guidance field strength curve 303b drops off at about 100 km. Finally, in FIG. 8C, the pilot field intensity curve 303C and the radiation field intensity curve 306C are generated at a frequency of 100 kilohertz (i.e.,. 1 megahertz). The guiding field strength curve 303c drops at between 4000-7000 km.

Note that if the frequency is low enough, the guided surface wave can be transmitted around the entire earth. It is believed that such frequencies may be about 20-25 khz or below. It should be noted that at such low frequencies, the lossy conducting medium 203 (fig. 6) is no longer planar, but instead becomes spherical. Therefore, when the lossy conducting medium 203 contains a terrestrial medium, the calculation of the guidance field strength curve will change to take into account the spherical shape at low frequencies where the propagation distance reaches the size of the terrestrial medium.

Given the foregoing, some general guidance in constructing a multi-phase guided probe 200 (fig. 6) using the earth's surface medium as the lossy conducting medium 203 in accordance with various embodiments is provided next. As a practical approach, an operating frequency may be specified and a desired field strength of the guided surface wave at a distance of interest from the corresponding polyphase waveguide probe 200 to be constructed is identified.

Given these parameters, it is then possible to determine the imposition of the upper charge terminal T₁(FIG. 6) to produce a charge Q of desired field strength at a specified distance₁(FIG. 6). In order to determine the required charge Q₁It will be necessary to obtain the dielectric constant epsilon of the earth at the site of transmission_rAnd a conductivity σ. These values may be obtained by measurement or by reference to a transmissibility table, for example, published by the federal communications commission or the international radio commission (CCIR). When it is at homeDielectric constant epsilon at specified distance_rThe required charge Q, with the conductivity σ and the desired field strength known₁Can be determined by directly calculating the field strength according to the zernike exact expression set forth in equations (21) - (23) above.

When determining the required charge Q₁Then, it will be necessary to identify the charge terminal T at what voltage V₁What self-capacitance C₁Will be at the charge terminal T₁To generate a desired charge Q₁. The charge Q on any charge terminal T is calculated as Q ═ CV. In one approach, what is considered to be placeable at the charge terminal T may be selected₁An acceptable voltage V on, and then a charge terminal T is constructed₁So as to make the required self-capacitance C₁Obtaining the required charge Q₁. Alternatively, in another approach, the charge terminal T may be relied upon₁To determine what is the self-capacitance C that can be obtained₁Then the resulting charge terminal T is connected₁Is boosted to the required voltage V to obtain the required charge Q₁。

In addition, in determining the charge terminal T₁Required self-capacitance C₁And will be forced on the charge terminal T₁At the upper voltage V, there is a problem that the operating bandwidth should be considered. In particular, the bandwidth of the polyphase waveguide probe 200 discussed herein is relatively large. This is given the self-capacitance C as described above₁Or voltage V, a high degree of flexibility is obtained. However, it should be understood that with self-capacitance C₁The resulting bandwidth of the polyphase waveguide probe 200 will decrease with a decrease in voltage V.

Experimentally, it should be noted that the smaller self-capacitance C₁A given polyphase waveguide probe 200 may be made to have a dielectric constant epsilon with respect to earth or near the site of propagation_rOr small changes in conductivity sigma. Dielectric constant ε_rOr such a change in conductivity sigma may be due to a change in climate caused by a transition between seasons or due to weather such as rainfall, drynessSuch changes in local weather conditions and/or other changes in local weather occur with the arrival of drought. Thus, according to one embodiment, the charge terminal T₁Can be specified as having a relatively large self-capacitance C that is achievable₁。

When the charge terminal T is determined₁Self-capacitance C₁And a voltage to be imposed thereon, the second charge terminal T will be determined next₂Self-capacitance C₂And physical location. As a practical matter, it has been found that it is easiest to put the charge terminal T into place₂Self-capacitance C₂Assigned to and charge terminal T₁Self-capacitance C₁The same is true. This can be done by making the charge terminal T₂Size and shape of and charge terminal T₁Are the same in size and shape. This will ensure that symmetry is maintained and two charge terminals T will be avoided₁And T₂Which may negatively affect the possibility of obtaining an unusual phase shift matching the complex brewster angle as described above. For two charge terminals T₁And T₂Self-capacitance C₁And C₂The same fact will lead to the charge terminal T₁And T₂The same voltage amplitude above. However, it is to be understood that the self-capacitance C₁And C₂May be different, and the charge terminal T₁And T₂May be different in shape and size.

To promote symmetry, the charge terminal T₂Can be directly disposed at charge terminal T along vertical axis z (fig. 6) as described above₁Below. Alternatively, the charge terminal T may be connected₂At some other location with some resulting effect.

Charge terminal T₁And T₂Should be specified to provide the best match between the field generated by the polyphase waveguide probe 200 and the guided surface waveguide mode at the delivery site. As a suggested starting point, the distance may be set such that the charge terminal T₁And T₂Mutual capacitance C between_M(FIG. 6) equal to or less than the charge terminal T₁Upper isolating capacitor C₁. Finally, the capacitance terminal T should be specified₁And T₂To make mutual capacitance C_MAs small as possible. The mutual capacitance C can be determined by measurement_MAnd the charge terminal T can be positioned accordingly₁And T₂。

Next, an appropriate height H ═ H for polyphase waveguide probe 200 is determined₁-H₂(FIGS. 7A-J). Here, the phenomenon of "complex depth of image" becomes significant. This will cause the pair to have a charge Q when the height h changes₁And Q₂Charge storage T₁And T₂And from charge Q₁And Q₂Of the subsurface image of (a) is considered of overlapping fields on the earth's surface. Due to the large number of variables to consider to ensure mode matching of a given polyphase waveguide probe 200 to the earth's guided surface waveguide mode at the site of transport, a feasible starting point is the charge reservoir T relative to ground₁And T₂A binding capacitance (bound capacitance) of each of the terminals is negligible so as to be connected with the charge terminal T₁And T₂The associated capacitances are essentially their isolated self-capacitances C, respectively₁And C₂Height h of (a).

An additional consideration to be considered in determining the height h associated with the polyphase waveguide probe 200 is whether to avoid radiation. In particular, the radiation resistance R is such that when the height h of the polyphase waveguide probe 200 is close to an appreciable fraction of the wavelength of the operating frequency_rWill grow twice as to the height h and the radiation will start to take precedence over the generation of the guided surface wave described above. One such basis for determining that a Zernike surface wave will take precedence over any radiation is to determine that the height is less than 10% of the wavelength of the operating frequency, although other bases may be specified. In some cases, it may be desirable to allow a degree of radiation to occur based on launching the guided surface wave, in which case the height h may be specified accordingly.

Next, the detector coupling circuit 209 (FIG. 6) is designated to provide the charge terminal T₁And T₂The voltage phase in between. The voltage phase appears to have a significant effect on creating a field that is mode matched to the guided surface waveguide mode at the delivery site. Suppose that the charge terminal T is placed along the vertical z-axis₁And T₂To promote symmetry, the detector coupling circuit 209 may be designated as being at the charge terminal T₁And T₂Providing a voltage differential of 180 degrees. That is, the probe coupling circuit 209 is designated such that the charge terminal T is₁Voltage V at with respect to the charge terminal T₂The voltages on are 180 degrees out of phase.

As described above, one exemplary method is at charge terminal T as described above with reference to polyphase waveguide probe 200a₁And T₂Between which a coil L is placed_1a(FIG. 7A), and the coil L is adjusted_1aUntil the resulting system is electronically half-wave resonant. This will be at the charge terminal T₁A voltage V is applied to the charge terminal T₂A voltage-V is applied so that a charge terminal T is provided₁And T₂The maximum voltages are applied 180 degrees out of phase.

An excitation source 213 (FIG. 6) may then be coupled to the detector coupling circuit 209 as described above, and the output voltage adjusted to achieve the desired voltage V to provide the desired charge Q₁. The excitation source 213 may be (directly) coupled to the detector coupling circuit 209 via magnetic coupling, capacitive coupling, or conductive coupling. Note that the output of the excitation source 213 may be stepped up using a transformer or via some other method if desired. Coil L_1aMay be at any location, such as the open elevation of the ground beside the excitation source 213. Alternatively, coil L according to best RF practice_1aPossibly directly in the charge reservoir T₁And T₂In the meantime. The principle of impedance matching may be applied when coupling the excitation source 213 to the detector coupling circuit 209.

Note that the phase difference does not necessarily have to be 180 degrees. For this purpose, with increasing or decreasing charge terminals T₁And/or T₂One or both of, adjusting the charge terminalSub T₁And/or T₂Or adjust the probe coupling circuitry 209 to adjust the voltage amplitude or phase options to create a field that most closely matches the guided waveguide mode to generate a guided surface wave.

Results of the experiment

The above discussion is supported by experimental measurements and literature. Referring to fig. 9, a graph presenting measured field strengths of electromagnetic fields delivered by one embodiment of an experimental polyphase waveguide detector measured by prunus in new hampshire on day 10, month 14, 2012 is shown. The frequency of transmission was 59MHz, at the charge terminal T of the polyphase waveguide probe tested₁A voltage of 60mV was imposed. Self-capacitance C of experimental polyphase waveguide probe₁Is 8.5 pF. The conductivity σ of the ground at the measurement site was 0.0002mhos/m and the dielectric constant of the ground at the test site was 5. These values are measured in situ at the frequency used.

The graph includes a guidance field intensity curve 400 labeled as a "zernike" curve for 80% efficiency and a radiation field intensity curve 403 labeled as a "norton" curve for the best possible 100% radiation efficiency. To this end, the radiated field strength curve 403 represents the radiated electromagnetic field that would be generated by a 1/4 wavelength monopole antenna operating at a frequency of 59 MHz. The circle 406 on the graph represents the measured field strength produced by the experimental polyphase waveguide probe. The field strength measurements were performed using a NIST trackable Potomac Instruments RIM-71 commercial VHF field strength meter. It can be seen that the measured field strength falls along the theoretical guide field strength curve 400. These measured field strengths are consistent with the propagation of guided or zernike surface waves.

Referring next to FIG. 10, a graph presenting measured phases of a transmitted electromagnetic wave from an experimental polyphase waveguide probe is shown. Curve J (r) indicates the current J₁And J₂Phase of the incident field and current J shown₁And J₂To transition between them. Curve 503 indicates the illustrated current J₁And curve 506 indicates the illustrated current J₂Asymptotes of the phases of (1). Near toA similar 45 degree difference typically exists for the corresponding current J₁And J₂Between the phases of (a). Circle 509 indicates a measurement of the phase of current J (r) generated by an experimental polyphase waveguide probe operating at 59MHz as in FIG. 9. As shown, circle 509 falls along curve J (r) indicating the transition of the phase of current J (r) from curve 503 to curve 506. This indicates the phase from near zone current J of the current J (r) generated by the experimental polyphase waveguide probe₁The generated phase transition to far zone current J₂. These phase measurements are therefore consistent with the presence of a guided or zernike surface wave.

Referring to FIG. 11, a graph is shown of a second set of measurement data illustrating field strengths of electromagnetic fields delivered by a second embodiment of an experimental polyphase waveguide detector measured near Ashland, New Hampshire and across the northern region of Wenpersky Hubei on 1/11/2003. The frequency of transmission was 1850kHz and the charge terminal T of the polyphase waveguide probe was tested₁The voltage imposed on it is 1250V. The experimental polyphase waveguide probe has H₁2 meters physical height. Self-capacitance C of the experimental polyphase waveguide probe in this experiment as a flat conducting disc of radius 1 meter₁Measured as 70 pF. The polyphase waveguide probe is arranged as shown in fig. 7J with a spacing H of 1 meter and the height of the charge terminal above ground (lossy conducting medium 203) is H₂1 meter. The average conductivity σ of the ground near the experiment was 0.006mhos/m, and the relative permittivity ε of the ground_rOn the order of 15. These are determined by the frequency at use.

The graph includes a curve labeled "Zernike" at 85% efficiency, a guided field intensity curve 600 emitted by the experimental polyphase waveguide probe, and the same height (H) from above the counterpoise containing 20 equally spaced radial lines each 200 feet in length labeled "Nuton" curve (H)₂2 meters) of the radiation field intensity curve 603 of the resonant monopole radiation. For this purpose, the radiation field intensity curve 603 represents radiation from a conventional stub monopole antenna operating at 1850kHz above the lossy earthThe conventional norton ground wavefield. The circle 606 on the graph represents the measured field strength produced by the experimental polyphase waveguide probe.

It can be seen that the measured field strength drops off closely along the theoretical zernike guidance field strength curve 600. The field strength measured at the point where r-7 meters is possible to mention in particular. The field strength data points are measured adjacent the lake shore, and this may account for data at that location that deviates slightly above the theoretical zernike guidance field strength curve 600 (i.e., the constituent parameter ε)_rAnd/or σ) may have significantly deviated from the path average composition parameter.

The field strength measurements were made using a NIST traceable Potomac Instruments FIM-41MF/HF field strength meter. The measured field strength data is consistent with the presence of a guided or zernike surface wave. It is evident from experimental data that the measured field strength observed at distances less than 15 meters may not be due to conventional norton ground wave propagation, but may only be due to guided surface wave propagation launched by a multi-phase probe operating as disclosed above. At the given experimental conditions of 1.85MHz, a norton ground wave component eventually exceeds the zernike surface wave component at levels outside 20 meters.

Comparison of the measured zernike surface wave data shown in figure 9 at 59MHz with the measured data in figure 11 at 1.85MHz shows the great advantage of employing a polyphase waveguide probe according to various embodiments at lower frequencies.

These experimental data confirm that the present polyphase waveguide probe comprising multiple properly phased and adjusted charge terminals as taught herein results in phase-enhanced surface currents withAnd its field synthesizes surface illumination at the complex brewster angle of the lossy boundary, as disclosed herein. The result is according toRather than the effective emission of cylindrical zernike wave propagation guided by boundary interfaces as an asymptotic zero single conductor radial transmission line mode that is attenuated by the 1/d reduction of the radiation field due to geometric stretching.

Referring next to fig. 12A, 12B, and 13, examples of a general purpose receiving circuit for using surface guided waves in a wireless power delivery system are shown. Fig. 12A and 12B include a linear detector 703 and a tuned resonator 706. Figure 13 is a magnetic coil 709 according to various embodiments of the present disclosure. According to various embodiments, each of the linear probe 703, the tuned resonator 706, and the magnetic coil 709 may be employed to receive power transmitted in the form of a guided surface wave (fig. 6) on the surface of the lossy conducting medium 203 according to various embodiments. As described above, in one embodiment, the lossy conducting medium 203 comprises a terrestrial medium.

Referring specifically to fig. 12A, the open terminal voltage on the output terminal 713 of the linear detector 703 depends on the effective height of the linear detector 703. For this purpose, the terminal point voltage can be calculated as

Wherein E is_incThe intensity of the electric field in a vector on the linear detector 703 in volts per meter, dl is the integrating element along the direction of the linear detector 703, and h_eIs the effective height of the linear detector 703. The electrical load 716 is coupled to the output terminal 713 through an impedance matching network line 719.

When the linear detector 703 is subjected to a guided surface wave as described above, a voltage is generated across the output terminal 713 that may be applied to the electrical load 716 through the conjugate impedance matching network 719 as the case may be. To facilitate power flow to the electrical load 716, the electrical load 716 should be substantially impedance matched to the linear detector 703 as will be described below.

Referring to fig. 12B, the tuned resonator 706 includes a charge terminal T that is raised above the lossy conducting medium 203_R. Charge terminal T_RWith self-capacitance C_R. In addition, depending on the charge terminal T_RAt a height above the lossy conducting medium 203, at the charge terminal T_RAnd the lossy conducting medium 203 may also have a binding capacitance (not shown). Preferably, the bound capacitance should be minimized as much as possible, although this may not be entirely necessary in every instance of the polyphase waveguide probe 200.

The tuned resonator 706 further includes a coil L_R. Coil L_RIs coupled to the charge terminal T_RAnd a coil L_RAnd the other end is coupled to a lossy conducting medium 203. For this purpose, at the charge terminal C_RAnd a coil L_RIn series, the tuned resonator 706 (which may also be referred to as a tuned resonator (L)_R-C_R) Including series-tuned resonators. Tuning resonator 706 by adjusting charge terminal T_RAnd/or height of and/or adjustment coil L_RIs tuned such that the reactive impedance of the structure is substantially eliminated.

For example, by self-capacitance C_RThe reactance presented is calculated asNote that the total capacitance of the tuned resonator 706 may also include a charge terminal T_RAnd the lossy conducting medium 203, wherein it is appreciated that the total capacitance of the tuned resonator 706 may also be based on the self-capacitance C_RAnd any bound capacitance. According to one embodiment, the capacitor terminal T_RMay be raised to a height to substantially reduce or eliminate any bound capacitance. Can be based on the charge terminal T_RThe presence of the binding capacitance is determined by a capacitance measurement with the lossy conducting medium 203.

By discrete element coils L_RThe inductive reactance presented can be calculated as j ω L, where L is the coil L_RLumped element ofAn inductor. If the coil L_RIs a distributed element, its equivalent endpoint inductive reactance may be determined by conventional methods. To tune the tuned resonator 706, an adjustment is made so that the coil L is turned on_RThe inductive reactance presented is equal to the capacitive reactance presented by the tuned resonator 706 such that the resulting net reactance of the tuned resonator 706 is substantially zero for the operating frequency. An impedance matching network 723 may be interposed between probe terminal 721 and electronic load 726 in order to affect a conjugate match condition to the maximum (maximum) power transfer of electrical load 726.

With the guided surface wave generated at the frequency of the tuned resonator 706 and the conjugate matching network 723 as described above placed, maximum power will be delivered from the surface guided wave to the electrical load 726. That is, when a conjugate impedance match is established between the tuned resonator 706 and the electrical load 726, power will be delivered from the structure to the electrical load 726. To this end, an electrical load 726 may be coupled to the tuned resonator 706 by magnetic coupling, capacitive coupling, or conductive (direct tap) coupling. It will be appreciated that the elements of the coupling network may be lumped components or distributed elements. In the embodiment shown in fig. 12B, magnetic coupling is employed, in which the coil L serving as the primary of the transformer is opposed to_RPlacing a coil L_SAs a secondary level. It will be appreciated that the coil L_SThe linking coupling to the coil L may be done by geometrically winding it around the same core structure and adjusting the coupled magnetic flux_R. Additionally, although the tuned resonator 706 comprises a series tuned resonator, parallel tuned resonators, and even distributed element resonators, may be used.

Referring to figure 13, magnetic coil 709 includes a receive circuit coupled to a power load 736 through an impedance coupling network 733. To facilitate receiving and/or extracting electronic power from the guided surface wave, the magnetic coil 709 may be positioned such that the guided surface wavePasses through the magnetic coil 709, thereby inducing a current in the magnetic coil 709 and at its outputAn endpoint voltage is generated at terminal 729. The magnetic flux of the guided surface wave coupled to the single turn coil is represented as

Where ψ is the coupling magnetic flux, μ_rIs the effective relative permeability, μ, of the core of magnetic coil 709₀Is the permeability of free space, H is the incident magnetic field strength vector, n is the unit vector normal to the cross-sectional area of the turn, and A_CSIs the area surrounded by each ring. For a directional N-turn magnetic coil 709 that is maximally coupled to an incident magnetic field that is uniform across the cross-sectional area of magnetic coil 709, the open circuit induced voltage present at output terminal 729 of magnetic coil 709 is

Wherein the variables are defined above. The magnetic coil 709 may be tuned to the guided wave frequency, as the case may be, depending on the distributed resonator or by an external capacitor across its output terminal 729 and then impedance matched with an external power load 736 through a conjugate impedance matching network 733.

Assuming that the resulting circuitry presented by magnetic coils 709 and electrical load 736 is properly conditioned and conjugate impedance matched via impedance matching network 733, the current drawn in magnetic coils 709 may be used to optimally power electrical load 736. The receiving circuit presented by magnetic coil 709 provides the following advantages: it does not have to be physically connected to the ground.

Referring to fig. 12A, 12B, and 13, each of the receive circuits represented by the linear probe 703, the tuned resonator 706, and the magnetic coil 709 facilitates receiving electrical power delivered from any of the embodiments of the polyphase waveguide probe 200 described above. To this end, it may be appreciated that the received energy may be used to supply power to the electronic loads 716/726/736 via a conjugate matching network. This is in contrast to signals transmitted in the form of radiated electromagnetic fields that can be received in a receiver. Such signals have very low available power and the receiver of such signals does not load the transmitter.

The guided surface wave generated using the polyphase waveguide probe 200 described above is further characterized in that the receive circuit presented by the linear probe 703, the tuned resonator 706, and the magnetic coil 709 will load the excitation source 213 (fig. 3) applied to the polyphase waveguide probe 200, thereby generating a guided surface wave applied to such receiver circuit. This reflects the fact that: the guided surface wave generated by a given polyphase waveguide probe 200 described above contains a transmission line mode. In contrast, the receivers are not loaded with a power source that drives a radiating antenna that generates radiating electromagnetic waves, regardless of the number of receivers employed.

Thus, in summary, a given polyphase waveguide probe 200 and receiving circuitry in the form of linear probe 703, tuned resonator 706 and/or magnetic coil 709 may together comprise a wireless distribution system. Given that the distance of propagation of a guided surface wave using a polyphase waveguide probe 200 as described above depends on frequency, wireless power distribution can be achieved across a wide area or even globally.

Conventional wireless power transfer/distribution systems in much of today's research include "energy harvesting" from radiated fields and sensors coupled to inductive or reactive near fields. In contrast, the wireless power system does not waste power in the form of radiation that is lost forever if not intercepted. The disclosed wireless power system is not limited to very short range and conventional mutual reactance coupled near-field systems. The wireless power systems disclosed herein detect coupling to a novel surface guided transmission line mode, which is equivalent to delivering power to a load through a waveguide or to a load wired directly to a remote power generator. The power required to maintain the transmit field strength and dissipated in the waveguide is not calculated and is not significant at very low frequencies relative to the transmit losses in a conventional high voltage power line at 60 Hz. When the electrical load demand is terminated, the source power generation is relatively idle.

Referring next to fig. 14A, a schematic diagram showing a linear detector 703 and a tuned resonator 706 is shown. Figure 14B shows a schematic diagram representing a magnetic coil 709. The linear detector 703 and the tuned resonator 706 may each be considered to be powered by an open terminal voltage source V_SAnd idle network endpoint impedance Z_SThevenin shown is equivalent. The magnetic coil 709 may be considered as being sourced by a short-ended current source I_SAnd idle network endpoint impedance Z_SNorton equivalent of representation. Each electrical load 716/726/736 (FIGS. 12A-B and 13) may be controlled by a load impedance Z_LTo indicate. Source impedance Z_SContaining real and imaginary components and taking the form Z_s＝R_s+jX_s。

According to one embodiment, the electrical loads 716/726/736 are impedance matched to each of the receive circuits, respectively. Specifically, each electrical load 716/726/736 is designated as being equal to Z by virtue of its respective impedance matching network 719/723/733_L′＝Z_s ^*＝R_s-jX_sZ of (A)_L′＝R_L′+jX_L' Z of_L' wherein the presented load impedance Z_L' is the actual source impedance Z_SThe complex number of (c) is conjugated. Then, the conjugate matching theorem (which states that in a cascaded network, if a conjugate match occurs at any terminal pair, it will occur at all terminal pairs) asserts that the actual electrical load 716/726/736 will also see an impedance Z for it_LConjugate matching of' is performed. See "communication engineering" by Everitt, w.l. and g.e.tanner (McGraw-Hill, 3 rd edition, 1956, page 407). This ensures that the respective electrical loads 716/726/736 are impedance matched to the respective receiving circuits and that maximum power transfer is established for the respective electrical loads 716/726/736.

In addition to the foregoing, various embodiments of the present disclosure include, but are not limited to, the embodiments set forth in the following clauses.

A method as in clause 1, comprising the steps of: energy delivered in the form of guided surface waveguide modes along the surface of the terrestrial medium is transmitted by exciting a polyphase waveguide probe.

Clause 2. the method of clause 1, wherein the step of delivering energy delivered in the form of guided surface waveguide modes along the surface of the terrestrial medium by exciting the polyphase waveguide probe further comprises the step of synthesizing a plurality of fields that substantially match the guided surface waveguide modes of the terrestrial medium.

Clause 3. the method of any one of clauses 1 or 2, wherein the radial surface current density of the guided surface waveguide mode is substantially represented by

Wherein γ is a group ofGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the ground medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide detector, ε₀Is the dielectric constant of free space, epsilon_rIs the relative permittivity of the ground medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate of the radial direction,z is a vertical coordinate orthogonal to the ground medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

Clause 4. the method of any of clauses 1-3, wherein guiding the surface waveguide mode is substantially represented as

And is

Wherein the content of the first and second substances,is the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the ground medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide detector, ε₀Is the dielectric constant of free space, epsilon_rIs the relative permittivity of the ground medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate, z is the vertical coordinate orthogonal to the surface medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first-order Hankel function with the complex parameter-j γ ρ, H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

Clause 5. the method of any of clauses 2-4, wherein the field sufficiently synthesizes a wavefront incident at a complex brewster angle of the terrestrial medium, resulting in negligible reflection.

Clause 6. the method of any one of clauses 1-5, wherein the polyphase waveguide detector comprises a plurality of charge terminals, the method further comprising the step of adjusting the polyphase waveguide detector by adjusting the height of at least one charge terminal.

Clause 7. the method of any one of clauses 1-5, wherein the polyphase waveguide probe includes a plurality of charge terminals, the method further comprising the step of tuning the polyphase waveguide probe by adjusting the distance between the charge terminals.

Clause 8. the method of any of clauses 1-5, wherein the polyphase waveguide probe includes a plurality of charge terminals, the method further comprising the step of tuning the polyphase waveguide probe by adjusting the size of at least one of the charge terminals.

Clause 9. the method of any of clauses 1-5, wherein the polyphase waveguide probe includes a plurality of charge terminals, the method further comprising the step of tuning the polyphase waveguide probe by adjusting a probe coupling circuit coupled to the charge terminals.

The article 10. an apparatus, comprising: a multi-phase waveguide probe configured to create a plurality of resultant fields that are sufficiently mode-matched to Zernike surface wave modes on a surface of a lossy conducting medium.

Clause 11. the apparatus of clause 10, wherein the lossy conducting medium further comprises a terrestrial medium.

Clause 12. the apparatus of any one of clauses 10 or 11, wherein the radiation resistance of the polyphase waveguide detector is substantially 0.

Clause 13. the apparatus of any of clauses 10-12, wherein the height of the polyphase waveguide probe is less than at the operating frequency of the polyphase waveguide probeWhere λ is the wavelength of the operating frequency.

Article 14. the apparatus of any of claims 10-13, wherein the resultant field is sufficiently synthesized for a wavefront incident at a complex brewster angle of the lossy conducting medium to result in a reflection of substantially 0.

Clause 15. the apparatus of any of clauses 10-14, wherein the excitation source is electrically coupled to the polyphase waveguide detector.

An apparatus according to any of clauses 10-15, wherein the radial surface current density of the zernike surface wave mode consists essentially of

It is shown that, among others,gamma is a reaction ofGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε₀Is the dielectric constant of free space, epsilon_rIs the relative permittivity of the lossy guiding medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

An apparatus according to any of clauses 10-16, wherein the zernike surface wave modes are substantially represented as

And is

Wherein H_φIs the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the guided lossy medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first-order Hankel function with the complex parameter-j γ ρ, H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

Clause 18. the apparatus of any one of clauses 10-17, wherein the polyphase waveguide probe further comprises a plurality of charge terminals, the polyphase waveguide probe further configured to impose a plurality of voltage amplitudes and a plurality of phases on the charge terminals.

Clause 19. the apparatus of any one of clauses 10-18, wherein the polyphase waveguide probe further comprises a probe coupling circuit coupled to the charge terminal, the probe coupling circuit configured to impose a voltage magnitude and phase on the charge terminal.

Clause 20. the apparatus of any of clauses 10-19, wherein both the voltage magnitude and phase change as a function of the geometric position of the charge terminals relative to each other.

Clause 21. the apparatus of any one of clauses 10-20, wherein the voltage magnitude and phase both vary as a function of the geometric position of each of the charge terminals relative to the lossy conducting medium.

Clause 22. the apparatus of any of clauses 10-21, wherein the voltage magnitude and phase both vary as a function of the physical size of the charge terminals.

Clause 23. the apparatus of any of clauses 10-22, wherein both the voltage magnitude and phase change as a function of the circuit.

The apparatus of any of clauses 10-23, wherein the charge terminals are disposed along the axis.

Clause 25. the apparatus of any of clauses 10-24, wherein the excitation source is coupled in series to the polyphase waveguide detector.

Clause 26 the apparatus of any one of clauses 10-17, wherein the polyphase waveguide probe further comprises a coil coupled to both the first charge terminal and the second charge terminal.

Clause 27. the apparatus of any one of clauses 10-17, wherein the polyphase waveguide probe further comprises a first coil and a second coil, wherein the first coil is coupled to both the first charge terminal and the second charge terminal, and the second coil is coupled to the second charge terminal and the lossy conducting medium.

The apparatus of any of claims 10-17 during clause 28, wherein the polyphase waveguide probe further comprises: a coil having a first end coupled to the first charge terminal and a second end coupled to the lossy conducting medium; and a tap coupled to the second charge terminal and disposed along the coil.

Clause 29. the apparatus of any of clauses 10-17, wherein the polyphase waveguide probe further comprises a first coil and a second coil, wherein the first coil is coupled to both the first charge terminal and the lossy conducting medium, and the second coil is coupled to both the second charge terminal and the lossy conducting medium.

Clause 30. the apparatus of any of clauses 10-17, wherein the polyphase waveguide probe further comprises a coil coupled to the first charge terminal and the lossy conducting medium and a resistor coupled to the second charge terminal and the lossy conducting medium.

The apparatus of any of clauses 10-17, wherein the polyphase waveguide probe further comprises a coil coupled to both the first charge terminal and the counterpoise.

The apparatus of any of clauses 10-17, wherein the polyphase waveguide detector further comprises: a first coil coupled to a first charge terminal and a second charge terminal; a second coil coupled to the lossy conducting medium and the capacitor; and the capacitance is further coupled to a second charge terminal.

Clause 33. the apparatus of clause 32, wherein the capacitance is a variable capacitance.

Clause 34. the apparatus of clauses 10-17, wherein the polyphase waveguide detector further comprises: a first coil coupled to both the first charge terminal and the second charge terminal; and a second coil coupled to the terminal and the lossy conducting medium, wherein the terminal is positioned relative to a second charge terminal resulting in a coupling capacitance between the terminal and the second charge terminal.

The apparatus of any of clauses 10-17, wherein the polyphase waveguide detector further comprises: a first coil coupled to both the first charge terminal and the second charge terminal; a second coil coupled to a terminal, wherein the terminal is positioned relative to a second charge terminal resulting in a coupling capacitance between the terminal and the second charge terminal; and wherein the excitation source is coupled to the second coil and the lossy conducting medium.

Clause 36. the apparatus of any one of clauses 10-17, wherein the polyphase waveguide probe further comprises a plurality of charge terminals, wherein a respective one of the terminals comprises a ball or a disk.

The apparatus of any of clauses 10-17, wherein the polyphase waveguide detector further comprises: a coil having a first end coupled to a first charge terminal and a second end coupled to a second charge terminal; and a tap coupled to the lossy conducting medium and disposed along the coil.

Clause 38. the apparatus of any one of clauses 26-34, 36 and 37, further comprising an excitation source coupled to the primary coil, wherein the primary coil is magnetically coupled to the polyphase waveguide detector.

An apparatus, comprising: a polyphase waveguide probe configured to create a plurality of resultant fields; and wherein the resultant field is substantially mode-matched to a Zernike surface wave mode on the surface of the terrestrial medium.

Clause 40. the apparatus of clause 39, wherein the resultant field sufficiently synthesizes a wavefront incident at the complex brewster angle of the terrestrial medium, resulting in a reflection of substantially 0.

Article 41. the device of any of articles 39 or 40, wherein the radial surface current density of the zernike surface wave modes consists essentially of

Wherein γ is represented byGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the ground medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide detector, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the ground medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate, z is the vertical coordinate orthogonal to the surface medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

Clause 42. the device of any of clauses 39-41, wherein the zernike surface wave mode is substantially represented as

And is

Wherein H_φIs the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the ground medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide detector, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the ground medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate, z is the vertical coordinate orthogonal to the surface medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first-order Hankel function with the complex parameter-j γ ρ, H₀ ⁽²⁾(. gamma. rho.) is e^+jωtWith time variable having a complex parameter-j ω ρThe zeroth-order hankel function of (1), where t is time.

Clause 43. the apparatus of any one of clauses 39-42, wherein the polyphase waveguide probe further comprises a pair of charge terminals, the polyphase waveguide probe further configured to impose a plurality of voltage amplitudes and a plurality of phases on the charge terminals.

Clause 44. the apparatus of clause 43, wherein the polyphase waveguide detector further comprises a distribution circuit coupled to the charge terminal.

Clause 45. the apparatus of clause 44, wherein the power source is coupled to the distribution circuit.

Clause 46. the device of any one of clauses 44 or 45, wherein the distribution circuit further comprises a coil.

Clause 47 the apparatus of clause 43, wherein the polyphase waveguide detector further comprises a coil coupled between the charge terminals.

Clause 48. the apparatus of clause 43, wherein the voltage magnitude and phase both vary as a function of the geometric position of the charge terminals relative to each other.

Clause 49 the apparatus of clause 43, wherein the voltage magnitude and phase both vary as a function of the geometric position of each of the charge terminals relative to the ground medium.

Clause 50. the apparatus of clause 43, wherein the voltage magnitude and phase both vary as a function of the physical size of the charge terminals.

Clause 51. the apparatus of clause 43, wherein the voltage magnitude and phase both vary as a function of the circuit.

Clause 52. the apparatus of any of clauses 39-44 and 46-51, wherein the excitation source is electrically coupled to the polyphase waveguide detector.

An article 53. a method comprising the steps of: positioning a receiving circuit relative to a surface medium; and receiving, via a receive circuit, energy conveyed in the form of a zernike surface wave on a surface of a terrestrial medium.

Clause 54. the method of clause 53, wherein an electrical load coupled to the receive circuit loads an excitation source coupled to a polyphase waveguide probe that generates the zernike surface wave.

Clause 55 the method of clause 53 or 54, wherein the energy further comprises electrical power, and the method further comprises the step of applying the electrical power to an electrical load coupled to the receive circuit, wherein the electrical power is used as a power source for the electrical load.

Clause 56. the method of any of clauses 53-55, further comprising the step of impedance matching the electrical load to the receive circuit.

Clause 57. the method of any of clauses 53-56, further comprising the step of establishing a maximum power transfer from the receiving circuit to the electrical load.

Clause 58 the method of any of clauses 53-57, wherein the receiving circuit further comprises a magnetic coil.

Clause 59. the method of any of clauses 53-57, wherein the receive circuit further comprises a linear detector.

Clause 60. the method of any of clauses 53-57, wherein the receive circuit further comprises a tuned resonator coupled to the terrestrial medium.

An apparatus, as in clause 61, comprising: a receive circuit to receive energy delivered in the form of a Zernike surface wave along a surface of a lossy conducting medium.

Clause 62. the apparatus of clause 61, wherein the lossy conducting medium further comprises a terrestrial medium.

Clause 63. the apparatus of any of clauses 61 or 62, wherein an electrical load coupled to the receive circuit loads an excitation source coupled to a polyphase waveguide probe that generates the zernike surface wave.

Clause 64. the apparatus of any one of clauses 61 or 62, wherein the energy further comprises electrical power, and the receiving circuit is coupled to an electrical load, and wherein the electrical power is applied to the electrical load, the electrical power being used as a power source for the electrical load.

Clause 65. the apparatus of any one of clauses 63 or 64, wherein the electrical load is impedance matched to the receiving circuit.

The apparatus of any of clauses 61-65, wherein the receiving circuit further comprises a magnetic coil.

Clause 67. the apparatus of any one of clauses 61-65, wherein the receive circuit further comprises a linear detector.

Clause 68. the apparatus of any of clauses 61-65, wherein the receive circuit further comprises a tuned resonator.

Clause 69 the apparatus of clause 68, wherein the tuned resonator comprises a series tuned resonator.

Clause 70 the apparatus of clause 68, wherein the tuned resonator comprises a parallel tuned resonator.

Clause 71 the apparatus of clause 68, wherein the tuned resonator comprises a distributed tuned resonator.

An article 72, a power delivery system, comprising:

a multi-phase waveguide probe that transmits electrical energy in the form of a guided surface wave along a surface of a terrestrial medium; and a receiving circuit that receives the electric energy.

Clause 73. the power delivery system of clause 72, wherein an electrical load coupled to the receive circuit loads the polyphase waveguide probe.

Clause 74. the power delivery system of clause 72, wherein an electrical load is coupled to the receive circuit and the electrical energy is used as a power source for the electrical load.

Clause 75. the power transfer system of any of clauses 73 or 74, wherein the electrical load is impedance matched to the receive circuit.

Clause 76. the power delivery system of any of clauses 73 or 74, wherein a maximum power transfer from the receive circuit to the electrical load is established.

Clause 77 the power delivery system of any of clauses 72-76, wherein the receive circuit further comprises a magnetic coil.

Clause 78 the power delivery system of any of clauses 72-76, wherein the receive circuit further comprises a linear detector.

Clause 79. the power transfer system of any of clauses 72-76, wherein the receive circuit further comprises a tuned resonator.

Clause 80. the power delivery system of any of clauses 72-79, wherein the polyphase waveguide probe is configured to create a plurality of resultant fields that are substantially mode-matched to the guided surface wave mode on the surface of the terrestrial medium.

Clause 81. the power delivery system of any of clauses 72-80, wherein the radiation resistance of the polyphase waveguide detector is substantially 0.

Clause 82. the power delivery system of any of clauses 72-81, wherein the height of the polyphase waveguide probe is less than at the operating frequency of the polyphase waveguide probeWhere λ is the wavelength of the operating frequency.

Clause 83. the power transfer system of clause 80, wherein the resultant field sufficiently synthesizes a wavefront incident at a complex brewster angle of the lossy medium, resulting in a reflection of substantially 0.

Clause 84. the power delivery system of any of clauses 72-83, wherein the excitation source is electrically coupled to the polyphase waveguide detector.

Clause 85. the power delivery system of clause 80, wherein the radial surface current density of the guided surface wave mode consists essentially of

Wherein γ is represented byGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the lossy medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the lossy medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate, z is the vertical coordinate orthogonal to the lossy medium,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

Clause 86. the power transfer system of clause 80, wherein the guided surface wave mode is substantially represented as

And is

Wherein H_φIs the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the lossy medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the lossy medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toρ is the radial coordinate and z is orthogonal to the lossy mediumThe vertical coordinate of the mass of the object,is the azimuthal coordinate,/_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first-order Hankel function with the complex parameter-j γ ρ, H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiments without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims. In addition, all optional and preferred features and modifications of the described embodiments and dependent claims are applicable to all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims as well as all optional and preferred features and modifications of the described embodiments can be combined and interchanged with further features and modifications where appropriate. To this end, the different embodiments described above disclose elements that may optionally be combined in various ways depending on the desired implementation.

Claims (75)

1. A method of energy transfer, comprising:

disposing a plurality of charge terminals of a polyphase waveguide probe over a lossy conducting medium, wherein the plurality of charge terminals are coupled to an excitation source;

exciting the plurality of charge terminals via an excitation source, the excitation generating an electromagnetic field that is substantially mode-matched to a Zernike surface wave mode of the lossy conducting medium; and

energy in the form of a guided surface wave along the surface of a lossy conducting medium generated by a multi-phase waveguide probe in a zernike surface wave mode is transmitted.

2. The method of claim 1, wherein the energizing of the plurality of charge terminals synthesizes a plurality of fields that substantially match a zernike surface wave mode of the lossy medium, wherein the plurality of charge terminals are arranged such that the plurality of fields synthesizes a wavefront incident at a complex brewster angle of the lossy conducting medium, resulting in negligible reflection.

3. An energy transfer device, comprising:

a polyphase waveguide probe formed from a plurality of charge terminals located over a lossy conducting medium; and

an excitation source coupled to the plurality of charge terminals, wherein the excitation source is configured to excite the plurality of charge terminals, the plurality of charge terminals generating a plurality of electromagnetic fields that are substantially mode-matched to a Zernike surface wave mode on a surface of the lossy conducting medium.

4. The apparatus of claim 3, wherein the lossy conducting medium is or comprises a terrestrial medium.

5. The apparatus of any of claims 3-4, wherein the excitation source and the plurality of charge terminals are configured such that a radiation resistance of the polyphase waveguide detector is substantially 0.

6. The apparatus of any of claims 3-4, wherein a height of the polyphase waveguide probe above a surface of the lossy conducting medium is less than at an operating frequency of the polyphase waveguide probeWhere λ is the wavelength of the operating frequency.

7. The apparatus of any of claims 3-4, wherein the arrangement and excitation of the plurality of charge terminals causes the electromagnetic field to sufficiently synthesize a wavefront incident at a complex Brewster angle of the lossy conducting medium, resulting in a reflection of substantially 0.

8. The device of any of claims 3-4, wherein the radial surface current density of the Zernike surface wave modes consists essentially of

Wherein Y is represented byGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative dielectric constant of the lossy conducting medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, and H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

9. The apparatus of any of claims 3-4, wherein the Zernike surface wave modes are substantially represented as

And is

Wherein H_φIs the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the lossy conducting medium, ωEqual to 2 pi f, where f is the excitation frequency of the polyphase waveguide probe, epsilon_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the conducting lossy medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first order hank function with the complex parameter-j γ ρ, and H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

10. The apparatus of any of claims 3-4, wherein the excitation source is configured to apply a plurality of voltage amplitudes and a plurality of phases to the plurality of charge terminals.

11. The apparatus of claim 10, wherein the polyphase waveguide probe further comprises a coil coupled between the plurality of charge terminals.

12. An energy receiving method, comprising:

placing a receiving circuit above a ground medium; and

energy transmitted from a multiphase waveguide probe in the form of a zernike surface wave along a surface of a terrestrial medium is received via a receive circuit.

13. The method of claim 12, wherein an electrical load coupled to the receive circuit loads an excitation source coupled to a polyphase waveguide probe that generates the zernike surface wave.

14. The method of claim 12, wherein the energy comprises electrical power, and the method further comprises applying the electrical power to an electrical load coupled to the receive circuit, wherein the electrical power is used as a power source for the electrical load.

15. The method of any of claims 12-14, further comprising impedance matching the electrical load with the receive circuit.

16. The method of any of claims 13-14, further comprising establishing a maximum power transfer from the receive circuit to the electrical load.

17. An energy receiving device, comprising:

a receive circuit for receiving energy transmitted from the multi-phase waveguide probe in the form of a Zernike surface wave along a surface of the lossy conducting medium when the receive circuit is positioned over the lossy conducting medium.

18. The apparatus of claim 17, wherein the lossy conducting medium is or comprises a terrestrial medium.

19. The apparatus of any of claims 17-18, wherein an electrical load coupled to the receive circuit loads an excitation source coupled to a polyphase waveguide probe that generates the zernike surface wave.

20. The apparatus of any of claims 17-18, wherein the receiving circuit comprises a magnetic coil.

21. A power delivery system, comprising:

a polyphase waveguide probe formed by a plurality of charge terminals disposed relative to a surface of a lossy conducting medium;

an excitation source coupled to the plurality of charge terminals, wherein the excitation source is configured to excite the plurality of charge terminals, the excitation of the plurality of charge terminals generating a plurality of electromagnetic fields that are sufficiently mode-matched to a Zernike surface wave mode on a surface of a lossy conducting medium; and

a receive circuit to receive electrical energy from the multi-phase waveguide probe via a guided surface wave along a surface of a lossy conducting medium.

22. The power delivery system of claim 21, wherein an electrical load coupled to the receive circuit loads the polyphase waveguide probe.

23. The power delivery system of claim 21 wherein an electrical load is coupled to the receive circuit and the electrical energy is used as a power source for the electrical load.

24. The power transfer system of any of claims 22-23, wherein a maximum power transfer from the receive circuit to the electrical load is established.

25. The method of any of claims 1-2, wherein the radial surface current density of the zernike surface wave modes is substantially represented by

Wherein γ is a group ofGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative dielectric constant of the lossy conducting medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, and H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo of the time variables having the complex parameter-j γ ρA first-order hankel-like function, where t is time.

26. The method of any of claims 1-2, wherein the zernike surface wave modes are substantially represented as

And is

Wherein the content of the first and second substances,is the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative dielectric constant of the lossy conducting medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first order hank function with the complex parameter-j γ ρ, and H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

27. The method of any of claims 1-2, comprising adjusting the polyphase waveguide probe by adjusting a height of at least one of the plurality of charge terminals.

28. The method of any of claims 1-2, comprising tuning a polyphase waveguide probe by adjusting a distance between at least two of the plurality of charge terminals.

29. The method of any of claims 1-2, comprising tuning a polyphase waveguide probe by adjusting a size of at least one of the plurality of charge terminals.

30. The method of any of claims 1-2, comprising tuning a polyphase waveguide probe by adjusting a probe coupling circuit coupled to the plurality of charge terminals.

31. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe includes a probe coupling circuit coupled to the plurality of charge terminals, the probe coupling circuit configured to impose a plurality of voltage amplitudes and a plurality of phases on the plurality of charge terminals.

32. The apparatus of claim 10, wherein both the plurality of voltage magnitudes and the plurality of phases vary according to a geometric position of the plurality of charge terminals relative to each other.

33. The apparatus of claim 10, wherein both a plurality of voltage amplitudes and a plurality of phases vary according to a geometric position of each of the plurality of charge terminals relative to the lossy conducting medium.

34. The apparatus of claim 10, wherein both the plurality of voltage magnitudes and the plurality of phases vary according to a physical size of the plurality of charge terminals.

35. The apparatus of claim 10, wherein both the plurality of voltage amplitudes and the plurality of phases vary according to a circuit.

36. The apparatus of any of claims 3-4, wherein the plurality of charge terminals are disposed along an axis.

37. The apparatus of any of claims 3-4, wherein the excitation source is coupled in series to the polyphase waveguide probe.

38. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a coil coupled to both the first charge terminal and the second charge terminal of the plurality of charge terminals.

39. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a first coil and a second coil, wherein the first coil is coupled to both the first charge terminal and the second charge terminal of the plurality of charge terminals, and the second coil is coupled to the second charge terminal and the lossy conducting medium.

40. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises:

a coil having a first end coupled to a first charge terminal of the plurality of charge terminals and a second end coupled to a lossy conducting medium; and

a tap coupled to a second charge terminal of the plurality of charge terminals and disposed along the coil.

41. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a first coil coupled to both a first charge terminal of the plurality of charge terminals and the lossy conducting medium and a second coil coupled to both a second charge terminal of the plurality of charge terminals and the lossy conducting medium.

42. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a coil coupled to a first charge terminal of the plurality of charge terminals and the lossy conducting medium and a resistor coupled to a second charge terminal of the plurality of charge terminals and the lossy conducting medium.

43. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a coil coupled to both the first charge terminal of the plurality of charge terminals and a counterpoise.

44. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises:

a first coil coupled to a first charge terminal and a second charge terminal of the plurality of charge terminals; and

a second coil coupled to the lossy conducting medium and the capacitor; and the capacitance is further coupled to a second charge terminal.

45. The apparatus of claim 44, wherein the capacitance is a variable capacitance.

46. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises:

a first coil coupled to both a first charge terminal and a second charge terminal of the plurality of charge terminals; and

a second coil coupled to a terminal and a lossy conducting medium, wherein the terminal is positioned relative to a second charge terminal resulting in a coupling capacitance between the terminal and the second charge terminal.

47. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises:

a first coil coupled to both a first charge terminal and a second charge terminal of the plurality of charge terminals;

a second coil coupled to a terminal, wherein the terminal is positioned relative to a second charge terminal resulting in a coupling capacitance between the terminal and the second charge terminal; and is

Wherein the excitation source is coupled to the second coil and the lossy conducting medium.

48. The apparatus of any of claims 3-4, wherein a respective one of the plurality of charge terminals comprises a ball or a disk.

49. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises:

a coil having a first end coupled to a first charge terminal of the plurality of charge terminals and a second end coupled to a second charge terminal of the plurality of charge terminals; and

a tap coupled to the lossy conducting medium and disposed along the coil.

50. The apparatus according to any one of claims 3-4, wherein the excitation source is coupled to a primary coil, wherein the primary coil is magnetically coupled to the polyphase waveguide probe.

51. The apparatus of any of claims 3-4, wherein the polyphase waveguide probe further comprises a distribution circuit coupled to the plurality of charge terminals.

52. The apparatus of claim 51, wherein the excitation source is a power source coupled to the distribution circuit.

53. The device of claim 51, wherein the distribution circuit further comprises a coil.

54. The apparatus of claim 10, wherein the excitation source is electrically coupled to the polyphase waveguide probe.

55. The method of any of claims 12-14, wherein the receive circuit further comprises a magnetic coil.

56. The method of any of claims 12-14, wherein the receive circuit further comprises a linear detector.

57. The method of any of claims 12-14, wherein the receive circuit further comprises a tuned resonator coupled to the terrestrial medium.

58. The apparatus of any of claims 17-18, wherein the energy comprises electrical power, and the receiving circuit is coupled to an electrical load, and wherein the electrical power is applied to the electrical load, the electrical power being used as a power source for the electrical load.

59. The apparatus of claim 58, wherein the electrical load is impedance matched to the receive circuit.

60. The apparatus of any one of claims 17-18, wherein the receive circuit further comprises a linear detector.

61. The apparatus of any of claims 17-18, wherein the receive circuit further comprises a tuned resonator.

62. The device of claim 61, wherein a tuned resonator comprises a series tuned resonator.

63. The device of claim 61, wherein tuning resonators includes parallel tuning resonators.

64. The device of claim 61, wherein a tuned resonator comprises a distributed tuned resonator.

65. The power transfer system of any of claims 22-23, wherein the electrical load is impedance matched to the receive circuit.

66. The power transfer system of any of claims 21-23, wherein the receive circuit comprises a magnetic coil.

67. The power delivery system of any of claims 21-23, wherein the receive circuit comprises a linear detector.

68. The power transfer system of any of claims 21-23, wherein the receive circuit comprises a tuned resonator.

69. The power transfer system of any of claims 21-23, wherein the lossy conducting medium is a terrestrial medium.

70. The power delivery system of any of claims 21-23, wherein the radiation resistance of the polyphase waveguide detector is substantially 0.

71. The power delivery system of any of claims 21-23, wherein the height of the polyphase waveguide probe is less than at an operating frequency of the polyphase waveguide probeWhere λ is the wavelength of the operating frequency.

72. The power transfer system of claim 69, wherein the plurality of electromagnetic fields combine sufficiently to produce a wavefront incident at a complex Brewster angle of the lossy conducting medium that a reflection of substantially 0 results.

73. The power delivery system of any of claims 21-23, wherein the excitation source is electrically coupled to a polyphase waveguide probe.

74. The power delivery system of claim 69, wherein the radial surface current density of the Zernike surface wave modes consists essentially of

Wherein γ is represented byGiven a surface wave radial propagation constant, and u₂Is formed byGiven a vertical propagation constant, whereinσ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative permittivity of the lossy medium and the number k of free-space waves_oIs equal toWherein λ_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is a radial coordinate, z is a vertical coordinate orthogonal to the lossy conducting medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, H₁ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of first order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.

75. The power delivery system of claim 69, wherein the Zernike surface wave modes are substantially represented as

And is

Wherein H_φIs the azimuthal magnetic field strength, E_ρIs the radial electric field strength, E_zIs the vertical electric field intensity, where γ isGiven the radial propagation constant, u, of the surface wave₂Is formed byGiven the vertical propagation constant, where,σ is the conductivity of the lossy conducting medium, ω is equal to 2 π f, where f is the excitation frequency of the polyphase waveguide probe, ε_oIs the dielectric constant of free space, epsilon_rIs the relative dielectric constant of the lossy conducting medium and the number k of free-space waves_oIs equal toWherein λ is_oIs the free space wavelength of the polyphase waveguide probe, j is equal toP is the radial coordinate, z is the vertical coordinate orthogonal to the lossy medium,is an azimuthal coordinate, I_oIs the net multiphase detector current, H₁ ⁽²⁾(-j γ ρ) is a class two first-order Hankel function with the complex parameter-j γ ρ, H₀ ⁽²⁾(. gamma. rho.) is e^+jωtTwo classes of zeroth-order hankel functions of the time variable with the complex parameter-j γ ρ, where t is time.