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WO2018173032A9 - Système et procédé pour atténuer une dispersion optique - Google Patents

Système et procédé pour atténuer une dispersion optique Download PDF

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Publication number
WO2018173032A9
WO2018173032A9 PCT/IL2017/050369 IL2017050369W WO2018173032A9 WO 2018173032 A9 WO2018173032 A9 WO 2018173032A9 IL 2017050369 W IL2017050369 W IL 2017050369W WO 2018173032 A9 WO2018173032 A9 WO 2018173032A9
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WIPO (PCT)
Prior art keywords
signal
optical
filter
optical signal
dispersion
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Application number
PCT/IL2017/050369
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English (en)
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WO2018173032A1 (fr
Inventor
Erel Granot
Shalom BLOCH
Shmuel Sternklar
Original Assignee
Ariel Scientific Innovations Ltd.
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Application filed by Ariel Scientific Innovations Ltd. filed Critical Ariel Scientific Innovations Ltd.
Priority to PCT/IL2017/050369 priority Critical patent/WO2018173032A1/fr
Publication of WO2018173032A1 publication Critical patent/WO2018173032A1/fr
Publication of WO2018173032A9 publication Critical patent/WO2018173032A9/fr

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/66—Non-coherent receivers, e.g. using direct detection
    • H04B10/69—Electrical arrangements in the receiver
    • H04B10/697—Arrangements for reducing noise and distortion
    • H04B10/6972—Arrangements for reducing noise and distortion using passive filtering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2507—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion
    • H04B10/2513—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to chromatic dispersion
    • H04B10/25133—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to chromatic dispersion including a lumped electrical or optical dispersion compensator
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B2210/00—Indexing scheme relating to optical transmission systems
    • H04B2210/25—Distortion or dispersion compensation
    • H04B2210/252—Distortion or dispersion compensation after the transmission line, i.e. post-compensation

Definitions

  • the present invention in some embodiments thereof, relates to optics and, more particularly, but not exclusively, to a system and a method for mitigating optical dispersion.
  • Dispersion is a known constraint in optical communication systems.
  • dispersion is problematic at high bit rates (e.g., in excess of 10 Gb/s) in fiber optic systems.
  • Conventional dispersion compensation techniques include fiber Bragg gratings, dispersion compensating fibers, and digital dispersion compensation in coherent detection.
  • the dispersed light is directed to a fiber Bragg grating.
  • the short wavelengths have a higher group velocity, therefore they are ahead of the other wavelengths, and longer wavelengths are trailing.
  • the pitch and the chirp in the pitch of the Bragg grating is selected so that the shorter wavelengths are delayed with respect to the longer wavelengths by just the right amount to compensate the dispersion.
  • Dispersion compensating fiber systems include a spool of fiber with an inverse dispersion profile to counteract dispersion over a specific length of fiber, which length is typically not longer than a few tens of kilometers.
  • the detection is coherent, and therefore the detected currents are proportional to the electromagnetic field, and the dispersion can thus be mitigated by applying a digital Finite Impulse Response (FIR) filter on the detected electric signals.
  • FIR Finite Impulse Response
  • Another solution to the dispersion constraint is a duo-binary modulation scheme that has a narrow spectrum of an optical signal and thereby less influenced by the dispersion of an optical fiber. Additional methods, include Nyquist Sine pulses, and Orthogonal Frequency Division Multiplexing (OFDM).
  • OFDM Orthogonal Frequency Division Multiplexing
  • a method of mitigating dispersion in an optical signal modulated relative to a DC component comprises: detecting the signal by a non-coherent optical detector generating an electrical signal; and applying a linear finite impulse response
  • an AC component of the modulated optical signal is less than half the DC component. According to some embodiments of the invention an AC component of the modulated optical signal is less than a third of the DC component. According to some embodiments of the invention an
  • AC component of the modulated optical signal is less than a fifth of the DC component.
  • an AC component of the modulated optical signal is less than a tenth of the DC component.
  • a modulation frequency of the optical signal is up-shifted, and the method comprises down- shifting a frequency of the electrical signal, following the application of the FIR filter.
  • the method comprises applying a band pass filter to the electrical signal, prior to the application of the FIR filter, to remove harmonics generated by the optical detector.
  • a method of transmitting a signal comprises: obtaining an optical signal and an electrical signal selected for modulating the optical signal to carry a data stream; up-shifting a frequency of an AC component of the electrical signal; modulating the optical signal relative to a DC component using the electrical signal; and coupling the optical signal, inclusive of both the AC and the DC components, into a single mode optical fiber.
  • the method comprises applying a linear FIR filter to the electrical signal, prior to the modulation.
  • a method of transmitting an optical signal modulated to carry a data stream comprises: executing the method as described above; detecting the signal at an exit end of the optical fiber by a non-coherent optical detector generating an electrical signal; applying a band pass filter to the electrical signal to remove harmonics generated by said optical detector; and applying a FIR filter to the electrical signal, thereby mitigating dispersion in the optical signal.
  • a system for mitigating dispersion in an optical signal modulated relative to a DC component comprises: a non-coherent optical detector detecting the signal to generate an electrical signal; electronic circuitry configured for applying a linear FIR filter to the band-pass filtered electrical signal, thereby mitigating dispersion in the optical signal.
  • a modulation frequency of the optical signal is up-shifted, and the electronic circuitry is configured for down-shifting a frequency of an electrical signal output by the FIR filter circuit.
  • the electronic circuitry configured for applying a band pass filter to the electrical signal to remove harmonics generated by the optical detector.
  • the optical signal is transmitted over an optical fiber, wherein the non-coherent optical detector is coupled to receive the optical signal from the optical fiber.
  • the optical signal is transmitted over a single mode optical fiber, wherein the non-coherent optical detector is coupled to receive the optical signal from the optical fiber.
  • a system of transmitting a signal comprises: electronic circuitry configured for receiving an electrical signal and up- shifting a frequency of an AC component of the electrical signal; an optical modulator configured for receiving an optical signal and the up-shifted electrical signal, and modulating the optical signal using the up-shifted electrical signal to carry the data stream; and an optical coupler configured for coupling the modulated optical signal into a single mode optical fiber.
  • the electronic circuitry is configured for applying a linear FIR filter to the electrical signal, prior to the modulation.
  • a system of transmitting an optical signal modulated to carry a data stream comprises: a single mode optical fiber having a transmitting end and a receiving end; the system according to any of claim 40-44 coupled to the transmitting end; a non-coherent optical detector coupled to the receiving end and configured for detecting the signal to generate an electrical signal; and electronic circuitry configured for applying a band pass filter to the electrical signal to remove harmonics generated by the optical detector, and for applying a FIR filter to the band-pass filtered electrical signal, thereby mitigating dispersion in the optical signal.
  • the FIR filter is a digital filter operating in a time domain.
  • the FIR filter is characterized by a cutoff parameter ⁇ , which is higher than 10% of a modulation depth of the optical signal.
  • the FIR filter is characterized by a cutoff parameter ⁇ , which is less than 50% of the modulation depth.
  • the cutoff parameter ⁇ equals about one third of the modulation depth.
  • the FIR filter is a digital filter, operating in a time domain, and having a plurality of terms wherein a number of the terms is about 2N+1, and wherein N is a nearest integer above or below ⁇ 2 ⁇ 2 ⁇ , where ⁇ 2 is a dispersion parameter, optionally and preferably a second-order dispersion parameter), z is a distance propagated by the signal, and At is a sampling period characterizing a digitization of the signal.
  • the optical signal is transmitted over an optical fiber.
  • a length of the optical fiber is at least 1 km.
  • a length of the optical fiber is at least 10 km.
  • a length of the optical fiber is at least 100 km.
  • the optical signal is transmitted over a single mode optical fiber.
  • the optical signal carries a data stream at a bit rate of at least 20 Gb per second.
  • the optical signal comprises a plurality of pulses having a predetermined shape
  • the FIR filter is an inverse of a filter whose convolution with a single pulse of the plurality of provides a dispersion distortion which is characteristic to the singe pulse.
  • the optical signal is selected from the group consisting of a pulse amplitude modulation (PAM) signal, an on-off keying (OOK) signal, a quadrature amplitude modulation (QAM) signal, a phase shift keying (PSK) signal, a binary PSK (BPSK) signal, a quadrature PSK (QPSK) signal, an octal PSK (OPSK) signal, a differential PSK (DPSK) signal, an amplitude shift keying (ASK) signal, a frequency shift keying (FSK) signal, a radio over fiber (RoF) signal, a frequency-division multiplexing (FDM) signal and an orthogonal FDM (OFDM) signal.
  • PAM pulse amplitude modulation
  • OOK on-off keying
  • QAM quadrature amplitude modulation
  • PSK phase shift keying
  • BPSK binary PSK
  • QPSK quadrature PSK
  • OPSK octal PSK
  • DPSK differential
  • Implementation of the method and/or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and/or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system.
  • a data processor such as a computing platform for executing a plurality of instructions.
  • the data processor includes a volatile memory for storing instructions and/or data and/or a non-volatile storage, for example, a magnetic hard-disk and/or removable media, for storing instructions and/or data.
  • a network connection is provided as well.
  • a display and/or a user input device such as a keyboard or mouse are optionally provided as well.
  • FIG. 1 is a flowchart diagram describing a method suitable for mitigating dispersion in an optical signal propagating in a dispersive medium, such as, but not limited to, an optical fiber, according to some embodiments of the present invention
  • FIG. 2 is a flowchart diagram describing a method suitable for transmitting an optical signal, according to some embodiments of the present invention
  • FIG. 3 is a schematic illustration of a system for transmitting an optical signal and a system for mitigating dispersion in an optical signal, according to some embodiments of the present invention
  • FIG. 4 is a schematic illustration of a system studied in experiments performed according to some embodiments of the present invention.
  • FIG. 5 shows a ratio between a second harmonic and a first harmonic, as obtained in experiments performed according to some embodiments of the present invention
  • FIG. 6 is a graph showing shows a value of a parameter for which an error has a minimum as a function of a modulation depth, obtained in experiments performed according to some embodiments of the present invention
  • FIGs. 7 A and 7B show a signal as a function of the time, for a first dispersion factor, as obtained in experiments performed according to some embodiments of the present invention
  • FIGs. 8 A and 8B show a signal as a function of the time, for a second dispersion factor, as obtained in experiments performed according to some embodiments of the present invention
  • FIGs. 9A-F show eye patterns for different values of a dispersion factor, as obtained in experiments performed according to some embodiments of the present invention
  • FIG. 10 shows normalized eye-openings, obtained in experiments performed according to some embodiments of the present invention.
  • FIG. 11 shows the bit error rate of FIG. 10
  • FIGs. 12A-C show SNR penalty, obtained in experiments performed according to some embodiments of the present invention.
  • FIG. 13 is a schematic illustration of a suitable system for transmitting a signal over RFoF link, according to some embodiments of the present invention.
  • FIGs. 14A-D show power spectra, obtained in experiments performed according to some embodiments of the present invention.
  • FIGs. 15A-C show logarithmic plots of power spectra of a signal for weak modulation, as obtained in experiments performed according to some embodiments of the present invention
  • FIGs. 16A-D show various spectra and spectrum differences as obtained in experiments performed according to some embodiments of the present invention.
  • FIGs. 17A-C show comparison between spectra of initial transmitted signal (FIG. 17A), a non-compensated received signal (FIG. 17B) and a reconstructed signal (FIG. 17C), as obtained in experiments performed according to some embodiments of the present invention;
  • FIGs. 18A and 18B show a comparison between an original signal and a detected signal after propagating in a first medium, as obtained in experiments performed according to some embodiments of the present invention
  • FIGs. 19A and 19B show a comparison between an original signal and a detected signal after propagating in a second medium, as obtained in experiments performed according to some embodiments of the present invention.
  • FIGs. 20A-C show a relative error function as a function of a normalized dispersion coefficient, as obtained in experiments performed according to some embodiments of the present invention. DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION
  • the present invention in some embodiments thereof, relates to optics and, more particularly, but not exclusively, to a system and a method for mitigating optical dispersion.
  • FIG. 1 is a flowchart diagram describing a method suitable for mitigating dispersion in an optical signal propagating in a dispersive medium, such as, but not limited to, an optical fiber, according to some embodiments of the present invention.
  • the method is particularly useful when the optical signal includes a non-zero DC component and is modulated relative to the DC component.
  • the method begins at 10 and continues to 11 at which the optical signal is detected, optionally and preferably by a non-coherent optical detector, which can be placed, for example, at the exit of the dispersive medium, e.g., optical fiber, carrying the optical signal.
  • the optical detector generates an electrical signal.
  • non-coherent optical detector refers to an optical detector that generates an electrical signal that is proportional to the optical intensity of the optical signal.
  • the received optical signal is typically a dispersed optical signal, wherein an optical pulse is widened during the propagation of the signal in the dispersive medium, e.g., optical fiber.
  • the dispersive medium e.g., optical fiber.
  • dispersion is a linear optical process, wherein the dispersion distortion can be expressed as a convolution between the electromagnetic field and the impulse response of the dispersive medium, the dispersion is not a linear process with respect to the electrical signal generated by the non-coherent optical detector providing signals indicative of the optical intensity. This is because the optical intensity is proportional to the square of the optical electromagnetic field, so that the optical detector destroys the linearity by generating an electrical signal which is nonlinear with respect to the optical electromagnetic field.
  • the technique of the present embodiments successfully mitigates the dispersion exhibited by the optical signal, even though the dispersion is non-linear with respect to the generated electrical signal.
  • the optical signal is optionally and preferably transmitted over an optical fiber having a length from about 100 m to more than 500 km.
  • the optical fiber has a length of at least 10 km or at least 20 km or at least 30 km or at least 40 km or at least 50 km or at least 60 km or at least 70 km or at least 100 km at least 200 km or at least 300 km or at least 400 km or more.
  • the optical fiber is preferably other than a dispersion compensating fiber.
  • the optical fiber can be a single mode optical fiber.
  • the optical signal can optionally and preferably carry a data stream.
  • the bit rate of the data stream can be at least 20 Gb per second or at least 50 Gb per second or at least 100 Gb per second or at least 200 Gb per second or at least 400 Gb per second or at least 800 Gb per second or more.
  • the optical signal can alternatively carry an analog data stream.
  • the duplication of the length of the optical fiber by the square of the bitrate is at least 40,000 m(Gb) .
  • the method optionally and preferably continues to 12 at which a band pass filter is applied to the electrical signal so as to remove harmonics generated by the optical detector.
  • the cutoff frequencies of the band pass filter are selected so that the modulation frequency of the optical signal is maintained and the harmonics generated by the optical detector are filtered out. This operation is particularly useful when a modulation frequency of the optical signal is up-shifted.
  • the cutoff frequencies of the band pass filter are selected so that the up-shifted modulation frequency of the optical signal is maintained, and the harmonics generated by the optical detector are filtered out.
  • the method preferably continues to 14 at which a linear finite impulse response (FIR) filter is applied to the electrical signal, optionally and preferably the band-pass filtered electrical signal.
  • FIR linear finite impulse response
  • a FIR filter is a signal processing circuit, which processes a signal to provide an output signal composed of a summation of successive samples weighted by individual coefficients, wherein the samples are not fed by a feedback loop.
  • a FIR filter circuit is typically described by a mathematical filtering function, but the circuit is a physical circuit, and its output is a physical signal
  • the filtering function optionally and preferably provides the individual coefficients and the number of samples.
  • the FIR filter of the present embodiments is linear in the sense that in the time domain, it includes only teams that are linearly proportional to the respective sample, and, in some embodiments, also constant terms. Representative examples of filtering functions suitable for the present embodiments are provided below and in the Examples section that follows
  • the FIR filter circuit optionally and preferably operates on a sampled version of the signal.
  • the sampling of the signal can be performed downstream FIR filter circuit, at the FIR filter circuit, or upstream of the FIR filter circuit, as desired.
  • the FIR filter is a digital filter operating in the time domain.
  • the filtering function that describes the FIR filter is characterized by a cutoff parameter ⁇ .
  • the cutoff parameter ⁇ is preferably dimensionless.
  • the cutoff parameter ⁇ can be an imaginary part of a complex argument of a function (e.g., a secant) in the complex frequency plane.
  • the cutoff parameter ⁇ can correspond to a number of terms in a series expansion of the FIR filter.
  • the number of terms in the series expansion can be about l/ ⁇ , e.g., the nearest integer of l/ ⁇ or the floor of l/ ⁇ or the ceiling of 1/ ⁇ .
  • the number of the terms of the filter is optionally and preferably about 2N+1, wherein N is a nearest integer above or below ⁇ 2 ⁇ 2 ⁇ , where ⁇ 2 is a dispersion parameter, z is a distance propagated by the signal (e.g., a length of the optical fiber carrying the signal), and At is a sampling period characterizing a digitization of the signal.
  • the dispersion parameter ⁇ 2 can be defined as the derivative of the reciprocal of the characteristic group velocity of the dispersive medium with respect to the frequency ⁇ of the signal.
  • the dispersive medium is an optical fiber characterized by fiber mode propagation constant ⁇
  • ⁇ 2 can be defined as the second derivative of ⁇ with respect to the frequency ⁇ of the propagated signal.
  • the cutoff parameter ⁇ is higher than 10% or higher than 15% or higher than 20% or higher than 25% or higher than 30% or of a modulation depth of the optical signal. In various exemplary embodiments of the invention the cutoff parameter ⁇ is less than 50% or less than 45% or less than 40% or less than 35% of the modulation depth. Preferably, the cutoff parameter ⁇ is from about 15% to about 45% or from about 20% to about 40% or from about 25% to about 35%, e.g., about one third of the modulation depth. In some embodiments, the cutoff parameter ⁇ is less than 0.1 or less than 0.05 or less than 0.01 for any value of the modulation depth.
  • a representative example of a filtering function G(co) suitable in any of the embodiments in which the FIR filter operates in the frequency domain is:
  • ⁇ is the frequency of the optical signal
  • ai and a 2 are constants
  • z is the length of the optical fiber carrying the signal.
  • ai equals or approximately equals half of the characteristic group velocity dispersion parameter, ⁇ 2 , of characteristic the dispersive medium.
  • ⁇ 2 is typically defined as the derivative of the reciprocal of the characteristic group velocity of the dispersive medium with respect to co.
  • ⁇ 2 can be defined as the second derivative of ⁇ with respect to co.
  • the constant a 2 can be set to zero.
  • a 2 optionally and preferably correlates with a.
  • a 2 can be set to be arctan(a).
  • a representative example of a filtering function g(t) suitable in any of the embodiments of the present invention is:
  • the notation [1/ ⁇ ] represents the nearest integer of 1/ ⁇ .
  • a representative example of a filtering function g(nAt), when a digital FIR filter is employed is:
  • qmax is a predetermined parameter.
  • a preferred value of qmax is from about [2/m] to about [5/m], e.g., about [3/m], m being the modulation depth.
  • EQs. 2 and 3 above are suitable, it is to be understood that other forms of the functions g(t) and g(nAt) are contemplated.
  • the dispersion can be mitigated by a function that is simpler than EQ. 2 in the sense that the values of the filter's coefficients decays faster than in the case presented by EQ.
  • a filter shorter than the filter exemplified in EQ. 3 can be used with a sampling period which is approximately equal to the duration of a single bit, and it is not necessary to employ shorter sampling periods.
  • the FIR filter can be an inverse of a filter whose convolution with a single pulse provides the dispersion distortion.
  • Such an inverse filter can be obtained, by deconvolution as known in the art.
  • the method can optionally and preferably continue to 15 at which the modulation frequency is down-shifted.
  • This embodiment is particularly useful when the modulation frequency of the optical signal is up-shifted prior to its transmission.
  • the down-shift is preferably by the same amount as the up-shift.
  • FIG. 2 is a flowchart diagram describing a method suitable for transmitting an optical signal, according to some embodiments of the present invention.
  • the method begins at 20 and optionally and preferably continues to 21 at which an electrical signal suitable for modulating an optical signal to carry a data stream is received.
  • the electrical signal is an RF signal.
  • the method can optionally and preferably continue to 22 at which a frequency of an AC component of the electrical signal is up-shifted.
  • This embodiment is particular useful, for example, when the electrical signal is used to generate a modulated optical signal that is to be transmitted over a dispersive medium (e.g., optical fiber) to a remote location, where it is detected, for example, by a non-coherent optical detector.
  • the up-shifting is preferably excited such that the frequency after the up-shifting is at least 1.1 times or at least 1.2 times or at least 1.3 times or at least 1.4 times or at least 1.5 times the frequency before the up- shifting.
  • the method applies 23 a linear FIR filter to the electrical signal.
  • the FIR filter is applied after 21.
  • the FIR filter is applied after 22.
  • the FIR filter can be the linear FIR filter as further detailed hereinabove.
  • operation 23 is skipped and not executed. These embodiments are useful when the signal is detected and processed by method 10, in which case it is sufficient to apply the
  • the electrical signal is used for modulating an optical signal to carry the data stream.
  • the modulation can be either a direct modulation or an external modulation, and of any type known in the art, including, without limitation, pulse amplitude modulation (PAM), on-off keying, quadrature amplitude modulation, phase shift keying (PSK), binary PSK (BPSK), quadrature PSK (QPSK), octal PSK (OPSK), differential PSK (DPSK), amplitude shift keying (ASK), frequency shift keying (FSK) signal, radio over fiber (RoF) modulation, and any combination thereof.
  • the signal can also be multiplexed, according to any multiplexing scheme, including, without limitation, frequency-division multiplexing (FDM) and orthogonal FDM (OFDM).
  • FDM frequency-division multiplexing
  • OFDM orthogonal FDM
  • moduleating is intended to include all such new technologies a priori.
  • the modulation depth is optionally and preferably selected based on the length of the dispersive medium along which the signal is to be transmitted, wherein for longer lengths a weaker modulation depth is employed.
  • the modulation 24 can be done by an optical modulator.
  • the working modulation point of the optical modulator is preferably selected such that the modulated signal includes a DC component.
  • the working modulation point can be set by the electrical signal that drives the optical modulator.
  • the driving signal is such that the modulated signal includes a DC component.
  • optical signal is coupled into an optical fiber.
  • both the AC and up-shifted DC components are coupled into the optical fiber.
  • the optical fiber can be of any of the types and lengths described above.
  • FIG. 3 is a schematic illustration of a system 30 for transmitting an optical signal and a system 50 for mitigating dispersion in an optical signal, according to some embodiments of the present invention.
  • the signal transmitted by system 30 is received by system 50, but the present embodiments also contemplate a configuration in which only system 30 is employed and the signal is received by another system, and a configuration in which only system 50 is employed and the signal is transmitted by another system.
  • system 30 comprises an optical modulator 32 configured for modulating an optical signal 34 to carry a data stream.
  • Optical modulator 32 can be a direct or indirect modulator, and be configured to apply any type of optical modulation as further detailed hereinabove. In the representative illustration of FIG. 3, which is not to be considered as limiting, optical modulator 32 applies a direct modulation to an optical field generated by a light source 36. Modulator 32 preferably provide a modulated optical signal that includes a DC component.
  • System 30 can also comprise electronic circuitry 38 that up-shifts a frequency of an AC component of the optical signal, as further detailed hereinabove.
  • system 30 comprises an optical coupler 40 that couples the modulated optical signal 34 into an optical fiber 42, as further detailed hereinabove.
  • the optical fiber 42 can be of any of the types and lengths described above.
  • electronic circuitry 38 applies a linear FIR filter according to a filtering function, as further detailed hereinabove.
  • the FIR filter can be applied before or after the modulation.
  • modulator 32 applies a direct modulation
  • the FIR filter preferably is applied to the electrical signal generated by modulator 32 before the modulation.
  • System 50 is optionally and preferably positioned at the receiving end of fiber
  • System 50 can comprise an optical detector 52 that detects the optical signal 34, for example, at the exit of fiber 42, and generate an electrical signal 54.
  • Optical detector can be of any type known in the art, preferably of a non-coherent type.
  • Representative examples of optical detectors suitable for use as detector 52 include, without limitation, a photodiode (e.g., a pin photodiode, an avalanche photodiode), a photomultiplier, a photocell, a light-sensitive integrated circuit (e.g., CCD, CMOS) and the like.
  • an optical coupler (not shown) is provided between detector 52 and the exit of fiber 42 so as to out-couple signal 42 from fiber 42 and in- couple signal 42 into detector 52.
  • System 50 can further comprise electronic circuitry 56 that applies a band pass filter to electrical signal 54 to remove harmonics generated by optical detector 52, as further detailed hereinabove.
  • electronic circuitry 56 can apply the linear FIR filter, as further detailed hereinabove, to the band-pass filtered electrical signal.
  • electronic circuitry 56 transformed signal 54, optionally and preferably after the application of the band-pass filter, to the frequency domain, as further detailed hereinabove.
  • the FIR filter of the present embodiments is applied at the receiving end of fiber 42 (by system 50 in the illustration of FIG. 3). This is advantageous since the FIR filter can also block parasitic noises.
  • compositions, method or structure may include additional ingredients, steps and/or parts, but only if the additional ingredients, steps and/or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure.
  • a compound or “at least one compound” may include a plurality of compounds, including mixtures thereof.
  • range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.
  • Dispersion is a linear process that operates in the electromagnetic (EM) domain.
  • a schematic illustration of a system studied in the present example is illustrated in FIG. 4.
  • the system includes a laser, a dispersive fiber a detector and a filter.
  • the laser can be directly modulated (excluding the need for external modulation), and the electronic filter can be placed at the receiver end (A) or transmitter end (B).
  • the transmitted and received electronic signals are denoted by Vi n (t) and v ou t(t), respectively.
  • vi n (t) and v ou t(t) are proportional to 5pi n (t) and 5p ou t(t),
  • the kernel of EQ. (1.8) is optionally and preferably be replaced with
  • An imaginary term is optionally and preferably introduced to the function's argument, namely,
  • EQ. (1.16) can be reduced to the finite summation, which is also the impulse response of the filter:
  • the cutoff parameter ⁇ determines the number of terms that describe the filter.
  • the present inventors found that the optimum value of ⁇ is approximately mG, where m is the modulation depth. If the time period between adjacent measurements is At, then, the dispersion can be mitigated with the following FIR filter:
  • brackets correspond to the nearest integer value.
  • the reconstructed signal consists of at least two harmonics (the higher ones are ignored due to the weak modulation depth):
  • T is the time slot of a single bit
  • NRZ nonreturn- to-zero
  • RZ return to zero
  • Equation (1.26) is equivalent to launching the EM field signal:
  • a finite dispersive medium e.g., a fiber with spectral response
  • the detected signal which is proportional to the detected optical power (after the reduction of the DC) obeys
  • the reconstructing filter EQ. (1.16)
  • EQ. (1.16 the reconstructing filter
  • EQs. (1.31) and (1.32) show agreement with the experimental results. Since the modulation bandwidth is larger than 10 GHz, and since there is no coherent detection, the laser bandwidth can be from less than 1 MHz to about 10 MHz without affecting the analysis. To evaluate the optimum value for ⁇ , the error ⁇ ( ⁇ ) can be evaluated as a function of ⁇ :
  • FIG. 6 shows value of ⁇ for which the error has a minimum, as a function of the modulation depth.
  • the output-reconstructed signals are plotted for different values of the normalized distance which is a measure of the dispersion effect in the communication link.
  • a similar process can be applied to the reconstructed signal to obtain the eye opening of the reconstructed signal
  • the improvement in the eye-opening is emphasized, when the Gaussian optical filter is replaced with a smooth rectangular filter (like a super- Gaussian in wavelength division multiplexing (WDM) networks) with a spectral width of about 2/ ⁇ .
  • thermal noise is independent of the detected signal, and both shot noise and RIN depend on the DC power of the transmitted signal, and therefore, none of the noise sources is affected by the eye-opening decrease.
  • bit error rate (BER) evaluation counterpart is defined as
  • R is the load resistance and N is the power noise consists of both thermal and shot-noise terms.
  • the BER of FIG. 10 is plotted in FIG. 11 for 0 dBm transmit power source at 50 Gb/s, for the case in which the detection is by a high-quality detector whose sensitivity is bounded only by thermal noise and shot noise.
  • the presented method yields superior performances beyond ⁇ > 0.3 (6 km), and the forward-error-correction (FEC) limit (BER ⁇ 10 ) is reached only at ⁇ of about 1.4 (28 km).
  • the non-compensated performance is illustrated by the vertical dashed line, and the FEC limit is marked by the horizontal dotted line.
  • a measure of performances for low-cost detectors is the SNR penalty.
  • the SNR penalty of the non-reconstructed signal is practically infinite for ⁇ > 0.3.
  • the SNR penalty remains finite for any distance.
  • the link can operate for distances in excess of 40 and even 50 km, even with additional link losses of less than 10 dB.
  • a dispersion compensation for RFoF links is exemplified. While analog and digital links share the same basic components, there are some fundamental differences between them. Two unique properties of RFoF links can be exploited to compensate dispersion-based distortions with an affordable approach. Firstly, unlike digital optical transmission, analog data is usually transmitted with weak modulation, since only weak modulation can insure linear operation. Secondly, RFoF data is carried by a high frequency RF carrier, which typically not the case in digital data links (in both cases there is an optical carrier but in the analog case there is an additional carrier in the RF domain).
  • Ai n (t) and A out (t) are the field amplitudes at the two ends of the fiber and the kernel is expressed as
  • the power equations can be replaced with voltage (or current) equations.
  • the input RF signal is Vi n (t) which is carried over a bias DC voltage VDC
  • the output voltage is v out (tX then EQ. (2.8) can be re laced with
  • FIG. 13 A schematic illustration of a suitable system for transmitting a signal over RFoF link is illustrated in FIG. 13.
  • a local oscillator is used to shift the input signal to a higher spectral band.
  • the RF mixer uses the same oscillator signal to shift it back to the base-band.
  • modulation depth (interchangeable referred to as modulation index) is denoted a.
  • the power at the end of the fiber in the spectral sub-band is, therefore:
  • a weak dispersion can be defined as or less), in which case or less).
  • the filter of the present embodiments has no correcting effect on the third harmonic, and therefore the filter only compensates the first harmonic with ne ligible additional nonlinear contribution:
  • both the modulation depth and dispersion are weak, so that both a «l and ⁇ «1.
  • the filter of the present embodiments successfully reduces the distortions in a typical RFoF channel to a negligible level in comparison to the original signal.
  • the relation between the modulated power p ou t(t), which up do a DC level is proportional to the detected signal, and the modulating signal's voltage Vi n (t) is:
  • T MZ the modulator losses
  • o the lasers' power
  • ⁇ ⁇ the voltage required to change the Mach-Zehnder output power from its minimum value to its maximum value. Therefore, in this case, the noting the signal's amplitude by VQ:
  • EQ. (2.29) is smaller than the back-to- back nonlinearity of EQ. (2.34) caused by the modulator itself, so that this contribution can be neglected as well.
  • expressions of the form of EQ. 2.34 can be canceled or at least suppressed using, for example, a non-linear amplifier.
  • the effect of an additional p increment is smaller so that the frequency shifting of the present embodiments advantageously reduces the second harmonic.
  • FIGs. 14A-D Results of such an analysis are illustrated in FIGs. 14A-D.
  • a signal consisting of two frequencies is transmitted through the dispersive fiber.
  • FIGs. 14A-D show the power spectra is the Fourier transform of r
  • the spurious harmonics are distributed throughout the spectral bandwidth ⁇ /2 much like white noise.
  • the signal is transmitted with low modulation and with the dispersion compensating filter, most of the noise is reduced substantially. Even the second harmonic component is reduced, albeit it does not disappear.
  • the second harmonic when the signal is frequency- shifted, so that the data is carried over a high-frequency carrier and then filtered, the second harmonic can be substantially reduced and preferably eliminated with the cost of increasing the third harmonic power.
  • the third harmonic component is considerably lower than the second harmonic, and therefore the nonlinearities are lower.
  • x n is a random sequence with uniform probability in the range [-0.5,0.5]
  • FIGs. 15A-C A typical scenario is illustrated in FIGs. 15A-C.
  • the power spectrum of the original spectrally-bounded signal is plotted in logarithmic scale.
  • the center panel shows the spectrum of the received signal. This is the case when no FS was introduced, therefore, in addition to considerable spectral broadening nonlinear distortions arise, even within the original spectral band.
  • FS lower panel
  • the spectral filter (2.13) can easily filter them out.
  • the compensating filter is sufficient for compensating the dispersion distortions. Numerical simulations have been performed to demonstrate the performance of the compensating filter.
  • FIG. 16D shows the difference between the original spectrum and the non-compensated received spectrum.
  • FIG. 16A top-left shows the spectrum of the received signal with the compensating filter
  • FIG. 16B top-right shows the difference between the compensated spectrum and the original spectrum. Note that the frequencies are normalized to the spectral band, and therefore were subtracted in the plots. As shown in FIGs.
  • the non-compensated signal is completely distorted: while the third harmonic is clearly seen, the main distortion is due to different amplitudes of the original harmonic spectral lines.
  • the compensating filter did not eliminate the third harmonic power but it almost completely eliminates the original harmonic distortion.
  • the pseudo-random analog sequence (2.39) was also simulated.
  • the spectra are bounded in a spectral bandwidth ⁇ , and therefore the transmitted signal's spectrum has a rectangular profile.
  • FIGs. 17A-C show comparison between the spectra of the initial transmitted signal (FIG. 17A), the non-compensated received signal (FIG. 17B) and the reconstructed signal (FIG. 17C).
  • the spectrum of the detected signal is distorted due to dispersion and the compensating filter reconstructs the spectrum to its initial form.
  • the distortion reaches a high level of about 50%., although the original signal can still be recognized.
  • the curves for the original and detected signals substantially overlap, indicating.
  • the curves for the original and detected signals substantially overlap.
  • FIGs. 18B and 19B demonstrate that the compensating filter reconstructs the signal with great accuracy.
  • FIGs. 20A-C Plots of the relative error function as a function of the normalized dispersion coefficient is presented in FIGs. 20A-C as a function of modulation depth. In all these plots there is a clear transition. For small ⁇ the curve is smooth and the value of ⁇ can be arbitrarily small. However, when the dispersion coefficient reaches the point where the compensatin filter diverges, namely
  • the curve starts to fluctuate. For smaller the fluctuations are larger.
  • the value of ⁇ can be considerably smaller than the values in Example 1, and therefore it is advantageous to use this filter to mitigate dispersion distortions.
  • ⁇ 0 the error decreases by 10 orders of magnitudes for low modulation (FIG. 20C), but even for larger modulations index (FIGs. 20B-C) it decreases by 4-5 orders of magnitudes.
  • ⁇ > ⁇ 0 ⁇ error decreases by at least 3 orders of magnitudes.
  • This example described a technique for dispersion compensation in RFoF channels. The technique is based on two properties that are usually present in these channels: the modulation depth is lower than in digital links (e.g., lower than 1 to mitigate nonlinear effects), and the data's spectral bandwidth is narrower than the signals' carrier frequency.
  • the first property ensures that distortions due to nonlinearities appear only in terms that are of high order of the modulation depth, and therefore can be neglected in the low modulation regime.
  • the second property ensures the elimination of the second order nonlinear distortions.
  • the nonlinear distortions are of the third order, and in many cases can be neglected in comparison to the back- to-back third order distortions.
  • the system can be regarded as a linear one, and therefore the linear distortions can be compensated by a low-cost linear filter.

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Abstract

L'invention concerne un procédé pour atténuer une dispersion dans un signal optique modulé par rapport à un composante CC qui consiste à détecter un signal par un détecteur optique non cohérent générant un signal électrique; et à appliquer un filtre à réponse impulsionnelle finie linéaire (FIR) au signal électrique, atténuant ainsi la dispersion dans le signal optique.
PCT/IL2017/050369 2017-03-24 2017-03-24 Système et procédé pour atténuer une dispersion optique WO2018173032A1 (fr)

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US7558480B2 (en) * 2003-07-31 2009-07-07 Corning Incorporated Unrepeatered optical communication system with suppressed SBS
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US8265491B2 (en) * 2008-09-22 2012-09-11 At&T Intellectual Property I, L.P. Method for improving the performance of digital coherent optical receiver using single ended photo-detection
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