LU503450B1 - Polarization rotation device and faraday isolator - Google Patents

Abstract

Provided is a polarization rotation device (12) suitable to rotate a polarization direction of a laser radiation (14). The polarization rotation device (12) comprises a Faraday medium (16), and a multipass arrangement (18) having the Faraday medium (16) arranged at least partly within the multipass arrangement (18), wherein the multipass arrangement (18) is adapted such that the laser radiation (14) carries out multiple roundtrips in the multipass arrangement (18) and multiple passes through the Faraday medium (16) when coupled into the multipass arrangement (18). Moreover, the polarization rotation device comprises a magnetic element (20) suitable to provide a magnetic field at the position of the Faraday medium (16) inside the multipass arrangement (18). The polarization rotation device is characterized in that the Faraday medium (16) has a thickness, through which the laser radiation (14) propagates at each of the multiple passes, of 2 mm or more.

Description

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 1/37 LU503450

POLARIZATION ROTATION DEVICE AND FARADAY ISOLATOR

Provided are a polarization rotation device and a faraday isolator. The disclosure

Is, thus, related to laser technology.

Conventional optical isolators are an often crucial component of laser systems which are sensitive to back reflections of laser radiation. Usually, optical isolation is realized with Faraday isolators. In conventional Faraday isolators the polarization of an incident laser radiation is rotated employing the Faraday effect within a Faraday medium between two linear polarizers by 45° against each other.

A magnetic field is applied to the Faraday medium, whereby the magnetic field is aligned parallel to the propagation direction of the laser radiation through the

Faraday medium. For a laser radiation entering the Faraday isolator from one side, the resulting Faraday effect rotates the polarization typically by an angle of 45° so that essentially full transmission through the second polarizer (polarizer 2) is granted. When the laser radiation exiting the Faraday isolator is eventually reflected back into the Faraday isolator, its polarization is also rotated by an angle of about 45°. But with regard to the corresponding wave vector, the direction of the

Faraday rotation reverses, leading to an essentially complete rejection at the respective second linear polarizer (polarizer 1). Viewed from a fixed laboratory frame, the polarization rotation for both beams adds up, resulting in a polarization oriented 90° towards the polarizer 1. The rotation angle for a single pass of the laser radiation though the Faraday medium is given by: l 0 = v | Biz

The rotation angle is determined by the medium’s Verdet constant V, the component of the applied magnetic field Bz parallel to the propagation direction of the laser radiation, and the propagation length within the material I. A magnetic

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 2137 LU503450 field antiparallel to the propagation direction of the laser radiation requires a change in the sign and thus reverses the direction of polarization rotation with regard to the wave vector. However, when observed from the fixed laboratory frame the Faraday rotator rotates the electric field vector of the passing electromagnetic wave always in the same direction. Therefore, the rotation angle of the electric field vector is accumulating when an electromagnetic wave is passing through a Faraday medium a second time after being reflected back into it by a reflecting surface. It is trivial, but important to note that the reflecting surface is changing the direction of propagation, but not the orientation of the electric field.

In conventional Faraday isolators for near-infrared (NIR) lasers with high average powers, Terbium Gallium Garnet (TGG) is a commonly used Faraday medium (see K. T. Stevens et al.: “Promising Materials for High Power Laser Isolators,”

LTJ 13, 18-21 (2016); and |. L. Snetkov et al.: “Review of Faraday Isolators for

Kilowatt Average Power Lasers,” IEEE J. Quantum Electron. 50, 434-443 (2014)).

It offers a high Verdet constant of about 39 rad/(T-m) at a wavelength of 1 um and an absorption coefficient of about 1-103 cm. Another emerging Faraday medium is potassium terbium fluoride (KTF) with a similar Verdet constant and an order of magnitude lower absorption and thermo-optic coefficients, allowing for the handling of higher average powers, but coming with the disadvantage of being more difficult to grow (see K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising Materials for High Power Laser Isolators,” LTJ 13, 18— 21 (2016)). Typically, a rod of TGG with a length of a few millimeters is placed inside a system of permanent ring magnets providing the axial magnetic field with the order of magnitude of 1 T. Practically, the operation is limited to average powers of a few 100 W (see |. L. Snetkov, A. V. Voitovich, O. V. Palashov, and E.

A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,”

IEEE J. Quantum Electron. 50, 434-443 (2014)). The limiting factor in such a conventional Faraday isolator is the degrading isolation performance due to temperature gradients from absorption of optical radiation. Whereas thermal lensing and temperature dependent shifts in the Verdet constant are problematic, the main limitation arises from birefringence induced by the photo-elastic effect

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 3/37 LU503450 (see E. A. Khazanov et al.: “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116-1122 (1999)). Intricate schemes for compensation of the birefringence within the isolator allow for average powers beyond 1 kW while maintaining an isolation performance of 30 dB (see E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29, 59-64 (1999)). Another conventional approach has been proposed, in which the thermal gradients inside the Faraday medium are reduced by a cooling geometry known for its effective application in high power thin-disk lasers (see DE 10 2010 028 213 A1; and

A. Giesen et al.: “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994)). Thereby the Faraday medium is prepared in the form of a thin-disk and mounted from one side onto a water cooled heatsink. The reduced thickness of the thin-disk results in a reduced Faraday rotation, which has to be compensated by several passes over the disk. Besides the significant cost and complexity of this approach, it requires producing the

Faraday medium in the shape of an anti-reflection-coated thin-disk with desirably low thickness and large aperture. Moreover, a strong and homogeneous magnetic field has to be applied over the aperture of the disk to produce the necessary effect and to avoid depolarization. This requires a magnetic system located below the thin-disk instead of surrounding it like in readily available designs of other conventional Faraday isolators. Furthermore, this magnetic system is prone to conflict with the water cooling system locally.

The problem solved by the presented disclosure, thus, relates to providing a polarization rotation device and a Faraday isolator overcoming limitations of conventional polarization rotation devices and Faraday isolators. More specifically, the problem solved by the disclosure may relate to providing a polarization rotation device having reduced requirements regarding the usable Faraday medium.

This problem is solved by a polarization rotation device and a Faraday isolator having the features of the respective independent claim. Optional embodiments are provided in the dependent claims and the description.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 4/37 LU503450

In one aspect, a polarization rotation device suitable to rotate a polarization direction of a laser radiation is provided. The polarization rotation device comprises a Faraday medium, and a multipass arrangement having the Faraday medium arranged at least partly within the multipass arrangement, wherein the multipass arrangement is adapted such that the laser radiation carries out multiple roundtrips in the multipass arrangement and multiple passes through the Faraday medium when coupled into the multipass arrangement. Moreover, the polarization rotation device comprises a magnetic element suitable to provide a magnetic field atthe position of the Faraday medium inside the multipass arrangement. The polarization rotation device is characterized in that the Faraday medium has a thickness, through which the laser radiation propagates at each of the multiple passes, of 2 mm or more.

In another aspect, a Faraday isolator comprising a polarization rotation device according to the disclosure is provided.

A polarization rotation device relates to an optical device adapted to rotate the polarization direction of laser radiation propagating through the polarization rotation device. The polarization rotation device may be adapted to have the highest polarization rotation efficiency at a predetermined design wavelength. The predetermined design wavelength may correspond to a central wavelength of a laser system, in combination with which the polarization rotation device is intended to be used.

The term “laser radiation” is used in the present disclosure for any kind of optical electromagnetic radiation and in particular for coherent electromagnetic radiation.

The laser radiation may be provided as laser pulses, i. e., as pulsed laser radia- tion. Pulsed laser radiation may be a laser radiation provided as a train of pulses or single isolated pulses. The pulsed laser radiation may also be provided as a burst of laser pulses. The pulse duration of the laser pulses may for instance be 1 ps or less and optionally as short as 100 fs or less. The laser oscillator system

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 5/37 LU503450 may apply mode-locking in order to provide the pulsed laser radiation. Values for pulse durations provided throughout the disclosure are specified as full width at half-maximum (FWHM) assuming a Gaussian pulse shape, if not specified other- wise. Laser radiation and pulsed laser radiation may be used synonymously throughout the present disclosure.

A polarization rotation device is an optical device, which allows rotating the polari- zation of laser radiation, in particular pulsed laser radiation, coupled into the polari- zation rotation device. After rotating the polarization of the laser radiation coupled

Into the polarization rotation device, the laser radiation may be coupled out from the polarization rotation device. Laser radiation having a linear polarization may be particularly suitable or required for causing a polarization rotation based on the

Faraday effect.

A multipass arrangement is an arrangement of optical elements which deflects a laser radiation coupled into the multipass arrangement in such a way that it propagates several times in the multipass arrangement before the laser radiation is coupled out of the multipass arrangement. The redirection of the laser radiation optionally takes place by reflections of the laser radiation, so that the laser radiation changes its propagation direction in the multipass arrangement. In contrast to arrangements which guide the laser radiation by means of optical fibers through total internal reflection, the propagation of the laser radiation in the multipass arrangement may take place in free space without a mode of the laser radiation being restricted by an optical fiber at any point along the optical path of the laser beam or laser pulse. The central axis of the multipass arrangement may be a central axis of the mode volume of the multipass arrangement. The central axis may at least partially coincide with an optical axis of a first mirror and/or a second mirror of the multipass arrangement. The central axis does not necessarily have to be a straight line, but may comprise one or more kinks, for instance when the multipass arrangement comprises one or more intermediate mirrors for reflecting the laser radiation on a propagation between the first mirror and the second mirror. The distance of a first mirror from a second mirror of the multipass

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 6/37 LU503450 arrangement may be a separation distance between the first and the second mirror measured along the central axis, in particular between a respective center point of the reflective surface of said mirrors. The multipass arrangement may be configured as, or comprise a Herriott cell, a White cell and/or a Pfund cell. The multipass arrangement may have a central axis, which may be folded by one or more further mirrors. The first and/or the second mirror of the multipass arrangement may have a flat or a convex shape, whereas the other mirror, respectively, has a concave shape. In other words, the multipass arrangement may have a convex-concave or concave-flat configuration. Optionally, the first and the second mirror may have a concave shape. According to an optional embodiment, the multipass arrangement may in particular consist of, or comprise a Herriott cell.

The roundtrips of the laser radiation in the multipass arrangement may each have very similar optical paths through the multipass arrangement. In particular, in every, or most, of the roundtrips the laser radiation may be deflected by the same optical elements of the multipass arrangement, in particular a first mirror and a second mirror of the multipass arrangement. For instance, the first roundtrip may include an incoupling and/or the last roundtrip may include an outcoupling of the laser radiation into / out of the multipass arrangement. Thus, the first and/or the last roundtrip may deviate from the other roundtrips with respect to the optical ele- ments deflecting the laser radiation. Optionally, a roundtrip does not exactly revert the optical path of the laser radiation propagating in the multipass arrangement, but after completing one entire roundtrip, the laser radiation may hit the respective optical element, i.e. the first mirror and/or the second mirror, at a position strongly deviating from the position at the beginning of the roundtrip. In particular, the laser radiation may propagate in the multipass arrangement on an individual optical path in each roundtrip, wherein the individual optical paths may not overlap with each other. The first mirror and/or the second mirror may have a hole for incoupling and/or outcoupling the laser radiation into and out of the multipass arrangement, respectively.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 7137 LU503450

The Faraday medium may be a medium being optically at least partially transpar- ent for the laser radiation, wherein the Faraday effect occurs when laser radiation propagates through the Faraday medium. The Faraday effect is also convention- ally known as magneto-optical effect. The Faraday effect causes a polarization ro- tation which is proportional to a projection of an applied magnetic field along the propagation direction of the laser radiation through the Faraday medium. The Far- aday effect may typically be caused by left and right circularly polarized light waves propagating at slightly different speeds, a property known as circular bire- fringence, wherein linear polarization may be decomposed into a superposition of two circularly polarized components of equal amplitude and of opposite handed- ness and different phase. The effect of a relative phase shift, induced by the Fara- day effect, is to rotate the orientation of a wave's linear polarization.

A pass of the laser radiation through the Faraday medium represents a propaga- tion of the laser radiation through the Faraday medium. In some embodiments, each roundtrip of the laser radiation in the multipass arrangement may include two passes through the Faraday medium, for instance one pass in a first direction and one pass in a second direction being opposite to the first direction. In other em- bodiments, each roundtrip may include only one pass through the Faraday me- dium. For instance, the optical path of the roundtrip may be configured such that the laser radiation passes through the Faraday medium only in one direction but does not pass through the Faraday medium in a second direction. Each roundtrip may optionally include more than one pass, in particular two passes, through the

Faraday medium. Optionally, some roundtrips may not include a pass through the

Faraday medium. For instance, the polarization rotation device and in particular the multipass arrangement may be arranged such that in some roundtrips, such as directly after coupling the laser radiation into the multipass arrangement and/or di- rectly before coupling the laser radiation out of the multipass arrangement, no pass through the Faraday medium is included.

A magnetic element may be any suitable element adapted to provide the magnetic field at the position of the Faraday medium inside the multipass arrangement in a

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 8/37 LU503450 sufficient manner to cause the intended Faraday effect and polarization rotation of the laser radiation. The magnetic element may comprise one or more permanent magnets and/or one or more electromagnets. The magnetic element may be adapted to provide a magnetic field at the position of the Faraday medium, in par- ticular in a direction parallel or antiparallel to the propagation direction of the laser radiation, having a field strength of 0,1 T or more, optionally 0,2 T or more, option- ally 0,5 T or more, optionally 0,75 T or more and optionally 1 T or more. This may ensure a large magnitude of the Faraday effect experienced by the laser radiation when propagating through the faraday medium. The thickness of the Faraday me- dium may relate to a spatial extension of the Faraday medium along an average propagation direction of the laser radiation through the Faraday medium. The term “Average propagation direction” may refer to a direction, along which the laser ra- diation commonly passes when propagating through the Faraday medium alt- hough in each path the propagation direction may be slightly different due to the varying propagation paths within the multipass arrangement. The “thickness through which the laser radiation propagates at each of the multiple passes” may relate to an effective thickness experienced by the laser radiation when propagat- ing through the Faraday medium. The thickness may further relate to an average thickness based on multiple respective thicknesses experienced by the laser radi- ation in multiple passes through the Faraday medium.

The thickness of the Faraday medium may optionally be 20 mm or less and op- tionally 10 mm or less. This may allow providing the Faraday medium and option- ally the multipass arrangement and optionally the polarization rotation device in a compact manner.

The disclosure provides the advantage that a polarization rotation device may be provided offering a significantly increased propagation length through the Faraday medium as compared to conventional polarization rotation devices having only one pass through a Faraday medium or being limited to a very thin Faraday medium having a thickness of only 1 mm or less.

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Accordingly, the disclosure provides the further advantage that such materials may be used as Faraday medium having a lower Verdet constant than many conventionally used materials, such as TGG. In particular, as the propagation length of the laser radiation through the Faraday medium due to the multiple passes may be orders of magnitude higher than in conventional single-pass polarization rotation devices, a Faraday medium may be chosen according to the disclosure having a Verdet constant being orders of magnitude lower than in conventional Faraday media. This dramatically increases the selection of possible materials to be used as Faraday medium and, thus, allows choosing a material having other properties optimized for the intended purpose and design wavelength.

In particular, this allows using such materials as Faraday medium having a lower absorption at the wavelength of the laser radiation, which may correspond to the design wavelength, but having a lower Verdet constant. For instance, materials such as quartz and/or fused silica may be used as Faraday medium offering an exceptionally low absorption coefficient at a wavelength of 1 um, which is about two orders of magnitude lower than the absorption coefficient of TGG. Moreover, these materials offer a lower thermo-optic coefficient offering lower temperature gradients and, thus, a reduced depolarization due to temperature gradients as compared to TGG. Due to the Faraday medium being arranged in a multipass arrangement, the total thickness of the Faraday medium may yet be kept moderate, as the effective thickness, i. e. a cumulated thickness, is increased due to a large number of round trips.

Moreover, the disclosure provides the advantage that a polarization rotation device may be provided for such design wavelengths, which are often not realizable when using conventional Faraday media, such as TGG. Since TGG typically exhibits color centers, TGG suffers from a high absorption in the visible and ultraviolet spectral range and thermal degradation and is, thus, typically not suitable to serve as a Faraday medium in the ultraviolet and visible spectral range (K. T. Stevens,

W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising Materials for

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 10/37 LU503450

High Power Laser Isolators,” LTJ 13, 18-21 (2016). In particular, according to the disclosure, a polarization rotation device may be provided for a design wavelength in the ultraviolet spectral region, such as in a wavelength range from 200 nm to 450 nm. For instance, the disclosure may allow using materials such as Ce- rium(III)-Fluoride (CeF3) and/or Magnesium Fluoride (MgF2) as Faraday medium (see M. J. Weber, Handbook of Optical Materials (CRC Press, 2018); and D. L.

Steinmetz et al.: “A polarizer for the vacuum ultraviolet,” Applied optics 6, 1001— 1004 (1967)), which offer a high transmission down to a wavelength of 200 nm but, again, suffer from a significantly lower Verdet constant than TGG (E. Munin,

C. B. Pedroso, and A. B. Villaverde, “Magneto-optical constants of fluoride optical crystals and other AB2 and A2B type compounds,” Faraday Trans. 92, 2753 (1996)). Due to the polarization rotation device according to the disclosure includ- ing a multipass arrangement offering multiple passes of the laser radiation through the Faraday medium, the lower Verdet constant may be compensated by a large effective propagation length through the Faraday medium and, thus, may allow ex- ploiting the advantageous transmission properties of these materials.

Moreover, the disclosure provides the advantage that the manufacturing costs for polarization rotation devices may be reduced as the polarization rotation devices may be manufactured without the need for cost-intensive materials for the Faraday medium. This may allow integrating one or more polarization rotation devices in low-budget laser systems and applications.

Moreover, the disclosure may provide the advantage that the length or volume, over which a high magnetic flux is to be provided may be kept small. In particular, as the propagation length of the laser radiation through the Faraday medium may be kept small for each individual pass, the length or volume of the magnetic field may be restricted to the small dimensions of the interaction volume of the laser radiation with the Faraday medium.

The polarization rotation device may be adapted such that the laser radiation carries out at least five and optionally at least ten passes through the Faraday

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 11/37 LU503450 medium. This may ensure a large, effective propagation length of the laser radiation through the Faraday medium and, thus, may allow cumulating a high

Faraday rotation even though the Faraday medium may exhibit only a moderate

Verdet constant.

The Faraday element may have a Verdet constant of 20 rad/(T-m) or less at a predetermined design wavelength of the polarization rotation device. This may allow for a wide range of materials having favorable properties, such as a high transmission at the design wavelength, in particular at a design wavelength in the visible and/or ultraviolet spectral range, and/or a low thermal expansion, and/or a low thermo-optic coefficient and, thus, a low depolarization due to thermal effects.

Accordingly, this may allow providing a polarization rotation device with a high extinction ratio. Moreover, the Faraday element may be chosen to offer a Verdet constant of 0,5 rad/(T-m) or more and optionally of 1 rad/(T-m) or more at the predetermined design wavelength of the polarization rotation device. This may ensure an efficient polarization rotation of the laser radiation. The Faraday medium may be provided as a separate medium comprising one or more solid Faraday elements and/or one or more gaseous Faraday medium having predetermined extensions and/or predetermined physical properties and in particular a predetermined Verdet constant at the design wavelength of the polarization rotation device.

The Faraday medium may comprise a solid Faraday element. This may provide the advantage that the technical complexity of the polarization rotation device may be kept low. Moreover, this may provide the advantage that the Faraday medium may be provided with a precisely predetermined Verdet constant and/or precisely predetermined spatial dimensions.

The polarization rotation device may be adapted such that in each pass through the solid Faraday element the laser radiation enters the Faraday medium at a different surface of the solid Faraday element than the surface, at which the laser radiation exits the solid Faraday element. In other words, in each pass the laser

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 12/37 LU503450 radiation is transmitted through the Faraday medium but not totally internally reflected. This may provide the advantage that the Faraday medium may be used in transmission and, hence, may be inserted into the optical path of the multipass arrangement without reconfiguring the multipass arrangement. Moreover, this may provide the advantage that the thickness of the Faraday medium, i. e., its spatial extension in the propagation direction of the laser radiation, may be chosen to be longer than its lateral extension in the directions perpendicular to the propagation direction without suffering from clipping the beam of the laser radiation.

The solid Faraday element may consist of or comprise at least one of the following materials: fused silica, quartz, MgF2, CaF», Al203 (Sapphire), YAG, GdsAl5012,

KBr, ZnS, ZnSe, and ZnTe. These materials may offer lower Verdet constants than materials conventionally used as Faraday medium, such as TGG, but may offer advantageous optical properties, such as a high transmission in a wide spectral range, a high transmission in the visible and/or ultraviolet spectral range, a high laser-induced damage threshold, good thermal properties avoiding or reducing undesired thermal effects and temperature gradients, and an availability in good optical quality at moderate costs.

Alternatively or additionally, the Faraday medium may comprise or consist of a gaseous Faraday medium. This may provide the advantage of low absorption of the laser radiation, which may reduce performance limiting thermal effects inside the Faraday medium. The absence of temperature or pressure induced birefringence, which can occur in solid materials, may decrease the amount of performance limiting depolarization. Furthermore, the magnitude of polarization rotation may be tuned by varying a pressure of the gaseous Faraday medium.

Moreover, this may provide the advantage of varying the properties of the Faraday medium by providing a mixture of different gases as Faraday medium. The gaseous Faraday medium may optionally consist of or comprise one or more of the following gases: He, Ne, Ar, Kr, Xe, Hz, D2, O2, N2, CO», and CH4. The polarization rotation device may further comprise a pressure cell containing the gaseous Faraday medium, wherein the multipass arrangement may be arranged

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 13/37 LU503450 at least partly inside the pressure cell. Alternatively, a pressure cell may be arranged inside the multipass arrangement and in particular within the beam path of the pressure cell. The pressure cell may comprise a window for coupling the laser radiation into the pressure cells and a window for coupling the laser radiation out of the pressure cell. The pressure of the gaseous Faraday medium inside the pressure cell may be in a range from 1 bar to 1.000 bar and in particular in a range from 1 bar to 100 bar.

The gaseous Faraday medium may have a pressure dependent Verdet constant.

Moreover, the pressure dependent Verdet constant may be 1 mrad/(T-m-bar) or more. The gaseous Faraday medium may be provided at an absolute pressure of 1 bar or more. A density of the gaseous Faraday medium consisting of a pure gas at a pressure of 1 bar may be 1 amagat = 44,6 mol/m3. Optionally the pressure of the gaseous Faraday medium may be 10 bar or more. A density of the gaseous

Faraday medium consisting of a pure gas at a pressure of 10 bar may be 10 amagat = 446 mol /m3.

The Faraday medium comprises multiple solid Faraday elements and/or a mixture of different gases. The Faraday medium may optionally comprise at least one solid

Faraday element and a gaseous Faraday medium. This may allow a high flexibility for tuning the optical properties and the Verdet constant of the Faraday medium.

The magnetic element may comprise or consist of a permanent magnet. This may provide the advantage that the magnetic field used for causing the Faraday effect may be provided without the need of providing electrical energy to the magnetic element. This may allow for providing the polarization rotation device as an entirely passive device without a need for a supply of electrical energy. This may, thus, facilitate an implementation of the polarization rotation device in other devices, such as laser systems or other optical apparatuses. In addition, this may provide the advantage of providing a favorable ratio of provided magnetic field strength and spatial dimensions of the magnetic element. Furthermore, this may reduce the cost for manufacturing and operating the polarization rotation device.

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The permanent magnet may be ring-shaped and adapted to provide a magnetic field along a central axis of the ring-shaped permanent magnet. The ring-shaped permanent magnet may surround the Faraday medium at least partially within the multipass arrangement. This may allow to optimize the use of the total magnetic flux provided by the magnetic element and, hence, may reduce the required performance, size and/or cost of the magnetic element.

The polarization rotation device may further comprise a first linear polarizer arranged before the multipass arrangement and/or a second linear polarizer arranged after the multipass arrangement. This may allow isolating those polarization components which have undergone an intended polarization rotation in the polarization rotation device while blocking other polarization components. In particular, this may allow for using the polarization rotation device as a Faraday isolator or in a Faraday isolator.

The Faraday medium may offer an optical transmission of 80% or more and optionally of 90% or more and optionally of 95% or more throughout a spectral range from 150 nm to 550 nm. This may allow for providing the polarization rotation device for a design wavelength in the visible or ultraviolet spectral range.

For instance, the Faraday medium may comprise or consist of a solid Faraday element made of quartz or fused silica, which offers a high transmission at least in the spectral range from 150 nm to 550 nm and is available in good optical quality at low cost.

The polarization rotation device may be adapted to rotate the polarization direction of the laser radiation by an angle in a range from 30° to 60° between coupling the laser radiation into the multipass arrangement and coupling the laser radiation out of the multipass arrangement. In particular, the polarization rotation device may be adapted to rotate the polarization direction of the laser radiation by an angle of 45° This may enable the polarization rotation device to be used as a Faraday isolator or in a Faraday isolator and, accordingly, to block laser radiation

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 15/37 LU503450 propagating in the opposite direction as compared to an intended direction according to the design of the polarization rotation device.

As mentioned above, a Faraday isolator comprising a polarization rotation device according to the disclosure presented above is provided. All features and properties disclosed with regard to the polarization rotation device shall be regarded as disclosed also for the Faraday isolator and vice versa.

The Faraday isolator may be adapted to rotate the polarization direction of the laser radiation by an angle in a range from 30° to 60° and in particular to rotate the polarization direction of the laser radiation by an angle of 45°. This may allow for efficiently blocking laser radiation propagating in a direction opposite to the intended propagation direction of the laser radiation, such as undesired back reflections.

The Faraday isolator may comprise multiple polarization rotation devices. The

Faraday isolator may comprise a cascaded arrangement of multiple polarization rotation devices. This may allow for accumulating a large quantity of polarization rotation while keeping the complexity of the used multipass arrangements low.

It is understood by a person skilled in the art that the above-described features and the features in the following description and figures are not only disclosed in the explicitly disclosed embodiments and combinations, but that also other technically feasible combinations as well as the isolated features are comprised by the disclosure. In the following, several optional embodiments and specific examples are described with reference to the figures for illustrating the disclosure without limiting the disclosure to the described embodiments.

Further optional embodiments will be illustrated in the following with reference to the drawings. The Figures show:

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Figure 1 a sketch of a Faraday isolator according to an optional embodiment;

Figure 2 and 3: a visualization of the magnetic field flux in different permanent magnets.

In the drawings the same reference signs are used for corresponding or similar features in different drawings.

Figure 1 shows in a schematic sketch a Faraday isolator 10 according to an optional embodiment comprising a polarization rotation device 12 according to an optional embodiment.

The polarization rotation device 12 is adapted to rotate a polarization direction of a laser radiation 14 by a rotation angle in a range from 30° to 60° and optionally by a rotation angle of 45°. The polarization rotation device 12 comprises a Faraday medium 16 and a multipass arrangement 18 having the Faraday medium 16 arranged at least partly within the multipass arrangement 18. The multipass arrangement 18 is adapted such that the laser radiation 14 carries out multiple roundtrips in the multipass arrangement 18 and multiple passes through the

Faraday medium 16 when coupled into the multipass arrangement 18. Moreover, the polarization rotation device 12 comprises a magnetic element 20 suitable to provide a magnetic field at the position of the Faraday medium 16 inside the multipass arrangement 18. The polarization rotation device is characterized in that the Faraday medium 16 has a thickness, through which the laser radiation 14 propagates at each of the multiple passes, of 2 mm or more. The thickness of the

Faraday medium 16 may coincide with a spatial extension of the Faraday medium 16 along a central axis 100 of the multipass arrangement 18. The thickness of the

Faraday medium 16 may, optionally, be 10 mm.

Moreover, the Faraday isolator 10 may comprise a first polarizer 22 and a second polarizer 24 arranged before the multipass arrangement 18 and after the multipass

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 17/37 LU503450 arrangement 18, respectively. The first and second polarizer 22 and 24 may be part of the polarization rotation device 12 or form separate parts of the Faraday isolator 10 not belonging to the polarization rotation device 12. The first polarizer 22 may provide the laser radiation 14 with a predetermined polarization, in particular a linear polarization having a predetermined direction, prior to coupling the laser radiation 14 into the polarization rotation device 12. The first polarizer 22 may be provided as a Glan-Taylor polarizer. The second polarizer 24 may be adjusted to transmit only such parts of the laser radiation 14 which has undergone a polarization rotation by a predetermined angle in the polarization rotation device 12. Possible other components which did not undergo the polarization rotation by the predetermined rotation angle are blocked by the second polarizer 24. The

Faraday isolator 10 according to the presented embodiment ensures that laser radiation traveling in the counter direction, as for example back reflections of the laser radiation 14, are blocked and hindered from reaching optical components arranged before the Faraday isolator 10.

Moreover, the Faraday isolator 10 may comprise various optical components, such as mirrors 26, for directing and possibly folding the beam of laser radiation 14 and for assisting in coupling the laser radiation 14 into the multipass arrangement 18 and out of the multipass arrangement 18.

Furthermore, Figure 1 depicts a laser source 28 providing the laser radiation 14.

However, the laser source 28 does not necessarily form a part of the Faraday isolator 10. The Faraday isolator 10 may be used with any kind of laser radiation 14 provided by any kind of source. The Faraday isolator 10 may be adapted to a design wavelength corresponding to the central wavelength of the laser radiation 14.

The multipass arrangement 18 may consist of or comprise a Herriott cell 30 comprising a first mirror 32 and a second mirror 34. Both the first and second mirror 32, 34 may be provided as concave mirrors, or as a combination of a concave mirror and a convex mirror or a concave mirror and a flat mirror.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 18/37 LU503450

The polarization rotation device 12 may be adapted such that the laser radiation 14 carries out at least five passes through the Faraday medium 18.

The Faraday medium 16 may have a Verdet constant of 20 rad/(T-m) or less at a predetermined design wavelength of the polarization rotation device 12. The

Faraday medium 16 may comprise a solid Faraday element, wherein the polarization rotation device 12 may be adapted such that in each pass through the solid Faraday element the laser radiation 14 enters the Faraday element at a different surface of the solid Faraday element than the surface, at which the laser radiation 14 exits the solid Faraday element.

The solid Faraday element may consist of or comprises at least one of the following materials: fused silica, quartz, MgF2, CaF», Al-Os (Sapphire), YAG,

GdsAlsO12, KBr, ZnS, ZnSe, and ZnTe.

Alternatively or additionally, the Faraday medium 16 may comprise a gaseous

Faraday medium 16. The gaseous Faraday medium 16 may consist of or comprise at least one of the following gases: He, Ne, Ar, Kr, Xe, Hz, D2, O2, N2, CO», and

CHa.

The Faraday medium 16 may comprise multiple solid Faraday elements and/or a mixture of different gases. The Faraday medium may optionally comprise at least one solid Faraday element and a gaseous Faraday medium.

The polarization rotation device may further comprise a pressure cell 36 containing the gaseous Faraday medium 16, wherein the multipass arrangement 18 is arranged at least partly inside the pressure cell 36. Alternatively, the pressure cell 36 may be integrated into the multipass arrangement 18. The Verdet constant of the gaseous Faraday medium 16 and, hence, a quantity of the Faraday effect experienced by laser radiation propagating through the gaseous Faraday medium

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 19/37 LU503450 16, may be adjusted by adjusting the pressure of the gaseous Faraday medium in the pressure cell.

The magnetic element 20 may comprise or consist of a permanent magnet, wherein the permanent magnet may be ring-shaped and adapted to provide a magnetic field along a central axis of the ring-shaped permanent magnet. The central axis of the ring-shaped permanent magnet may be parallel and optionally coinciding with the central axis 100 of the multipass arrangement 18. The ring- shaped permanent magnet may surround at least partly the Faraday medium 16 within the multipass arrangement 18.

The Faraday medium 16 may offer an optical transmission of 80% or more throughout a spectral range from 150 nm to 550 nm. The polarization rotation device 12 may be adapted to rotate the polarization direction of the laser radiation 14 by an angle in a range from 30° to 60° between coupling the laser radiation 14 into the multipass arrangement 18 and coupling the laser radiation 14 out of the multipass arrangement 18.

Accordingly, the Faraday isolator 10 may be adapted to rotate the polarization direction of a laser radiation 14 coupled into the Faraday isolator 10 by an angle in a range from 30° to 60° and in particular by an angle of 45°.

The Faraday isolator 10 may comprise a cascaded arrangement of multiple polarization rotation devices 12. This may allow for dividing the total desired rotation of the polarization angle.

In the following, further optional features of a Faraday isolator 10, according to an optional embodiment as presented in Figure 1, will be described, without the disclosure and embodiment being limited to said details.

Generally, Faraday media having a low absorption, lower thermal expansion, and a low thermo-optic coefficient are desired, in order to ensure low depolarization

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 20/37 LU503450 due to temperature gradients. At a wavelength of 1 um, quartz or fused silica offer a low absorption coefficient, up to two orders of magnitude lower than TGG, and also a slightly lower thermo-optic coefficient than TGG as presented in Table 1.

Popes [168 ae [Woh

Verdet 39 1,1 2,4 constant (1.064 nm) | (1064 nm, silica fiber) | (633 nm) (rad/(T-m)) 5,5 4.6 (515 nm, fused silica) | (458 nm) 7,0 (458 nm, fused silica)

Absorption 0,7—1,5 ca. 0,02 coefficient (1 um) (1 um, fused silica) <1/10 (103 cm”) (0o./un-pol., 290 nm)? <1/26 (o./un-pol., 220 nm)? 13/56 (0./un-pol., 200 nm)?

Thermal con- | 4,5 6,2/10,4 30 / 21 ductivity at (a/c-axis) (a/c-axis) 300 K (Wi(m-K))

Thermal ex- | 7,3 12,4/6,9 9,4 / 13,6 pansion at (a/c-axis) (a/c-axis) 300 K (ppm/K)

Thermo-optic | 17,9 ca. -8 1,1/0,6 coefficient at | (633 nm) (1 pm) (o/e-ray, 633 nm)” 300 K -6,2/7,0 0,9 (ppm/K) (546 nm) (458 nm) a) polarization normal to optical axis, i.e. ordinarily ray (0.), or unpolarized (un-pol.) b) ordinary (0) or extraordinary (e) ray

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 21/37 LU503450

The values presented in Table 1 are taken from the following publications:

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising Materials for High Power Laser Isolators,” LTJ 13, 18-21 (2016). . L. Snetkov, A. V. Voitovich, O. V. Palashov, and E. A. Khazanov, “Review of Faraday Isolators for Kilowatt Average Power Lasers,” IEEE J.

Quantum Electron. 50, 434—443 (2014).

M. J. Weber, Handbook of Optical Materials (CRC Press, 2018).

S. Asraf, Y. Sintov, and Z. Zalevsky, “Novel configuration for an enhanced and compact all-fiber Faraday rotator with matched birefringence,” Optics express 25, 18643-18655 (2017).

J. L. Cruz, M. V. Andres, and M. A. Hernandez, “Faraday effect in standard optical fibers: dispersion of the effective Verdet constant,”

Applied optics 35, 922-927 (1996).

E. Munin, J. A. Roversi, and A. B. Villaverde, “Faraday effect and energy gap in optical materials,” Journal of Physics D: Applied Physics 25, 1635— 1639 (1992).

E. Munin, C. B. Pedroso, and A. B. Villaverde, “Magneto-optical constants of fluoride optical crystals and other AB2 and A2B type compounds,”

Faraday Trans. 92, 2753 (1996).

T. C. Rich and D. A. Pinnow, “Total Optical Attenuation in Bulk Fused

Silica,” Appl. Phys. Lett. 20, 264-266 (1972).

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 22/37 LU503450

G. A. Slack and D. W. Oliver, “Thermal Conductivity of Garnets and

Phonon Scattering by Rare-Earth Ions,” Phys. Rev. B 4, 592-609 (1971).

R. Yasuhara, H. Nozawa, T. Yanagitani, S. Motokoshi, and J. Kawanaka, “Temperature dependence of thermo-optic effects of single-crystal and ceramic TGG,” Optics express 21, 31443-31452 (2013).

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” Journal of Physics D: Applied

Physics 16, L97-L100 (1983).

D. L. Steinmetz, W. G. Phillips, M. Wirick, and F. F. Forbes, “A polarizer for the vacuum ultraviolet,” Applied optics 6, 1001-1004 (1967).

Due to a comparably moderate Verdet constant of quartz and fused silica when compared to TGG, quartz and fused silica are conventionally often considered as impractical for a use in conventional Faraday isolators. However, already at a wavelength of 1 um the low absorption of quartz and fused silica, as compared to

TGG, may already partly compensate for the increased propagation length in terms of power limitation due to depolarization. In the visible to ultraviolet (UV) spectral range, TGG suffers increasingly from absorption due to color centers and therefore from enhanced thermal degradation. Other materials are desired as

Faraday materials in these spectral ranges. Faraday isolators at 405 nm and 355 nm have been already demonstrated based on Cerium(lll) fluoride (CeF3 (see

E. G Villora, K. Shimamura, and G. R. Plaza, “Ultraviolet-visible optical isolators based on CeF3 Faraday rotator,” Journal of Applied Physics 117, 233101 (2015)), which enables transmission down to 300 nm (see P. Molina, V. Vasyliev, E. G.

Villora, and K. Shimamura, “CeF3 and PrF3 as UV-visible Faraday rotators,” Optics express 19, 11786-11791 (2011)). For the UV range down to 200 nm PrF3 was presented as a potential Faraday medium with high Verdet constant (see P.

Molina, V. Vasyliev, E. G. Villora, and K. Shimamura, “CeFs and PrF3 as UV- visible Faraday rotators,” Optics express 19, 11786-11791 (2011)). On the other

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 23/37 LU503450 hand, materials like quartz and Magnesium fluoride (MgF2) are readily available and offer a similar transmission range down to about 200 nm. As the latter two materials suffer from lower Verdet constants, they may be used as a Faraday medium inside a Faraday isolator employing multiple passes through the medium.

Additionally, MgF2 exhibits a one order of magnitude lower thermo-optic coefficient than TGG and quartz, which could reduce thermal effects (see M. J.

Weber, Handbook of Optical Materials (CRC Press, 2018); and D. L. Steinmetz,

W. G. Phillips, M. Wirick, and F. F. Forbes, “A polarizer for the vacuum ultraviolet,”

Applied optics 6, 1001-1004 (1967).

In the following, we will discuss various aspects of using Faraday media with low

Verdet constants and present an approach enabling sufficient polarization rotation angles for Faraday isolators based on such materials having lower Verdet constants compared to TGG or other conventionally used Faraday media.

Moreover, the applicability of this approach to gases as Faraday media will be discussed, which could be beneficial when operating higher average powers, even though gases often exhibit even lower Verdet constants (see L. R. Ingersoll and D.

H. Liebenberg, “The Faraday Effect in Gases and Vapors I*,” J. Opt. Soc. Am. 44, 566 (1954); and L. R. Ingersoll and D. H. Liebenberg, “Faraday Effect in Gases and Vapors II*,” J. Opt. Soc. Am. 46, 538 (1956).

To achieve a polarization rotation on the order of 45° in materials with lower

Verdet constants compared to TGG, such as quartz and fused silica, magnetic fields with extraordinarily high flux densities may be applied to the material and/or the propagation length of the laser radiation in the Faraday medium may be increased drastically. The magnetic flux density provided by permanent neodymium magnets is typically on the order of magnitude of 1 T. Taking this as a practical limitation for the magnetic field, it becomes necessary to increase the propagation lengths to tens of centimeters if not several meters.

Following such an approach would come with the additional challenge of applying a magnetic field over such a long path. In an optional case, the Faraday medium

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 24/37 LU503450 may be surrounded by a ring-shaped permanent magnet. Increasing just the length of the ring magnet along with the length of the medium would lead to a reduced and possibly almost vanishing field inside the magnet, which is due to the inversion of the field direction in the far field of a magnetic dipole, as shown in

Figure 2.

Figure 2 shows on the left-hand side a simulation of the qualitative distribution of a magnetic flux density Bz in z-direction, i. e. in the direction along the central axis 302 of the permanent magnet 300, generated by a ring-shaped permanent magnet 300 (in a sectional view through a plane including the central axis) having a length along the central axis 302 of 20 mm. The right-hand side shows a respective simulation of the magnetic flux density Bz in z-direction generated by a ring- shaped permanent magnet 304 having a length of 80 mm.

To provide a suitable field strength for Faraday rotation, the diameter of the ring- shaped permanent magnet may be scaled by the same order of magnitude as its length. Permanent magnets with the resulting dimensions tend to be rather big and, thus, impractical for an implementation in many optical setups. On the other hand, electromagnets, i.e., solenoids, can in principle be scaled to the required lengths without sacrificing magnetic field inside. However, driving currents of several amperes would have to be supplied constantly. Unless sophisticated cooling mechanisms are applied, the magnetic field strength would be typically below that obtained with permanent magnets. In addition, current fluctuations are directly translated into fluctuations of the resulting polarization rotation. A polarization rotation device, as required in Faraday rotators, based on such a conventional approach would translate these fluctuations into amplitude noise.

Furthermore, polarization rotation fluctuations would lead to a degraded isolation performance in Faraday isolators. This makes it necessary to supply a sufficiently stable current when the setup is sensitive to noise or small back reflections.

The extended path length necessary when using Faraday media with low Verdet constants could be realized with optical fibers when considering fused silica as a

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 25/37 LU503450 medium. Faraday rotation of several degrees has been demonstrated inside a fused silica fiber rolled up multiple times through the magnetic field of solenoids (see S. Asraf, Y. Sintov, and Z. Zalevsky, “Novel configuration for an enhanced and compact all-fiber Faraday rotator with matched birefringence,” Optics express 25, 18643-18655 (2017)). Here, bend-induced birefringence in the optical fiber needs to be compensated to first of all still ensure a constructive buildup of

Faraday rotation after the polarization flips due to the birefringence (see G. W.

Day, D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, “Faraday rotation in coiled, monomode optical fibers: isolators, filters, and magnetic sensors,” Optics letters 7, 238 (1982)). Furthermore, small amounts of uncompensated birefringence generally lead to an elliptical polarization, which limits the isolation performance of the Faraday isolator. However, coupling into single mode fibers makes this approach challenging to use with powerful free-space laser beams.

Therefore, the disclosure provides an approach based on free-space optics to produce enhanced Faraday rotation in media with low Verdet constants for the potential use in Faraday isolators 10 as shown in Figure 1. For this approach, the

Faraday medium 16 is placed inside a multipass arrangement 18. The effective path length of the laser radiation 14 inside the Faraday medium 18 is increased to the desired amount by guiding the laser radiation 14 several times through the employed Faraday medium 14. In the case of solid Faraday media, the length of the Faraday medium 16 itself stays within several cm or even mm. For gases used as Faraday medium 16, longer distances or more passes may be appropriate. The desired amount of passes can be achieved at moderate level of complexity in a

Herriott cell (see Y. Wang, M. Nikodem, B. Brumfield, and G. Wysocki, “Compact multi-pass cell based Faraday rotation spectrometer for nitric oxide detection,” in 2012 Conference on Lasers and Electro-Optics (CLEO) (2012), pp. 1-2; H.

Adams, D. Reinert, P. Kalkert, and W. Urban, “A differential detection scheme for

Faraday rotation spectroscopy with a color center laser,” Appl. Phys. B 34, 179- 185 (1984); and D. Herriott, H. Kogelnik, and R. Kompfner, “Off-Axis Paths in

Spherical Mirror Interferometers,” Appl. Opt. 3, 523 (1964)). The multipassing approach according to the disclosure does not only reduce the requirement for the

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 26/37 LU503450 length of the Faraday medium 16, but it limits in the same way the area where a magnetic field has to be applied. Thereby, standard size systems of permanent ring magnets can be employed, simplifying the setup even further. As a proof of concept, we demonstrate in the following, employing a Herriott cell, a Faraday isolator 10 providing a polarization rotation with an angle of 22° inside a 6,35 mm long fused silica plate, as an example for a low Verdet constant Faraday medium 16, at the center of the visible range with a 532 nm alignment laser.

The Faraday isolator may be configured as schematically presented in Figure 1.

As a Faraday medium 16, an anti-reflection-coated fused silica plate with a length of 6,35 mm and a diameter of 12,7 mm is mounted onto the inside of a ring- shaped permanent magnet used as magnetic element 20 providing a mostly uniform magnetic field pointing in the direction of the surface normal of the plate.

Special care is taken during mounting to avoid any stress induced birefringence

Inside the fused silica plate. Even the slightest pressure on the plate could lead to significant disturbance of the resulting polarization rotation. The magnet is a neodymium magnet of the type N52. It has a length of 20 mm, an inner diameter of mm, and an outer diameter of 40 mm. A magnetic flux density of about 0,3 T was measured inside the magnet. The Herriott-cell-type multipass arrangement 18 20 Is built around the fused silica plate serving as Faraday medium 16 to propagate the laser radiation 42 times through the Faraday medium 16. This corresponds to an effective path length in the Faraday medium of 267 mm. The multipass arrangement comprises two 1-inch diameter concave spherical mirrors 32 and 34 with a radius of curvature (ROC) of 150 mm and 100 mm, respectively. The spacing between the first mirror 32 and the second mirror 34 along the central axis 100 of the multipass arrangement 18 was about 250 mm and precisely adjusted for alignment of the multipass arrangement 18. The laser radiation 14 was coupled into the multipass arrangement 18 via a hole in the second mirror 34. The beam was focused into the multipass arrangement 18 by another concave spherical

Mirror 26 with a ROC of 600 mm. Thereby, the ROC values of the mirrors 32, 34 and 26 were chosen to roughly match the eigenmode of the cell to the caustic of the incident laser radiation 14 with a central wavelength of 532 nm and a mode

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 27137 LU503450 radius of about 1.9 mm at its output. A clean linear polarization was ensured by placing a Glan-Taylor polarizer 22 before the multipass arrangement. The laser power after the polarizer was about 0.6 mW. The laser radiation 14 exiting the multipass arrangement 18 was collimated by the mirror 26. Incoming and exiting beams are separated by a spacing of a few millimeters. The polarization of the exiting laser radiation 14 was checked with an analyzing polarizer 24, which can be rotated around the propagation direction of the laser radiation 14. Here a

Wollaston polarizer used as second polarizer 34, or a second polarizer enables simple access to both beams with orthogonal polarization.

To measure the resulting polarization after the multipass arrangement 18, the analyzing polarizer 24 was rotated around the beam axis to minimize the power of one of the beams separated by the polarizer 24. For 42 passes through the

Faraday medium a polarization rotation of 22° was observed. The polarization rotation can be clearly attributed to Faraday rotation when the direction of the magnetic field is inverted. As expected, the polarization is rotated by 22° in the opposite direction, thus ruling out other potential causes like stress induced birefringence. Furthermore, the observed rotation of 22° agrees well with the expectation when the literature value for the Verdet constant of about 5 rad/(T-m) is taken as the basis for the calculation (see J. L. Cruz, M. V. Andres, and M. A.

Hernandez, “Faraday effect in standard optical fibers: dispersion of the effective

Verdet constant,” Applied optics 35, 922-927 (1996); and E. Munin, J. A. Roversi, and A. B. Villaverde, “Faraday effect and energy gap in optical materials,” Journal of Physics D: Applied Physics 25, 1635-1639 (1992)).

For high isolation performance of a Faraday isolator 10, it is necessary that the polarization of the laser radiation 14 with the rotated polarization stays linear.

Otherwise, the isolation performance may be reduced. We investigated the degree of linear polarization after the Faraday isolator 10 by measuring both powers of the orthogonally polarized beams of the laser radiation 14 after the analyzing polarizer 24. Therefore, the power in one of the beams is again minimized. The depolarization is characterized by the ratio y of the depolarized power, which is still

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 28/37 LU503450 in the minimized beam of the analyzing polarizer, to the total power of both beams from the analyzing polarizer 24:

After a polarization rotation of 22°, depolarization ratios y of 1:90 to 1:40 were measured. When the magnet is removed but the Faraday medium 16 is kept in place a depolarization y of < 1:450 was measured, which was limited by the measurement sensitivity. These results give an indication that the beam gets elliptically polarized during the Faraday rotation, whereas it stays perfectly linearly polarized when passing the cell without the magnetic field.

The results demonstrate clearly how the Faraday rotation inside Faraday medium 16 with low Verdet constants like fused silica can be scaled up inside a multipass arrangement 18, such as a Herriott cell. Employing a simple AR-coated plate of fused silica with a thickness of 6,35 mm as solid Faraday medium 16 resulted in a rotation angle of 22° at a wavelength of 532 nm. The angle of 45°, as often required for Faraday isolators 10, will be easily reached by increasing the thickness of the material by a factor of two. The required thickness of the Faraday medium 16 may even reduce when going to the ultraviolet spectral range due to an increasing Verdet constant at shorter wavelengths for many materials used as

Faraday medium 16. In the UV-vis range, fused silica, quartz and MgF2 might be promising candidates for the use in a Faraday isolator 10 when used in combination with a simple Herriott cell as multipass arrangement 18. When going towards a wavelength of 1 um, further scaling may be advantageous. Employing a stronger magnetic field with permanent magnets, like in state of the art Faraday isolators, will provide much stronger fields of about 2-3 T (see E. A. Mironov, A. V.

Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of more than 3 tesla,” Laser Phys. Lett. 17, 15001 (2020); |. Mukhin, A.

Voitovich, O. Palashov, and E. Khazanov, “2.1 Tesla permanent-magnet Faraday isolator for subkilowatt average power lasers,” Optics Communications 282, 1969— 1972 (2009); G. Trénec, W. Volondat, O. Cugat, and J. Vigué, “Permanent

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 29/37 LU503450 magnets for Faraday rotators inspired by the design of the magic sphere,” Applied optics 50, 4788-4797 (2011); and E. A. Mironov, |. L. Snetkov, A. V. Voitovich, and O. V. Palashov, “Permanent-magnet Faraday isolator with the field intensity of 25 kOe” Quantum Electron. 43, 740-743 (2013)), which should be sufficient to reach the desired rotation at a wavelength of 1 um with fused silica or quartz.

Further scaling potential lies in the number of passes. For a Herriott cell used as multipass arrangement 18, the number passes scale linearly with the diameter of the mirrors 32 and 34 of the multipass arrangement. Increasing the mirror diameter of the first mirror 32 and the second mirror 34 from 1 inch to 2 inches would imply another scaling factor of two. By these means, it appears to be within reach to realize a Faraday isolator with crystalline quartz used as Faraday medium 16 for high power lasers at a wavelength of 1 um. At high powers the thermal lens appearing within the Faraday medium can be easily compensated by adjusting the distance of the first and second mirror 32, 34 of the multipass arrangement 18.

Going further into the mid-IR region, Verdet constants are dropping even more.

Here again, the multipass approach using a Herriott cell could be employed to enable Faraday isolators 10 at wavelengths of several um with materials with

Verdet constants being insufficient for their use in conventional Faraday isolators.

For example, ZnSe, which transmits wavelengths up to 20 um has a Verdet constant of about only 8 rad/(T-m) at a wavelength of already 2 um (see E. A.

Mironov, O. V. Palashov, |. L. Snetkov, and S. S. Balabanov, “ZnSe-based

Faraday isolator for high-power mid-IR lasers,” Laser Phys. Lett. 17, 125801 (2020)). A Faraday isolator based on ZnSe proved already to be technically challenging, involving extremely strong magnetic fields and the cascading of two

Faraday rotators. Employing the multipassing approach with a Herriott cell could reduce the demand for high magnetic field and the length of a ZnSe rod used as solid Faraday element. Moreover, this approach allows the use of ZnSe as a

Faraday medium at much longer wavelengths where the Verdet constant is even lower.

When using quartz as Faraday medium 18, the birefringence of crystalline quartz has to be taken into careful consideration. However, a plate of c-cut quartz may be

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 30/37 LU503450 used and the c-axis is oriented parallel to the beam propagation direction. Though, inside the Herriott cell the angle of incidence on the plate is always deviating from perpendicular incidence. The angle can be minimized by considering long cells to minimize the effect of birefringence. Another approach would be to employ a pair of a-cut plates with orthogonal c-axes to compensate the birefringence. The same considerations apply to MgF2, as it shows similar birefringence.

When increasing the average power of the laser radiation 14 passing through a

Faraday isolator 10, eventually absorption and thermally induced birefringence may limit the isolation performance of a Faraday isolator. The use of gases as

Faraday medium 16 may be a potential way to circumvent the typical limitations arising in solids. Even though very low Verdet constants (compared to TGG) become more challenging here, multipassing inside a multipass arrangement 18 could help to overcome this obstacle. As a gas, Xenon still has a relatively high

Verdet constant of 18-107 rad/(T-m-bar) at 500 nm. To increase the effect, the whole isolator can be built up in a pressurized gas cell (referred to as pressure cell). Considering a pressure of 20 bar, this would lead to a Verdet constant of about 0.35 rad/(T-m), still an order of magnitude lower than in fused silica. This deficiency may be compensated with a longer propagation length inside the medium. Extending the length of the gas cell leads to the challenge to provide a magnetic field with sufficient flux density over the entire length of the pressure cell.

It turns out that simply extending the length of a given permanent ring magnet will result in a diminishing magnetic field within the magnet, as illustrated in Figure 2.

The underlying reason here may be the reversal of the magnetic field direction for a magnetic dipole, leading to destructive field components inside the ring magnet.

The field may be restored by increasing the outer diameter of the ring magnet. The field of a hypothetical magnet still within practical dimensions is depicted in Figure 3. Figure 3 shows on the left-hand side a visualization of a simulation of the magnetic flux density in z-direction in a magnet with a length of 200 mm. The right- hand side shows in a graph the magnetic flux density in z-direction over the z- coordinate, i. e. along the central axis of the magnet.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 31/37 LU503450

Here, the relevant parameter for the Faraday rotation is the field integrated over the beam path. For this magnet a value of 66 MT -m was calculated. With 20 bar of

Xenon and 35 passes, a rotation angle of 45° is resulting at a wavelength of 500 nm. In the UV range even smaller magnets with weaker fields can be applied due to the increasing Verdet constant. This clearly shows the feasibility of a

Faraday isolator 10 based on a gas as Faraday medium 16.

In summary, we presented a method to enable the use of materials with moderate

Faraday effect, i. e. low Verdet constants, as a Faraday medium 16 in a Faraday isolator 10. Guiding the incident laser radiation 14 several times through the

Faraday medium 16 in a multipass arrangement 18 leads to a cumulation of the

Faraday rotation angles from all passes due to the nonreciprocal nature of the

Faraday effect. The desired rotation angle of 45° can be principally reached with materials otherwise non-applicable in conventional Faraday isolator schemes.

Thereby, materials, e. g. crystalline quartz, fused silica, or magnesium fluoride become of interest for potential applications in ultraviolet, mid-infrared and high power Faraday isolators 10. Even gases can be used, which might turn out beneficial in avoiding limiting effects normally appearing in solids, like thermal lensing and/or stress induced birefringence. In a proof-of-principle experiment we demonstrated the applicability of the concept. The polarization of a 532 nm alignment laser has been rotated by an angle of 22° in a fused silica plate with the help of a Herriott-type multipass cell. Further scaling is possible by increasing the number of passes, the strength of the magnetic field, or just the length of the

Faraday medium 16.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 32/37 LU503450

List of reference signs 10 Faraday isolator 12 polarization rotation device 14 laser radiation 16 Faraday medium 18 multipass arrangement 20 magnetic element 22 first polarizer 24 second polarizer 26 optical element / mirror 28 laser source 30 Herriott cell 32 first mirror 34 second mirror 36 pressure cell 100 central axis of multipass arrangement 300 permanent magnet 302 central axis of permanent magnet 304 permanent magnet

Claims (21)

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 33/37 LU503450 Claims

1. Polarization rotation device (12) suitable to rotate a polarization direction of a laser radiation (14), the polarization rotation device (12) comprising: - a Faraday medium (16); - a multipass arrangement (18) having the Faraday medium (16) arranged at least partly within the multipass arrangement (18), wherein the multipass arrangement (18) is adapted such that the laser radiation (14) carries out multiple roundtrips in the multipass arrangement (18) and multiple passes through the Faraday medium (16) when coupled into the multipass arrangement (18); - a magnetic element (20) suitable to provide a magnetic field at the position of the Faraday medium (16) inside the multipass arrangement (18); characterized in that the Faraday medium (16) has a thickness, through which the laser radiation (14) propagates at each of the multiple passes, of 2 mm or more.

2. Polarization rotation device (12) according to claim 1, wherein the multipass arrangement (18) consists of or comprises a Herriott cell (30).

3. Polarization rotation device (12) according to claim 1 or 2, wherein the polarization rotation device (12) is adapted such that the laser radiation (14) carries out at least five passes through the Faraday medium (16).

4. Polarization rotation device (12) according to any one of the preceding claims, wherein the Faraday medium (16) has a Verdet constant of 20 rad/(T-m) or less at a predetermined design wavelength of the polarization rotation device (12).

5. Polarization rotation device (12) according to any one of the preceding claims, wherein the Faraday medium (16) comprises a solid Faraday element (16).

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 34/37 LU503450

6. Polarization rotation device (12) according to claim 5, wherein the polarization rotation device (12) is adapted such that in each pass through the solid Faraday element the laser radiation (14) enters the Faraday element at a different surface of the solid Faraday element than the surface, at which the laser radiation exits the solid Faraday element.

7. Polarization rotation device (12) according to claim 5 or 6, wherein the solid Faraday element consists of or comprises at least one of the following materials: fused silica, quartz, MgF2, CaF», Al2O3 (sapphire), YAG, Gds3AlsO12, KBr, ZnS, ZnSe, and ZnTe.

8. Polarization rotation device (12) according to any of the preceding claims, wherein the Faraday medium (16) comprises a gaseous Faraday medium.

9. Polarization rotation device (12) according to claim 8, wherein the gaseous Faraday medium consists of or comprises at least one of the following gases: He, Ne, Ar, Kr, Xe, Hz, D2, O2, N2, CO», and CHa.

10. Polarization rotation device (12) according to claim 8 or 9, further comprising a pressure cell (36) containing the gaseous Faraday medium, wherein the multipass arrangement (18) is arranged at least partly inside the pressure cell (36).

11. Polarization rotation device (12) according to any of the preceding claims, wherein the magnetic element (20) comprises or consists of a permanent magnet (300).

12. Polarization rotation device (12) according to claim 11, wherein the permanent magnet (300) is ring-shaped and adapted to provide a magnetic field along a central axis (302) of the ring-shaped permanent magnet (300), and wherein the ring-shaped permanent magnet (300) surrounds the Faraday medium (16) at least partially within the multipass arrangement (18).

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 35/37 LU503450

13. Polarization rotation device (12) according to any one of the preceding claims, further comprising a first linear polarizer (22) arranged before the multipass arrangement (18) and/or a second linear polarizer (24) arranged after the multipass arrangement (18).

14. Polarization rotation device (12) according to any one of the preceding claims, wherein the Faraday medium (16) offers an optical transmission of 80% or more throughout a spectral range from 150 nm to 550 nm.

15. Polarization rotation device (12) according to any one of the preceding claims, wherein polarization rotation device (12) is adapted to rotate the polarization direction of the laser radiation (14) by an angle in a range from 30° to 60° between coupling the laser radiation (14) into the multipass arrangement (18) and coupling the laser radiation (14) out of the multipass arrangement (18).

16. Polarization rotation device (12) according to any one of the preceding claims, wherein the Faraday medium (16) comprises multiple solid Faraday elements and/or a mixture of different gases.

17. Polarization rotation device (12) according to any one of the preceding claims, wherein the Faraday medium (16) comprises at least one solid Faraday element and a gaseous Faraday medium (16).

18. Faraday isolator (10) comprising a polarization rotation device (12) according to any one of the preceding claims.

19. Faraday isolator (10) according to claim 18, wherein the Faraday isolator (10) is adapted to rotate the polarization direction of the laser radiation by an angle in arange from 30° to 60°.

Tautz & Schuhmacher IP TUT1105P11LU February 7, 2023 36/37 LU503450

20. Faraday isolator (10) according to claim 18, wherein the Faraday isolator (10) is adapted to rotate the polarization direction of the laser radiation (14) by an angle of 45°.

21. Faraday isolator (10) according to any one of claims 18 to 20, wherein the Faraday isolator (10) comprises a cascaded arrangement of multiple polarization rotation devices (12) according to any one of the claims 1 to 17.