Faraday Rotators

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

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Definition: devices which can rotate the polarization state of light, exploiting the Faraday effect

Categories: general optics, photonic devices

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DOI: 10./s6z   Cite the article: BibTex plain textHTML   Link to this page!   LinkedIn

A Faraday rotator is a magneto-optic device, where the linear polarization direction of light propagating through a transparent optical medium is continuously rotated. That rotation is caused by a magnetic field to which the medium is exposed. The magnetic field lines have approximately the same direction as the beam direction, or the opposite direction.

Polarization Rotation Angle; Verdet Constant

The total rotation angle ($\beta$) can be calculated as

$$\beta = V\;B\;L$$

where ($V$) is the Verdet constant of the material, ($B$) is the magnetic flux density (in the direction of propagation), and ($L$) is the length of the rotator medium. Note that the Verdet “constant” usually exhibits a substantial wavelength dependence: It is smaller for longer wavelengths.

Non-reciprocal Behavior

The change in polarization direction is defined only by the magnetic field direction and the sign of the Verdet constant. If some linearly polarized beam is sent through a Faraday rotator and back again after reflection at a mirror, the polarization changes in the two passes add up, rather than canceling each other. This non-reciprocal behavior distinguishes Faraday rotators from various other optical devices with reciprocal behavior. For example, a waveplate may also rotate a polarization direction, but on the backward path (after reflection on a mirror), the polarization change would be reversed.

Effect on Circular Polarization

Concerning the physical origin of the polarization rotation, one may consider a linearly polarized beam as a superposition of two circularly polarized beams. The magnetic field causes a difference in phase velocity between these circularly polarized components, i.e., an induced circular birefringence. The resulting relative phase shift corresponds to a change in the linear polarization direction.

Construction Details of Faraday Rotators

Requirements on Magnets

The magnetic field is usually generated with an assembly of permanent magnets and ferromagnetic materials, which is optimized such that the following goals are achieved to some extent:

• The field strength should be as high as possible, such that a certain rotation angle (e.g. 45°) can be achieved with a short rotator medium. This reduces detrimental effects related to parasitic absorption (and the resulting thermal effects) and to nonlinearities of the medium.
• The magnetic flux density should be as uniform as possible over the region where light is sent through the medium. In that way, a spatially uniform rotation angle is achieved, as required e.g. to achieve high isolation of Faraday isolators.

These goals involve certain design trade-offs. In particular, a larger geometric cross-section with good field homogeneity tends to require stronger and bigger magnets or to reduce the achievable field strength. For such reasons, devices are optimized for different purposes. There are heavy and expensive high-power devices with a large aperture as well as much cheaper miniature devices for low power levels.

Magneto-optic Materials

Apart from a high Verdet constant, the Faraday medium should exhibit a high transparency in the spectral region of interest, a high optical quality, and sometimes also a high optical damage threshold. Besides, birefringence is unwanted. Different materials can be used:

• Often used Faraday media for the near-infrared spectral region are terbium–gallium garnet crystals (TGG), having high Verdet constants. For -nm YAG lasers and vanadate lasers, for example, this is a natural choice.
• Terbium-doped borosilicate glass can be fabricated more flexibly and at lower cost (particularly for large sizes complicated shapes), but exhibit lower Verdet constants and lower thermal conductivity.
• Bismuth-substituted iron garnets (BIG) are principal materials for Faraday rotators in telecommunications, especially around the 1.3–1.5-μm telecom spectral region. For example, one may start with YIG = yttrium iron garnet, Y3Fe5O12) and substitute some of the Y3+ ions with Bi3+ ions to obtain BixY3-xFe5O12 (e.g. with ($x$) = 1). BIG thick films, grown with liquid phase expitaxy, offer high specific Faraday rotation, good transparency for low insertion loss. They are available in several specialized compositions optimized for different operational requirements, e.g. with a focus on low losses or low temperature dependence. As BIG materials are strong ferrimagnets, exhibiting spontaneous magnetization, there are even “latching” devices which do not require an external bias magnet.
• It is also possible to replace some of the iron in BIG with gallium, leading to bismuth iron gallium garnet (BIGG). This can be used to extend the transparency range, but is not common.
• Gadolinium gallium garnet (Gd3Ga5O12) or substituted variants (e.g., SGGG) can be used at cryogenic temperatures.

High Power Operation

For operation with high optical average powers, parasitic absorption in a Faraday rotator can lead to substantial internal heating and consequently to thermal beam distortions. In particular, thermal lensing can occur. Both the power-dependence and the significant optical aberrations of the thermal lens can be very disturbing. A high thermal conductivity helps to reduce temperature gradients.

Additional aspects of high-power operation are discussed in the article on Faraday isolators.

Anti-reflection Coatings

In most cases, reflection losses on the input and output surface of a Faraday rotator are minimized with anti-reflection coatings, designed for the intended range of operation wavelengths. The often high refractive index of these materials makes this particularly important.

The operation bandwidth may be limited by the coatings, but the wavelength dependence of the Verdet constant is another factor.

Tunable Faraday Rotators

In principle, one could make a tunable Faraday rotator by using an electromagnet instead of permanent magnets. This approach is not common, however. Instead, one can introduce a variable relative position of magnets and the Faraday medium, which also effectively leads to a variable magnet field strength. This can be useful, for example, to achieve the optimum degree of rotation for different optical wavelengths.

Applications of Faraday Rotators

Faraday rotators find many applications in laser technology:

• A particularly important application is in Faraday isolators, as needed e.g. to protect lasers and amplifiers against back-reflected light. For that application, the rotation angle should be close to 45° in the spectral region of interest. A highly uniform polarization rotation is desirable for obtaining a large attenuation for back-reflected light.

• A Faraday rotator in a ring laser resonator can be used to introduce round-trip losses which depend on the direction and thus enforce unidirectional operation. As only a very small loss difference is often sufficient, a Faraday rotator providing only a very small rotation angle may be sufficient. An additional half-waveplate may be used to compensate the polarization rotation for one beam direction.

• A 45° rotator combined with an end mirror forms a Faraday mirror. If a laser beam is sent through some amplifier (see Figure 1), then reflected at such a Faraday mirror and sent back through the amplifier, the returning beam has a polarization direction which is orthogonal to that of the input beam – even if the polarization state is not preserved within the amplifier. Therefore, a polarizer can reliably separate the counterpropagating beams.
• The latter technique can also be utilized in similar form within laser resonators of certain high-power lasers for minimizing the polarization distortions and thus depolarization loss.
• Fiber-coupled Faraday mirrors are useful e.g. in fiber-optic interferometers and certain fiber lasers.

A variant of isolators are Faraday circulators, having three optical ports.

Related Articles

Suppliers

The RP Photonics Buyer's Guide contains 35 suppliers for Faraday rotators. Among them:

CSRayzer Optical Technology

CSRayzer offers free-space Faraday rotators with different clear aperture sizes, including diameters of 3, 5, 6, 7, 8 and 10 mm. The working wavelength can be customized, and typical operation wavelengths include 800/920/// nm, with wide adaptability. Using a high-power resistant TGG crystal, the optical pulse damage threshold can reach 10 J/cm2. The clear aperture of the Faraday rotator can be up to 30 mm.

DK Photonics

Our in-line Faraday rotator is characterized by low insertion loss, high return loss, high extinction ratio and excellent environmental stability and reliability. It is available with fiber input and output. It is ideal for polarization-maintaining fiber amplifiers, fiber lasers, and high-speed communication systems and instrumentation applications.

Bibliography

[1]R. H. Stolen and E. H. Turner, “Faraday rotation in highly birefringent optical fibers”, Appl. Opt. 19 (6), 842 (), [DOI:10./AO.19.] [2]D. S. Zheleznov et al., “Faraday rotators with short magneto-optical elements for 50-kW laser power”, IEEE J. Quantum Electron. 43 (6), 451 (), [DOI:10./JQE..] [3]L. Sun et al., “Compact all-fiber optical Faraday components using 65-wt%-terbium-doped fiber with a record Verdet constant of −32 rad/(Tm)”, Opt. Express 18 (12), (); https://doi.org/10./OE.18. [4]E. A. Mironov, O. V. Palshov and S. S. Balabanov, “High-purity CVD-ZnSe polycrystal as a magneto-active medium for a multikilowatt Faraday isolator”, Opt. Lett. 46 (9), (); https://doi.org/10./OL. [5]J. G. Meyer et al., “Multipass Faraday rotators and isolators”, Opt. Express 32 (17), (); https://doi.org/10./OE.

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1. INTRODUCTION

Devices that rotate the polarization plane of a linearly polarized light at a selected angle are key elements of polarization state manipulation. Typically, these devices employ either the magneto-optic effect (i.e., Faraday rotator), the birefringent effect, or total internal reflection [1–5].

The Faraday rotator is made of a magnetoactive medium that is placed inside a strong magnet. The magnetic field induces different refraction indices for the left and right circularly polarized light, and as a result, the plane of linear polarization is rotated [1–5]. However, the angle of rotation is strongly dependent on the wavelength of the light. Similarly, the polarization rotation of birefringent base instruments is substantially wavelength dependent. In contrast, Fresnel rhombs, which are designed to use total internal reflection, can operate over a wide range of wavelengths but induce optical beam displacement in the lateral direction [1–5].

It is the object of the present paper to overcome the main disadvantages of current state-of-the-art polarization rotation devices and to provide an optical scheme for rotating the polarization plane of linearly polarized light that is relatively simple, flexible, inexpensive, and easily tunable to different rotation angles. Moreover, the device can be used in either broadband or narrowband regime. Here we report an experimental demonstration of such a device, which comprises a sequence of ordinary half-wave plates rotated at specific angles with respect to their fast-polarization axes. For the broadband regime, the design is assembled according to the recent theoretical work of Rangelov and Kyoseva [6].

2. THEORY

The Jones matrix for a retarder with a phase shift φ rotated at an angle θ is conveniently parameterized in the left–right circular polarization (LR) basis as

where half- and quarter-wave plates rotated at an angle θ are described by Jθ(π) and Jθ(π/2), respectively.

A sequence of N wave plates, each with a phase shift φ and rotated at an angle θk, then realizes the total Jones matrix

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Our first goal is to design the sequence of half-wave plates such that the composite Jones matrix J(N) from Eq. (2) produces a Jones matrix of a half-wave plate that is highly robust to variations in the phase shift φ around a selected value of φ. For the broadband composite half-wave plate we require a flat rotation profile around phase shift φ=π [6], and for the narrowband composite half-wave plate we require a flat rotation profile around phase shift φ=2π. We achieve this through the use of the control parameter θk. That is, we fix one of the N rotation angles θk such that the Jones matrix J(N) from Eq. (2) is that of a half-wave plate. We use the other N−1 rotation angles to set the first (N−1)/2 nonvanishing derivatives of J(N) with respect to the phase shift φ to zero at the desired value of φ, either for broadband (BB) or narrowband (NB):

In such a manner we obtain a system of N coupled nonlinear algebraic equations for the N phases, which have multiple solutions for both broadband and narrowband conditions. Several solutions for the rotation angles θk of the individual half-wave plates for three and five composite sequences are shown in Table 1. The table shows sequences for broadband and narrowband half-wave plates, which we use for experimental realization of the polarization rotator. Then, for a given target polarization rotation angle α and a fixed number of half-wave plates N, one can find the exact values for the rotation angles θk in Table 2 of Ref. [6].

Table 1. Calculated Angles (in Degrees) of the Optical Axes of the Individual Half-Wave Plates to Implement Composite Sequences of Broadband and Narrowband Half-Wave Plates

3. EXPERIMENT

Once we have the recipes for broadband and narrowband composite half-wave plates (cf. Table 1), we can experimentally construct the respective polarization rotators. It is well known [6,7] that two crossed half-wave plates realize a polarization rotator, where the angle between their fast axes is half the angle of polarization rotation. Here, we extend the idea further and utilize two crossed identical broadband or narrowband composite half-wave plates. In detail, we construct the polarization rotators as a sequence of two composite half-wave plates with angles θk from Table 1, which are crossed at an angle with respect to their fast axes. Such an arrangement rotates the polarization plane of a linearly polarized light at an angle equal to twice the angle between the optical axes of the composite half-wave plates. We use both broadband and narrowband composite half-wave plates as building blocks to realize broadband and narrowband polarization rotators, respectively.

We study the experimental properties of the composite rotators by analyzing the polarization of the transmitted light. The experimental setup, shown in Fig. 1, consists of three main parts: a source of polarized white light, a composite polarization rotator, and the light-analyzing part. A collimated beam of polarized light with a continuous spectrum was obtained using a 10 W halogen-bellaphot (Osram) lamp with a DC power supply, iris, two lenses, and a polarizer. The iris I imitates a point source of white nonpolarized light, which has been placed in the focus of the first lens L1 (f=35mm) and additionally collimated by the second lens L2 (f=150mm). The light beam formed is linearly polarized after passing through the first polarizer P1 [Glan-Taylor, 210– nm, borrowed from a Lambda 950 spectrometer (Perkin Elmer)].

Fig. 1.

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We used composite half-wave plates comprising k={3,5} ordinary multi-order quarter-wave plates (WPMQ10M-780, Thorlabs), which perform as half-wave plates at λ=763nm. Each wave plate [aperture of 1 in. (0. m)] was assembled onto a separate RSP1 rotation mount, which can realize a 360° rotation. The optical axes of all wave plates were determined with an accuracy of 1°. Each of them was rotated at the respective theoretically calculated angle θk (Table 1). Lastly, the wave plates were slightly tilted [8] to reduce unwanted reflections.

The analysis of the rotation effect of the composite polarization rotator was done by a system made up of an analyzer P2 (same type as P1), a plano–convex lens L3 (f=20mm), and a two-axis micropositioner, which were used to focus the light beam onto the optical fiber entrance F connected to a grating monochromator (AvaSpec- fiber-optic spectrometer with controlling software AvaSoft 7.5). With the available light source and monochromator, we obtained reliable spectral transmission data in the range of 400– nm.

The measurement procedure was similar to the one described in Ref. [9]. We used a single beam spectrometer, and thus all experiments started with measurement of the dark and reference spectra. The dark spectrum, taken with the light path blocked, is further used to automatically correct for hardware offsets. The reference spectrum is usually taken with the light source on and using a blank sample rather than the sample under test. In our case, however, we measured the transmission spectrum of the already assembled composite polarization rotator, with the axes of the polarizer P1 and the analyzer P2 and the fast axis of the single wave plates all set to be parallel. The measured light spectrum was used as a reference for the subsequent measurements.

Finally, we assembled the two composite half-wave plates and rotated the first one at an angle α/4 clockwise and the second one at an angle α/4 counterclockwise. The analyzer P2 was set to α with respect to P1. The transmission spectrum of the realized composite polarization rotator was recorded and scaled to the reference spectrum. The unavoidable losses due to reflections and absorptions from any single wave plate were thereby taken into account.

We show the polarization rotation by the broadband and narrowband composite polarization rotators at four different rotation angles (α=40°, 60°, 80°, 100°) in Figs. 2 and 3, respectively. For easy reference and comparison of the broadband and narrowband behavior of the composite polarization rotators, we include the measured transmittance of a polarization rotator constructed of two ordinary half-wave plates. As predicted, we observe that the broadband and narrowband composite polarization rotators outperform the ordinary polarization rotator, and that the broadening and narrowing of the bandwidth increases with the number of half-wave plates in the sequence.

Fig. 2.

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Next we turn our attention to the problem of misalignment of the orientation angles of the optic axis for each wave plate in the array, as such errors are always present in an experimental setup. In the case of broadband rotators, such errors are compensated automatically and do not affect the spectra visibly. We can show this by introducing additional misalignment and realizing that the overall results in Fig. 2 are not changed. However, for narrowband rotators the precise control of the orientation angles is more crucial, and therefore better control of the orientation angles leads to considerable improvement in the narrowing of our spectrum in Fig. 3.

Fig. 3.

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4. CONCLUSION

In this paper, we demonstrated a novel, simple, multipurpose, and inexpensive composite polarization rotator that is capable of rotating the polarization plane of linearly polarized light at any desired angle. We showed that the bandwidth of the composite polarization rotator can be freely controlled by varying the number of constituent half-wave plates. Furthermore, we demonstrated that the constructed polarization rotator can be tuned to operate in both broadband and narrowband regimes by appropriately adjusting the rotation angles of each of the half-wave plates.

We note the universal principle that two crossed half-wave plates serve as a polarization rotator, and therefore any previously suggested achromatic half-wave plates [10–15] may be used to achieve a broadband polarization rotator.

ACKNOWLEDGMENTS

We acknowledge financial support by Singapore University of Technology and Design Start-Up Research Grant, Project No. SRG EPD 029 and SUTD-MIT International Design Centre (IDC) Grant, Project No. IDG . We are grateful to Georgi Popkirov for valuable discussion and suggestions.

REFERENCES

1. E. Hecht, Optics (Addison Wesley, ).

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5. F. J. Duarte, Tunable Laser Optics (Elsevier Academic, ).

6. A. A. Rangelov and E. Kyoseva, “Broadband composite polarization rotator,” Opt. Commun. 338, 574–577 (). [CrossRef]  

7. J. S. Kim and J. K. Chang, “Achromatic polarization rotator and circular polarizer consisting of two wave plates of the same material,” J. Korean Phys. Soc. 48, 51–55 ().

8. T. Peters, S. S. Ivanov, D. Englisch, A. A. Rangelov, N. V. Vitanov, and T. Halfmann, “Variable ultrabroadband and narrowband composite polarization retarders,” Appl. Opt. 51, – (). [CrossRef]  

9. E. Dimova, S. S. Ivanov, G. Popkirov, and N. V. Vitanov, “Highly efficient broadband polarization retarders and tunable polarization filters made of composite stacks of ordinary wave plates,” J. Opt. Soc. Am. A 31, 952–956 (). [CrossRef]  

10. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I: an achromatic circular polarizer,” Proc. Indian Acad. Sci. 41, 130–136 ().

11. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II: an achromatic quarter-WP,” Proc. Indian Acad. Sci. 41, 137–144 ().

12. C. J. Koester, “Achromatic combinations of half-wave plates,” J. Opt. Soc. Am. 49, 405–409 (). [CrossRef]  

13. A. M. Title, “Improvement of birefringent filters. 2: achromatic waveplates,” Appl. Opt. 14, 229–237 (). [CrossRef]  

14. C. M. McIntyre and S. E. Harris, “Achromatic wave plates for the visible spectrum,” J. Opt. Soc. Am. 58, – (). [CrossRef]  

15. A. Ardavan, “Exploiting the Poincaré–Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24 (). [CrossRef]  

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