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International audience; Faraday polarization rotators are commonly used in laser experiments. Most Faraday materials have a nonnegligible absorption, which is a limiting factor for high power laser optical isolators or for intracavity optical diodes. By using a stronger magnetic field and a shorter length of Faraday material, one can obtain the same polarization rotation and a reduced absorption. In this paper, we describe two permanent magnet arrangements that are easy to build and produce magnetic fields up to 1.7 T , substantially more than commonly used. The field homogeneity is largely sufficient for a 30 dB isolation ratio. We finally discuss the prospects for producing even larger fields with permanent magnets

We present a theory of the magneto-optical Faraday and Kerr effects of topological insulator (TI) films. For film thicknesses short compared to wavelength, we find that the low-frequency Faraday effect in ideal systems is quantized at integer multiples of the fine structure constant, and that the Kerr effect exhibits a giant $\pi/2$ rotation for either normal or oblique incidence. For thick films that contain an integer number of half wavelengths, we find that the Faraday and Kerr effects are both quantized at integer multiples of the fine structure constant. For TI films with bulk parallel conduction, we obtain a criterion for the observability of surface-dominated magneto-optical effects. For thin samples supported by a substrate, we find that the universal Faraday and Kerr effects are present when the substrate is thin compared to the optical wavelength or when the frequency matches a thick-substrate cavity resonance. Our theory applies equally well to any system with two conducting layers that exhibit quantum Hall effects., Comment: 14 pages, 5 figures. This work expands on our previous papers [Phys. Rev. Lett. 105, 057401 (2010); Phys. Rev. B 82, 161104(R) (2010)] by including thick topological insulator films and layered quantized Hall systems in general, as well as the effects of bulk conduction, substrate, and oblique light incidence that are relevant to experiments

Fiber optical current sensor (FOCS) is a technique considered to be compatible with the ITER nuclear environment. FOCS principle is based on the magneto-optic Faraday effect that produces non-reciprocal circular birefringence when a magnetic field is applied in the propagation direction of the light beam. The magnetic field or the electrical current is deduced from the modification of the state of polarization of light. The linear birefringence of the fiber related with non-perfect manufacturing, temperature changes or stress constitute a parasitic effect that reduces the precision and sensitivity of FOCS. A two-pass optical scheme with a Faraday mirror at the end has been proposed to compensate the influence of linear birefringence. In this paper we perform a Stokes analysis of the two-pass optical scheme to highlight the fact that the linear birefringence is not compensated perfectly by the Faraday mirror when non-reciprocal birefringence such as Faraday effect is also present.

Recent work demonstrating detection of nuclear spin magnetization via Faraday rotation in transparent fluids promises novel opportunities for magnetic resonance imaging and spectroscopy. Unfortunately, low sensitivity is a serious concern. With this motivation in mind, we explore the use of an optical cavity to augment the Faraday rotation experienced by a linearly polarized beam traversing a sample fluid. Relying on a setup that affords reduced sample size and high-frequency modulation, we demonstrate amplification of regular (i.e., nonnuclear) Faraday rotation of order 20. Extensions of the present methodology that take into account the geometric constraints imposed by a high-field magnet may open the way to high-sensitivity, optically-detected magnetic resonance in the liquid state.

We demonstrate modified Faraday polarization rotation of an optical field controlled by a pump beam in hot rubidium vapour. Induced rotations of greater than π/2 rad are seen with a transmission of 95%.

Resonant excitation of a paramagnetic system generate a effective magnetic field parallel to the excitation vector k, which play an interesting rule for the relaxation of the spin in the system.

The general theory of Faraday rotation in high-Q Whispering-Gallery optical cavities is investigated. We have studied the behavior of the transmission spectrum and identified the optimal condition for maximum sensitivity to external magnetic field.

We show that by enclosing graphene in an optical cavity, giant Faraday rotations in the infrared regime are generated and measurable Faraday rotation angles in the visible range become possible. Explicit expressions for the Hall steps of the Faraday rotation angle are given for relevant regimes. In the context of this problem we develop an equation of motion (EOM) method for calculation of the magneto-optical properties of metals and semiconductors. It is shown that properly regularized EOM solutions are fully equivalent to the Kubo formula., Comment: 27 pages, 19 figures. published version: references and appendixes updated, secs. II and III interchanged

Reported are experimental results of a Faraday anomalous dispersion optical filter (FADOF) at 780 nm using Rb atoms in the strong magnetic field range. Studied are Faraday anomalous dispersion spectra in a certain range of cell temperature and magnetic field strengths, the relations of the frequency displacement and bandwidth to the magnetic field strength, and obtained are a stable transmission T A of about 0.3, an out-of-band rejection of 10 4 and a detection sensitivity of 0.2μW.

Faraday rotation was measured in liquid-phase epitaxial (LPE) Hg1-xCdxTe (x approximately=0.22) at CO2 laser photon energies over the temperature range of 77 K to 300 K for magnetic fields up to 16 kG. The authors find that the Faraday rotation is composed of free-carrier, interband and spin-induced contributions. At 77 K, the interband and spin contributions dominate, resulting in large observed Faraday rotation, i.e. of the order of 102 deg cm-1 kG-1. All three contributions are needed to interpret the temperature and magnetic field dependence of the Faraday rotation in the samples. Resonant behaviour observed in the rotation angle is successfully described by impurity-to-band magneto-optical absorption. They conclude that Faraday rotation could serve as a viable technique for the non-contact measurement of carrier concentration in Hg1-xCdxTe.

Based on the recent theoretical deduction of the photon's static magnetic field operator BII, the optical Faraday effect and optical MCD are proposed. It is shown that BII rotates the plane of a linearly polarized probe, an effect which is frequency dependent and which gives rise to optical magnetic circular dichroism (optical MCD), in which the conventional magnet is replaced by a BII generator, a circularly polarized laser generating a magnetostatic field, each photon of which carries the quantum of flux BII.

For conformally stationary spacetimes it is possible to formulate the geometric optics approximation of light propagation purely in terms of the geometry of the three-dimensional manifold M consisting of the integral curves of the conformal Killing vector field. In this framework they derive the transport law for the polarization plane in M. If the conformal Killing field has a non-vanishing twist, the polarization plane undergoes a rotation similar to the familiar Faraday rotation in a magnetic field. This so-called gravitational Faraday effect is of particular interest in the gravitational field of rotating matter where is is coupled to the angular momentum of this matter. Therefore, they illustrate their general results with three rotating matter examples, namely (i) an Ozsvath-Schucking spacetime; (ii) the gravitational field outside a rotating body and (iii) a Kerr black hole embedded into a Robertson-Walker cosmos. Thereby they roughly estimate the observability of the gravitational Faraday effect in solar system experiments and in connection with the gravitational lens effect.

The anisotropy of the Faraday effect was studied on 15 optically uniaxial and biaxial crystals by an automated procedure of high resolution. The Faraday tensor of these crystals appears to be not quasi-isotropic. In the vicinity of phase transitions strong anomalies were observed.

We analyze the linearity and modulation depth of ac magnetic-field sensors or current sensors, using a ferrimagnetic or ferromagnetic film as the Faraday rotator and employing the detection of only the zeroth-order optical diffraction component from the rotator. It is theoretically shown that for this class of sensor the condition of a constant modulation depth and that of a constant ratio error give an identical series of curves for the relationship between Faraday rotation angle Θ and polarizer/analyzer relative angle Φ. We give some numerical examples to demonstrate the usefulness of the result with reference to a rare-earth iron garnet film as the rotator.

Faraday rotator mirror elements have been used in a number of applications as compensators for induced birefringence in retracing paths. In interferometric systems, such as the fiber-optic Michelson interferometer, this approach proved to be useful in providing maximum fringe visibility and insensitivity to the polarization state of light injected into the interferometer. However, it is found that, when the characteristics of the fiber coupler depend on the polarization state of the input beam, the efficiency of the Faraday mirror elements is limited. Theoretical analysis and experimental results in support of this statement are presented.

The measurements of electric field, voltage, magnetic field and current are often required to study high voltage, large current or other electromagnetic phenomena. As one of the methods for that, there is an optical method using electro- or magneto-optic effects. Taking up Faraday effect as an example, and using water as a Faraday material, the magnetic fields around a miniature power lines in the laboratory could be measured. From those results, it seemed that the magnetic field around real power lines, where the current of about 1000A flows, can be measured by using air as a Faraday material.

As we saw in Chapter 5, electromagnetic waves in isotropic materials are transverse, their electric and magnetic field vectors E and H being normal to the direction of propagation k . The direction of E or rather, as we shall see later, the electric displacement field D , is called the polarization direction, and for any given direction of propagation there are two independent polarization vectors, which can be in any two mutually orthogonal directions normal to k . However, when the medium through which the wave travels is anisotropic , which means that its properties depend on orientation, the choice of the polarization vectors is not arbitrary, and the velocities of the two waves may be different. A material that supports two distinct propagation vectors is called birefringent . In this chapter, we shall learn: about the various types of polarized plane waves that can propagate – linear, circular and elliptical – and how they are produced; how an anisotropic optical material can be described by a dielectric tensor ∈, which relates the fields D and E within the material; a simple geometrical representation of wave propagation in an anisotropic material, the n -surface, which allows the wave propagation properties to be easily visualized; how Maxwell's equations are written in an anisotropic material, and how they lead to two particular orthogonally polarized plane-wave solutions; […]

A reciprocal fiber-optic reflection interferometer for remote measurement of electrical current through the Faraday effect is described. The effects of polarization cross coupling because of nonideal elements are eliminated with a low-coherence source. Nonreciprocal birefringence phase modulation is employed for detection of the Faraday phase shift. The theoretical predictions are confirmed by measurements with a piece of straight fiber as the sensing element in a 100-turn solenoid. Currents from 0 to 40 A have been measured with a linear response and a noise limit of ∼0.015A/Hz.

The effective magnetic field induced by a femtosecond pulse of circularly polarized light, via the inverse Faraday effect, is shown to excite a magnetic-dipole forbidden exchange spin resonance in a lutetium iron garnet. An external magnetic field cannot excite this mode, as the iron sublattices have the same gyromagnetic ratio and no net torque can be applied between them. However, since the sublattices have different magneto-optical susceptibilities, the inverse Faraday effect induces different effective fields on different iron sites, allowing excitation.

We considered the possibility of the creation of Faraday rotator for optical switch on the basis of ferrite-garnet film with the "angular phase" magnetic anisotropy. The Faraday effect was researched under the extending of light in the plane of the film in the direction of the plane projection on axis of hard magnetization. Under the magnetization of the film by the field saturation of ≈ 50 Oe specific Faraday rotation in it with the wavelength of 1.31 and 1.55 µm was 46.4 h 34.8 °/mm, respectively. The degree of polarization on the exit of the rotator reached 0.98.

A highly efficient low magnetic field Faraday rotator is presented. A cavity filled with transparent liquid for visible and infrared radiation with a high Verdet coefficient is used. Light travels the cavity several times giving us the advantage of nonreciprocity of the Faraday effect. This cavity is designed in such a way (regarding geometry and the nature of reflecting materials) that it introduces no detectable alteration of the state of polarization of the light, except, under the effect of an applied field, a pure rotation of the polarization plane given by the Faraday law. A rotator using this sort of cavity has potential, in the form of a Faraday modulator, in high precision ellipsometric and polarimetric devices working in the visible and near infrared and using polarization modulation.

The polarization states of electromagnetic (EM) waves can be effectively manipulated through reflections by a Faraday chiral medium (FCM) reflector, and an arbitrary polarization conversion is feasible via adjusting constitutive parameters of the FCM. Reflection formulas of the FCM reflector are rigorously derived, and the deep mathematical analysis is conducted to propose approaches of manipulating polarization states of the reflected wave and realizing polarization conversion. Numerical results are obtained in this paper and compared with theoretical predictions — a good agreement is found.

Faraday rotation is obtained in highly birefringent single-mode fibers by using alternating or periodically spaced regions of magnetic field. This approach has potential applications in isolators, circulators, combination tuning and unidirectional elements, and for studying fiber birefringence.

Topological insulators can exhibit strong magnetoelectric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange-coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low-frequencies, $\theta_{\mathrm{F}} = \mathrm{tan}^{-1}\,\alpha$ where $\alpha$ is the vacuum fine structure constant, and that it has a giant Kerr rotation $\theta_{\mathrm{K}} = \pi/2$. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall conductivity of a topological insulator's helical quasiparticles., Comment: 5 pages, 4 figures

The resolution of a practical Faraday effect device is limited by birefringence. The case where both Faraday effect and birefringence are small is treated. Aleans for obtaining a high degree of linearity between Faraday rotation and applied magnetic field are investigated. With a method requiring two nearly identical sensors, a very significant over-all improvement is achieved. A second method of compensation, which acts on the polarization of the incoming light, gives an improvement for low fields only. A slight mismatch between the two sensors may be almost completely offset by superimposing the first and second compensation methods.

The Faraday rotation for light transmission through a bilayered structure composed of an electro-optic semiconductor film and a slab with high values of magneto-optic and magnetoelectric interactions is theoretically investigated. The influence of dispersion as well as an external electric field on the Faraday rotation is studied.

Larmor's theorem expresses the analogy between the motion of a charged particle in a homogeneous magnetic field and the motion in a system in uniform rotation. This analogy suggests that effects of a magnetic field may have a rotational counterpart. We discuss the differences and the analogies between the magnetic Faraday effect and the analogous effect induced by a rotation of the sample. A central issue is to what extent the macroscopic rotation of a material system is communicated to the wave functions of the electrons in the system.

Interaction of elliptically polarized laser radiation with plasma produced from a solid target generates magnetic fields simultaneously along axial and transverse directions. The axial magnetic field induces the plane of polarization of the incident laser beam to rotate due to the Faraday effect. Numerically the Faraday rotation has been calculated for interaction of Nd glass laser (λ=1.06 μm) in the subdense plasma in which the plasma density, temperature, and self‐generated magnetic field vary in the axial direction.

The formation of magnetic-field-induced spin-density-wave phases with quantized wavevectors in a quasi-two-dimensional organic conductor results in the quantization of the Hall conductance. The authors study the rotation of a polarized electromagnetic wave incident perpendicular to the molecular layer at a moderate magnetic field. Some interesting features are shown which should be useful in the investigation of Bechgaard salts.

Based upon the superposition principle of the interference of light, the relationship between Kerr rotation angle θ k and reflectivity R and optical constant and the thickness of transparent dielectric layers for double-layered films has been deduced theoretically. A simple and practical analyzed method for determining the off-diagonal and diagonal elements of the dielectric tensor of magneto-optical films has been developed using the relationship express of double-layered films and the measured results of Kerr rotation angle θ k and reflectivity R . Results show that this method can solve the problem simply. The validity of the method has been verified through determination of the elements of the dielectric tensor of TbFeCo perpendicular magnetic films in double-layered films of AlN/TbFeCo/glass.

The transformation of the state of polarization (SOP) of light from one state to another can be graphically illustrated by a trajectory on the Poincare sphere (PS). We use this method to illustrate the control of the azimuth SOP rotation on the PS. Traditionally, azimuth rotation is achieved by the use of a Faraday rotator or by the mechanical movements of birefringent wave plates. In this letter, an electrically controllable azimuth optical rotator is introduced theoretically and verified experimentally. It consists of two quarter-wave plates and one liquid-crystal variable wave plate and allows polarization rotation of an arbitrary polarized light by an angle determined by the magnitude of the applied field. This electrical approach avoids the errors and inconvenience associated with the magnetic field and the mechanical movements of other methods.

A method to miniaturize the Faraday rotator for an optical isolator is proposed. The rotator includes a half-wave plate, and magnets arranged with alternating polarities are used. The principle of operation of the rotator is confirmed by measurements. An isolator employing the rotator has a backward loss of 32 dB and a forward loss of 0.65 dB at 0.633-μm wavelength, where the forward loss is mainly due to Fresnel reflection losses.

It is shown that efficient Faraday rotation can be obtained in a fiber coil if the circumference of the coil is exactly equal to the beat length of the birefringence caused by bending. The essential elements of a practical, compact isolator based on this principle are demonstrated. Forty-five degrees of Faraday rotation were obtained in a 40-turn, 15-mm-diameter coil placed in the field of a permanent magnet (~0.29 T). The design of optical filters and magnetic sensors is also discussed.

An optical scanning electromagnetic field probe system, consisting of an electro-optic or magneto-optic crystal substrate and a galvano scanner, has been developed for high speed, low-invasive measurement of electromagnetic near field distribution. We demonstrate the measurement of electric field distributions using a LiNbO 3 crystal substrate and the probe system. We also measure magnetic field distributions above a microstrip line in the gigahertz range using a magnetic garnet thin film. The probe system is also used for measuring electromagnetic field distributions above a commercially available IC.

Magneto-optical spectra (Faraday effect) for nanometer-scale particles and collections of particles are calculated using a modification of the discrete dipole approximation (DDA). The approximation is used as a finite-element method for non-spherical particles whose dimensions are on the order of or smaller than the incident light wavelength, lambda. Also, we use the approximation to calculate scattering from arrangements of spherical nanoparticles with diameterslambda. We propose that for scattering from subwavelength magnetic particles, the specific Faraday rotation should be defined as the difference in optical extinction for left- and right-circularly polarized light. We apply the model to calculations of Faraday rotation from magnetite nanowires as well as a binary (two-component) nanoparticle arrangement. Enhancements in Faraday rotation are predicted for composites containing both noble metal and ferrite nanoparticles.

An optically scanning electromagnetic field probe system, consisting of an electro-optic or magneto-optic crystal substrate and a galvano scanner, has been developed for the high speed, low-invasive measurement of electromagnetic near field distribution. We present some examples of electromagnetic field distribution measurements above a microstrip line using a LiNbO 3 or a magnetic garnet crystal substrate and the probe system. We have also measured electromagnetic fields above a commercially available IC using the system.

Precession of magnetization via the inverse Faraday effect is investigated with a view of determining the fundamental limit on the precession speed. Such a limit could have important consequences for ultrafast magnetic switching. The angular momentum required for precession is shown to be supplied by the light. This indicates that there is no fundamental obstruction to magnetization reversal on the time scale of a laser pulse provided that a material with a sufficiently strong magneto-optical response can be found.

A computer simulation of the inverse Faraday effect in a chiral and achiral ensemble has shown the presence of dynamic magnetisation and second order orientational rise/fall transients due to the conjugate product of a circularly polarised visible frequency laser pulse. Neither effect is known analytically, and the simulated transients are potentially directly comparable with experimental data using modified Kerr effect apparatus.

First order electric field induced optical rotatory dispersion, the analogue of the Faraday effect, is investigated in liquid bromochlorofluoromethane with molecular dynamics computer simulation, using a time varying electric field to conserve reversality. Frequency dependent features are identified which are the spectral signatures of electric circular dichroism and birefringence. These results indicate clearly, and for the first time, that there exists, under the right conditions, an electric analogue of the Faraday effect, mediated by the molecular electric hyperpolarisability tensor.

Non-linear Faraday processes occurring at high laser intensities are experimentally demonstrated in a Cd 0.75 Mn 0.25 Te alloy. Both the polarization direction and the phase of the incident beam are modified through the non-linear interaction. The large non-linear susceptibilities measured for the material show that non-linear Faraday processes overcome two-photon absorption and Kerr effects for magnetic field of the order of few teslas.

Nonlinear Faraday processes occuring at high laser intensities are experimentally demonstrated in a Cd 0.75 Mn 0.25 Te alloy. Both the polarization direction and phase of the incident beam are modified through the nonlinear interaction. The large nonlinear susceptabilities measured for the material show that nonlinear Faraday processes are expected to overcome two-photon absorption and Kerr effects for magnetic field of the order of few Tesla.

The geometric phase is determined for the Faraday rotation. In the Faraday process the wave propagation direction is fixed, while the polarization of the light is rotated by the magneto-optic activity of the medium. Correspondingly, it is shown that the geometric phase equals π when the polarization vector is transported by afull cycle on the equator of the Poincare sphere. The Faraday rotation turns out to be a complete optical analogue of a spin- 1 2 particle in a magnetic field.

Fiber optic sensors dispose of some advantages in the field of electrical current and magnetic field measurement, like large bandwidth, linearity, light transmission possibilities. Unfortunately, they suffer from some parasitic phenomena. The crucial issue is the presence of induced and latent linear birefringence, which is imposed by the fiber manufacture imperfections as well as mechanical stress by fiber bending. In order to the linear birefringence compensation a promising method was chosen for pulsed current sensor design. The method employs orthogonal polarization conjugation by the back direction propagation of the light wave in the fiber. The Jones calculus analysis presents its propriety. An experimental fiber optic current sensor has been designed and realized. The advantage of the proposed method was proved considering to the sensitivity improvement.

Recently magneto-optic spatial light modulators (MOSLMs) using magnetic garnet materials have advantages of high switching speed. However, these materials are difficult to be used in short wavelength range, so that it appears huge light absorption by magneto optic effect of transmittance mode (Faraday effect). This problem can be solved by using the materials of metal magnetic films for magneto optic effect of reflection mode (Kerr effect). We suggest the new method, which is the switching of pixels by heating the pixels with semiconductor laser until Curie temperature and changing the direction of the driving current at the same time, for developing high speed MOSLM in broadband using amorphous TbFe films. TbFe films were fabricated by RF sputtering using the Tb 21 Fe 79 target, and we have confirmed Kerr rotation (over 0.4 degree from 400nm to 800 in wavelength), the curie temperature (130 degree Celsius), and the switching of pixels of 16μm × 16 µ m by heating the pixels with semiconductor laser and controlling magnetization from external bias magnetic field (15Oe) and driving current (20mA) of coil at 403, 532 and 633nm wavelength.

Waveguide optical isolators suitable for integrated optics are described, which include a nonreciprocal loss isolator and an interferometric one. A surface activated bonding technique is effective for incorporating a magneto-optic effect in a semiconductor waveguide.

We propose a dynamical model for description of the nonlinear Faraday rotation experienced by a short pulse propagating in a resonant medium subject to an ultra-strong static magnetic field. Under the assumptions of a sufficiently strong external magnetic field, such that the Zeeman splitting of the quantum system energy levels is large compared to the linewidth of the optical transitions involved and the bandwidth of the incident light, the light effectively interacts with a two-level system. Our numerical simulations show that the Faraday effect under these conditions is significantly distinctive from the one caused by weak to moderately strong magnetic field. Nonlinear coherent effects such as inhomogeneous polarization rotation along the pulse duration and an onset of a circularly polarized stimulated emission and coherent ringing have been demonstrated. Some views on the experimental observation of the predicted phenomena are given.

Wavelength, magnetic field, and temperature dependences of Faraday rotation (FR) in various compositions of the dilute magnetic semiconductors Cd 1- x Mn Te and Zn 1- x Mn Te have been experimentally investigated. Regularities of the Faraday effect dispersion connected with the change of rotation direction as a function of temperature and Mn concentration in the compound have been revealed. Deviation in FR saturation at helium temperatures and high magnetic fields is observed. According to the FR temperature dependence, the spontaneous Faraday effect is assumed to be a characteristic of the spin glass state of semimagnetic semiconductors. A rapid magnetic field sensor system as a possible application of this material has been proposed.

Measurements of the Faraday rotation and transmission of light in Fe 3 O 4 particle magnetic fluid were undertaken in the temperature range 100–325 K. Our results show that both the transmission and Faraday rotation exhibit a cusp at 225 K. For T T > 225 K following a generalized Curie-Weiss type behaviour.