Cotton-Mouton Effect Research Articles

Design of radial interferometer-polarimeter for internal magnetic and density fluctuation measurements at multiple space-time scales in the National Spherical Torus Experiment-Upgrade (NSTX-U).

A Faraday-effect radial interferometer-polarimeter is designed for the National Spherical Torus Experiment-Upgrade (NSTX-U) to measure multiscale magnetic and density fluctuations critical to understanding fusion plasma confinement and stability, including those originating from magnetohydrodynamic instabilities, energetic particle-driven modes, and turbulence. The diagnostic will utilize the three-wave technique with 5MHz bandwidth to simultaneously measure line-integrated magnetic and density fluctuations up to the ion-cyclotron frequency. Probe beams will be launched radially from the low-field side at the NSTX-U midplane, where the measured Faraday fluctuations mainly correspond to radial magnetic fluctuations that directly link to magnetic transport. A correlation technique will be employed to reduce the measurement noise to below 0.01° enabling detection of small amplitude fluctuations. Two toroidally displaced chords with 7° separation will be installed to measure toroidal mode numbers up to n = 25 for mode identification. Solid-state microwave sources operating at 321μm (935GHz) will be used to minimize the impact of the Cotton-Mouton effect.

Stimulated magneto-optics with different detunings for plasma local diagnostics

The polarization plane stimulated rotation angle of a probe signal in an intense laser field in plasma is calculated for arbitrary detunings of intense and weak laser waves compared with the resonant transition frequency of the medium. Estimates of the residual gas local density in a cesium plasma have been found based on the Faraday, Cotton–Mouton effects and on the effect of stimulated rotation of the polarization plane of the probe signal in an intense laser field. It is shown that the rotation in the medium has a complex structure consisting of the sum of only the influence of the magnetic field, only the influence of the intense laser field and the interfering part of the magnetic and intense laser fields.

Forward modelling of the Cotton-Mouton effect polarimetry on EAST tokamak

Measurement of plasma electron density by far-infrared laser polarimetry has become a routine and indispensable tool in magnetic confinement fusion research. This article presents the design of a Cotton-Mouton polarimeter interferometer, which provides a reliable density measurement without fringe jumps. Cotton-Mouton effect on Experimental Advanced Superconducting Tokamak (EAST) is studied by Stokes equation with three parameters . It demonstrates that under the condition of a small Cotton-Mouton effect, parameter contains information about Cotton-Mouton effect which is proportional to the line-integrated density. For a typical EAST plasma, the magnitude of Cotton-Mouton effects is less than 2 for laser wavelength of 432 . Refractive effect due to density gradient is calculated to be negligible. Time modulation of Stokes parameters ( , ) provides heterodyne measurement. Due to the instabilities arising from laser oscillation and beam refraction in plasmas, it is necessary for the system to be insensitive to variations in the amplitude of the detection signal. Furthermore, it is shown that non-equal amplitude of X-mode and O-mode within a certain range only affects the DC offset of Stokes parameters ( , ) but does not greatly influence the phase measurements of Cotton-Mouton effects.

Giant Parametric Amplification of the Inverse Cotton–Mouton Effect in Antiferromagnetic Crystals

The interaction of light with spins in a Heisenberg antiferromagnet with a negligibly low magnetic anisotropy as in RbMnF3 has been theoretically analyzed. In particular, an optical pump–probe experiment, where coherent terahertz magnons are excited by short pump laser pulses in the antiferromagnet and are then detected by a probe pulse delayed with respect to the pump pulse, has been simulated. It has been shown that the giant increase in the intensity of excitation of terahertz magnons under the influence of the inverse Cotton–Mouton effect occurs near parametric resonance, i.e., in the parametric instability region.

Active correction of window Faraday effects for ITER laser diagnostics

Measurement of the change in polarization of a laser beam traversing a magnetized plasma is a standard diagnostic technique for extracting key plasma parameters, including density and current profile. Depending on the polarization orientation of the incident laser beam relative to theplasma magnetic field, the polarization change is denoted as either Faraday rotation or Cotton-Mouton effect. On ITER three laser diagnostics will make use of this effect to make their measurements. Unfortunately, this effect is also evident when the laser beam passes through the vacuum window. The large magnetic field and finite verdet constant of the window material mean that on ITER this effect — in particular faraday rotation — is non-negligible, and needs to be disentangled from the desired measurement parameter. The Toroidal Interferometer-Polarimeter (TIP) and Density Interferometer-Polarimeter (DIP), in particular, are affected. Both diagnostics use lasers in the 5–10 μm range, and will use zinc-selenide (ZnSe) as the vacuum window material. In order to compensate for the unwanted window distortion a sensor is being developed to monitor the magnetic field perpendicular to the window and activelycorrectfor the faraday rotation in real time. The sensor consists of an inductive coil closely fitted just in front of the window disc. It comprises several turns of fine wire in center-tap configuration. Both the raw voltage signal, as well as the integrated signal, will be monitored to estimate the magnetic field through the window disk. The system is designed to measure fields up to B <1 T with an accuracy of 0.01 T, at frequencies of D.C. to 1 kHz. The backend electronics will leverage off similar technology developed for other ITER magnetics systems. Using the real-time magnetic field information, in conjunction with published and/or measured data on the verdet constant of the ZnSe window material, in-house developed software will estimate the faraday rotation induced by passing through the window.An initial prototype of the sensor has been fabricated and results from preliminary characterization trials of the system are presented. Detailed testing is planned for the future using the DIP system prototype currently under development.

Cotton-Mouton Effect Using Algebraic Diagrammatic Construction Schemes in the Intermediate State Representation Formalism.

The Cotton-Mouton effect is theoretically investigated for a selected set of molecules by using a novel computational methodology based on algebraic diagrammatic construction (ADC) schemes in the intermediate state representation (ISR) formulation. Therefore, the electronic contributions to the frequency-dependent polarizabilities and, for the first time, to the magnetizabilities as well as mixed electric and magnetic hypermagnetizabilities have been computed in the ADC/ISR framework. In addition to calculation of the Cotton-Mouton constant and the birefringence, the gauge origin dependence of the computed tensors and the applied methodology are thoroughly investigated. The new ADC/ISR methodology, employing the recently presented responsefun package, is applied to a test set of Ne and small molecules (H2, HF, O2, CO2, and benzene) and compared to data from the experiment as well as other ab initio methods. The presented theoretical ab initio ADC/ISR approach is a substantial extension of the available computational methods for the investigation of complex nonlinear properties, however, with a gauge origin dependence inherent to the method that decreases with increasing perturbation order.

The kinetics of aggregation of the Aβ1-40 peptide monitored by magnetooptical methods

Protein misfolding leads to the formation of amyloid fibrils, which presence is characterized for many serious diseases affecting millions of people worldwide. In the presented study we used, for the first time, magnetooptical (MO) methods such as Faraday and Cotton-Mouton effects (FE and CME respectively) to monitor the aggregation processes of one of the most studied peptides, amyloid β1-40 (Aβ1-40) which is associated with Alzheimer’s disease. Through the anisotropy of optical polarizability and magnetic susceptibility, CME is very sensitive to the shape of the studied species, which allows us to monitor their changes. The impact of incubation time (up to 40 days) and temperature (8, 23, 36 °C) on the aggregation of Aβ1-40 was evaluated by the measured coefficients that describe both effects. CME is found more suitable for monitoring protein aggregation than FE. Formation of Aβ1-40 fibrils and kinetic profile was also confirmed using the Thioflavin T fluorescence assay. Furthermore, CME was successfully used to demonstrate the self-assembly of phenylalanine, which is recognized as the crucial amino acid in the aggregation process of Aβ1-40. Our observations demonstrate the possible role of π-π interaction of aromatic rings in the self-assembly of amyloid fibrils.

Magnetically tunable zero-index metamaterials

Zero-index metamaterials (ZIMs) feature a uniform electromagnetic mode over a large area in arbitrary shapes, enabling many applications including high-transmission supercouplers with arbitrary shapes, direction-independent phase matching for nonlinear optics, and collective emission of many quantum emitters. However, most ZIMs reported to date are passive; active ZIMs that allow for dynamic modulation of their electromagnetic properties have rarely been reported. Here, we design and fabricate a magnetically tunable ZIM consisting of yttrium iron garnet (YIG) pillars sandwiched between two copper clad laminates in the microwave regime. By harnessing the Cotton–Mouton effect of YIG, the metamaterial was successfully toggled between gapless and bandgap states, leading to a “phase transition” between a zero-index phase and a single negative phase of the metamaterial. Using an S-shaped ZIM supercoupler, we experimentally demonstrated a tunable supercoupling state with a low intrinsic loss of 0.95 dB and a high extinction ratio of up to 30.63 dB at 9 GHz. We have also engineered a transition between the supercoupling state and the topological one-way transmission state at 10.6 GHz. Our work enables dynamic modulation of the electromagnetic characteristics of ZIMs, enabling various applications in tunable linear, nonlinear, quantum, and nonreciprocal electromagnetic devices.

Advances in magneto-optical birefringence effect of 2D materials with extremely large aspect ratio

Achieving giant magneto-optical birefringence is a long-standing goal in view of its intriguing physics and potential applications in transmitted light modulation. Due to the unique geometric features of two-dimensional materials with extremely large shape anisotropy, the resultant couplings among magnetic, electric, and optical properties enable giant magneto-optical birefringence effects, as represented by a record-breaking magneto-optical Cotton–Mouton coefficient in two-dimensional material systems. In this Perspective, we introduce the discovery of the giant magneto-optical birefringence effect in two-dimensional metal oxide dispersion in 2020, followed by analyses of the underlying mechanisms. We then discuss how the interplay of anisotropy and colloidal behavior affects the Cotton–Mouton effect. Finally, we proceed to potential applications and give our ideas about future developments in this emerging field.

Fundamentals of Magneto-Optical Spectroscopy

This paper provides a comprehensive review of magneto-optical (MO) spectroscopy. In the first place, different methods of MO measurements such as the Faraday effect, MO Kerr effect, and Cotton-Mouton effect are briefly introduced. Next, macroscopic and microscopic origin in magnetic materials is summarized. In the third part, measuring techniques for MO spectroscopies are reviewed, with a particular reference to the polarization modulation technique.

Giant quadratic magneto-optical response of thin Y3Fe5O12 films for sensitive magnetometry experiments

We report on observation of a magneto-optical effect quadratic in magnetization (Cotton-Mouton effect) in 50 nm thick layer of Yttrium-Iron Garnet (YIG). By a combined theoretical and experimental approach, we managed to quantify both linear and quadratic magneto-optical effects. We show that the quadratic magneto-optical signal in the thin YIG film can exceed the linear magneto-optical response, reaching values of 450 urad that are comparable with Heusler alloys or ferromagnetic semiconductors. Furthermore, we demonstrate that a proper choice of experimental conditions, particularly with respect to the wavelength, is crucial for optimization of the quadratic magneto-optical effect for magnetometry measurement.

High-frequency measurement of the interferometric phase, the Faraday rotation, and the Cotton-Mouton effect with a single detector in a far-infrared interferometer-polarimeter

A novel polarization modulation method is proposed, for a possible application in the measurement of the electron density and magnetic field profiles by an interferometer-polarimeter diagnostic in the Divertor Test Tokamak (DTT) device. Starting from the output of a CO2 pumped CHCOH3 far-infrared (FIR) laser (λ = 118.8 μm), three waves with frequencies ω, ω − δω, and ω + δω are generated and coherently combined to produce a polarization modulated laser beam suitable to probe the DTT plasma in a multichord, double-pass scheme. A second, coherently pumped, FIR cavity operating at the slightly detuned ω′ frequency, acts as a local oscillator for the interferometric measurement. By this polarization modulation method, it is possible to simultaneously measure the interferometric phase, the Faraday rotation angle, and the Cotton-Mouton effect, all by a single detector, while keeping to an acceptable value the perturbation of the interferometric phase due to the time modulated polarization. In this paper, we describe the principles of the method and discuss its possible application in the poloidal interferometer-polarimeter diagnostic of the DTT device. A single chord mock-up experiment is in preparation to experimentally test the technique.

Ultrafast opto-magnetic effects induced by nitrogen-vacancy centers in diamond crystals

The current generation of quantum sensing technologies using color centers in diamond crystals is primarily based on the principle that the resonant microwave frequency of the luminescence between quantum levels of the nitrogen-vacancy (NV) center varies with temperature and electric and magnetic fields. This principle enables us to measure, for instance, magnetic and electric fields, as well as local temperature with nanometer resolution in conjunction with a scanning probe microscope (SPM). However, the time resolution of conventional quantum sensing technologies has been limited to microseconds due to the limited luminescence lifetime. Here, we investigate ultrafast opto-magnetic effects in diamond crystals containing NV centers to improve the time resolution of quantum sensing to sub-picosecond time scales. The spin ensemble from diamond NV centers induces an inverse Cotton–Mouton effect (ICME) in the form of a sub-picosecond optical response in a femtosecond pump–probe measurement. The helicity and quadratic power dependence of the ICME can be interpreted as a second-order opto-magnetic effect in which ensembles of NV electron spins act as a source for the ICME. The results provide fundamental guidelines for enabling high-resolution spatial-time quantum sensing technologies when combined with SPM techniques.

Advances in the DTT poloidal interferometer/polarimeter design

A multi-channels poloidal interferometer/polarimeter is under development for the Divertor Tokamak Test (DTT) facility, a new tokamak device whose construction is starting in Italy. The aim of the diagnostics is the simultaneous measurement of the line integrated electron density, Faraday rotation and Cotton Mouton effect. The measurement of two polarimetric signals together with the interferometric one would allow for a robust electron density estimate, for the internal magnetic field measurement as well as for the magnetic equilibrium reconstruction. In this work, we present the advances in the diagnostics design whose characteristics are constrained by scientific requirements as well as the DTT structural aspects. In this regards, we have analyzed the possibility of accommodating up to 16 lines of sight in the available space and the contribution of different chords positions in the magnetic equilibrium reconstruction. In particular, we have used the VMEC and V3FIT codes to evaluate the expected interferometric/polarimetric signals and their contribution in the reconstruction of the q profile. These results have been used to optimize the chords positions. Eventually, we present a realistic CAD-driven design of the diagnostic, with details of the most critical components (e.g. the corner cube retroreflectors in the high field side), which would allow for the selected chords configurations implementation.

Polarization Dependent Scattering in Cavity Optomagnonics.

The polarization dependence of magnon-photon scattering in an optical microcavity is reported. Because of the short cavity length, the longitudinal mode-matching conditions found in previously explored, large path-length whispering gallery resonators are absent. Nonetheless, for cross-polarized scattering a strong and broadband suppression of one sideband is observed. This arises due to an interference between the Faraday and second-order Cotton-Mouton effects. To fully account for the suppression of the cross-polarized scattering, it is necessary to consider the squeezing of magnon modes intrinsic to thin-film geometry. A copolarized scattering due to Cotton-Mouton effect is also observed. In addition, the magnon modes involved are identified as Damon-Eshbach surface modes, whose nonreciprocal propagation could be exploited in device applications. This Letter experimentally demonstrates the important role of second-order Cotton-Mouton effect for optomagnonic devices.

Light-induced static magnetization: Nonlinear Edelstein effect

We theoretically and computationally demonstrate that static magnetization can be generated under light illumination via nonlinear Edelstein effect (NLEE). NLEE is applicable to semiconductors under both linearly and circularly polarized light, and there are no constraints from either spatial inversion or time-reversal symmetry. Remarkably, magnetization can be induced under linearly polarized light in nonmagnetic materials. With ab initio calculations, we reveal several prominent features of NLEE. We find that the orbital contributions can be significantly greater than the spin contributions. And magnetization with various orderings, including anti-ferromagnetic, ferromagnetic, etc., are all realizable with NLEE, which may facilitate many applications, such as unveiling hidden physical effects, creating a spatially varying magnetization, or manipulating the magnetization of anti-ferromagnetic materials. The relationship between NLEE and other magneto-optic effects, including the inverse Faraday effect and inverse Cotton-Mouton effect, is also discussed.

Characterization of signals for a Divertor Tokamak Test facility interferometer/polarimeter system.

In magnetically confined fusion experiments, laser interferometer/polarimeter systems allow one to determine plasma density, give valuable information on the internal magnetic fields, and contribute to the evaluation of the plasma magnetic equilibrium and to the real-time estimation of the q profile to allow feedback configuration control. This work presents an analysis of the interferometric and polarimetric signals of a multi-chord far-infrared interferometer/polarimeter for the divertor tokamak test facility, the new tokamak device currently under construction in Italy. The polarimetric signals are calculated both with approximate formulas and by solving the equation describing the evolution of the laser beam polarization inside the plasma using the Mueller formalism. The latter method correctly accounts for crosstalk between Faraday rotation and the Cotton-Mouton effect. The impact of the plasma birefringence on the interferometric phase shift is also studied, and it is found that a perturbation of the interferometric phase shift is present also in the case of an initial fixed linear polarization of the probe laser beam.

Nonlinear optics of optomagnetics: Quantum and classical treatments

Optomagnetics emerges as a growing field of research cross-linking optics, magnetism, and material science. Here we provide a microscopic quantum-mechanical and a macroscopic classical model to describe an optomagnetic medium, i.e., optical gyration coefficient from a nonlinear optics point of view. Our self-consistent quantum-mechanical formulation considers all orders of perturbing field and results not only in finding generalized Pitaevskii's relationship, where photoinduced magnetization can be expanded in terms of light power, but also provides compact and analytical expressions for optical gyration vector coefficients. Classical treatment is then developed based on the anharmonic Drude-Lorentz model showing that the photoinduced DC magnetization is proportional to odd harmonics of the light power. The difference in quantum and classical results is revealed and discussed. Having a pump-probe setup in mind, we describe how a probe light signal can propagate down an optomagnetic medium, i.e., a medium that is magnetized by intense circularly polarized pump light, via its permittivity tensor and find light propagation characteristics. Inverse Faraday and Cotton-Mouton effects are discussed as a result of circular and linear birefringences and their Verdet constants have been analytically found.

Phono-magnetic analogs to opto-magnetic effects

The magneto-optical and opto-magnetic effects describe the interaction of light with a magnetic medium. The most prominent examples are the Faraday and Cotton-Mouton effects that modify the transmission of light through a medium, and the inverse Faraday and inverse Cotton-Mouton effects that produce effective magnetic fields for the spin in the material. Here, we introduce the phenomenology of the analogous magneto-phononic and phono-magnetic effects, in which vibrational quanta take the place of the light quanta. We show, using a combination of first-principles calculations and phenomenological modeling, that the effective magnetic fields exerted by the phonon analogs of the inverse Faraday and inverse Cotton-Mouton effects on the spins of antiferromagnetic nickel oxide yield magnitudes comparable to and potentially larger than those of the opto-magnetic originals.

Ultrafast Spin Dynamics in the Iron Borate Easy-Plane Weak Ferromagnet

Ultrafast processes of the spin dynamics in iron borate FeBO3 are considered theoretically; the mechanisms responsible for excitation of quasi-ferromagnetic as well as quasi-antiferromagnetic spin resonance modes by a one-period terahertz pulse are indicated. In full agreement with experimental observations [27], the excitation of the high-frequency quasi-antiferromagnetic mode is resonant by nature, and its amplitude is a linear function of the electric field of the terahertz pulse. The amplitude of the low-frequency quasi-ferromagnetic mode is a quadratic function of the electric field of the pulse, and the excitation of this mode is governed by the mechanism of the inverse Cotton–Mouton effect.