Cotton-Mouton Effect Research Articles

Design of an interferometer/polarimeter for DTT

Laser interferometer/polarimeter systems are used in magnetically confined fusion experiments for simultaneous measurements of the line-integrated electron density and of the current-induced magnetic field. In this work, we present the design of the interferometer/polarimeter system for the Divertor Tokamak Test facility (DTT), a new tokamak device dedicated to investigate alternative power exhaust solutions for the nuclear fusion DEMOnstration Power Station (DEMO). The optical design is based on the exploitation of a 7+7 chords scheme, which allows determining density and poloidal field, contributes to evaluate the plasma magnetic equilibrium and can provide the real time estimate of the q profile. Since the optical scheme is thought to be compatible with a possible Double Null divertor configuration, an equatorial port is recommended. In order to protect the in-vessel optics, each chord employs a back reflecting mirror installed in the high field side inner wall close to the divertor, where some plasma-free space is available, and one retroreflector installed in the space behind the low field side outer first wall. With respect to polarimetric measurements and low effects of density gradients, the optimal laser source solution would be 100/50 μm. With this setup, in low/medium density conditions, the longer wavelength will provide a good magnetic field measurement, while the shorter wavelength will allow vibration compensation for density measurements. In high-density regimes, the short wavelength alone can provide both magnetic field information from Faraday rotation and density measurements from the Cotton-Mouton effect. The two wavelengths are close enough to each other also to provide a good sharing of optical components.

Liquid-Crystalline Suspensions of Photosensitive Paramagnetic CeF3 Nanodiscs.

The design of high-performance energy-converting materials is an essential step for the development of sensors, but the production of the bulk materials currently used remains costly and difficult. Therefore, a different approach based on the self-assembly of nanoparticles has been explored. We report on the preparation by solvothermal synthesis of highly crystalline CeF3 nanodiscs. Their surface modification by bisphosphonate ligands led to stable, highly concentrated, colloidal suspensions in water. Despite the low aspect ratio of the nanodiscs (∼6), a liquid-crystalline nematic phase spontaneously appeared in these colloidal suspensions. Thanks to the paramagnetic character of the nanodiscs, the nematic phase was easily aligned by a weak (0.5 T) magnetic field, which provides a simple and convenient way of orienting all of the nanodiscs in suspension in the same direction. Moreover, the more dilute, isotropic, suspensions displayed strong (electric and magnetic) field-induced orientation of the nanodiscs (Kerr and Cotton-Mouton effects), with fast enough response times to make them suitable for use in electro-optic devices. Furthermore, an emission study showed a direct relation between the luminescence intensity and magnetic-field-induced orientation of the colloids. Finally, with their fast radiative recombination decay rates, the nanodiscs show luminescence properties that compare quite favorably with those of bulk CeF3. Therefore, these CeF3 nanodiscs are very promising building blocks for the development and processing of photosensitive materials for sensor applications.

Terahertz modulation of the Cotton-Mouton effect

The ultrafast dynamics of the magneto-optical response triggered in the ferromagnetic semiconductor CdCr2Se4 by an intense nearly single cycle THz pulse is investigated. The dependence on the strength and the polarity of the external magnetic field, and the polarization of the THz pulse can be explained by a phenomenological expression that attributes the observed dynamics to the Cotton-Mouton effect at THz frequencies.

Terahertz Optomagnetism: Nonlinear THz Excitation of GHz Spin Waves in Antiferromagnetic FeBO_{3}.

A nearly single cycle intense terahertz (THz) pulse with peak electric and magnetic fields of 0.5 MV/cm and 0.16T, respectively, excites both modes of spin resonances in the weak antiferromagnet FeBO_{3}. The high frequency quasiantiferromagnetic mode is excited resonantly and its amplitude scales linearly with the strength of the THz magnetic field, whereas the low frequency quasiferromagnetic mode is excited via a nonlinear mechanism that scales quadratically with the strength of the THz electric field and can be regarded as a THz inverse Cotton-Mouton effect.THz optomagnetism is shown to be more energy efficient than similar effects reported previously for the near-infrared spectral range.

Optical current sensing mechanism under a non-uniform magnetic field.

The effect of the inhomogeneous magnetic field on the Faraday rotation angle and output light intensity was analyzed using finite element simulation, at different distances between the conductor and the magneto-optical glass. The results show that under an inhomogeneous magnetic field, the magnetic birefringence effect due to the Cotton-Mouton effect decreases the output light intensity of the straight-through optical path. The Faraday rotation angle is non-linearly inversely proportional to the distance. Based on these results, which were verified by the theoretical model, a reasonable geometric arrangement of the sensing component of a straight-through optical current sensor is proposed.

Space and time resolved measurement of surface magnetic field in high intensity short pulse laser matter interactions

Magnetic fields produced by the interaction of intense laser beams on the surface of flat solid targets have been characterized. Laser probe polarimetry diagnosed the spatial and temporal evolution of the magnetic field by measuring the changes in the probe beam polarization due to Cotton-Mouton and Faraday effects at different times with respect to a pump laser pulse. The results show that 1 ps after the interaction of the pump laser with the target, a magnetic field of the order of a few MG is already present over a region ≈150 μm in diameter centered around the interaction spot. From the spatial and temporal evolutions of the magnetic field, we infer information on the resistivity of the material, showing evidence of a strongly magnetized resistivity.

Time-Resolved Imaging of Magnetoelastic Waves by the Cotton-Mouton Effect

Time-resolved magneto-optical (TRMO) imaging with ultrashort laser pulses now allows direct observation of the excitation, propagation, and relaxation dynamics of magnetization, with the details of excitation still being studied. This article shows how to image the in-plane component of magnetization, modulated by propagating spin waves, via the birefringence that arises in a transverse magnetic field. The authors use this method to resolve the contribution from magnetoelastic coupling in an out-of-plane-magnetized film. This technique extends the scope of TRMO imaging for investigating laser-induced magnetization dynamics, which will enable work in spintronics.

Graviton-photon mixing

In the era of gravitational wave (GW) detection from astrophysical sources by LIGO/VIRGO, it is of great importance to take the quantum gravity effect of graviton-photon (GRAPH) mixing in the cosmic magnetic field to the next level. In this work, we study such an effect and derive for the first time perturbative solutions of the linearized equations of motions of the GRAPH mixing in an expanding universe. In our formalism we take into account all known standard dispersive and coherence breaking effects of photons such as the Faraday effect, the Cotton-Mouton (CM) effect, and the plasma effects in the cosmic magnetic field. Our formalism, applies to a cosmic magnetic field either a uniform or a slowly varying non-homogeneous field of spacetime coordinates with an arbitrary field direction. For binary systems of astrophysical sources of GWs at extragalactic distances with chirp masses $M_\text{CH}$ of a few solar masses, GW present-day frequencies $\nu_0\simeq 50-700$ Hz, and present-day cosmic magnetic field amplitudes $\bar B_0\simeq 10^{-10}-10^{-6}$ G, the power of electromagnetic radiation generated in the GRAPH mixing at present is substantial and in the range $P_\gamma\simeq 10^6-10^{15}$ (erg/s). On the other hand, the associated power flux $F_\gamma$ is quite faint depending on the source distance with respect to the Earth. Since in the GRAPH mixing the velocities of photons and gravitons are preserved and are equal, this effect is the only one known to us, whose certainty of the contemporary arrival of GWs and electromagnetic radiation at the detector is guaranteed.

Magnetic, magneto-optical and specific heat studies of the low temperature anomalies in the magnetodielectric DyIG ferrite garnet

Abstract Measurements of magnetization and Cotton Mouton effect (CM) under external magnetic field (Hex) combined with specific heat experiments at Hex = 0, were performed on dysprosium iron garnet Dy3Fe5O12 (or DyIG) single crystals. The low-temperature dependences of some magnetic, magneto-optical and thermodynamic quantities, such as spontaneous magnetization, both magnetic and CM susceptibilities and the excess specific heat due to the contribution of the Dy3+ ions only, give rise to the appearance of two types of anomalies. The first one which is related to the ‘low temperature paraprocess’ effect, occurs in the region of the ‘Belov point’ TB predicted at 42 K. Whereas the second one, which is due to the previous first-order spin reorientation phase transition, takes place at TSR = 15 K. The easy axis of magnetization defined by the resultant iron sublattice magnetization vector MFe, which remains along the 〈1 1 1〉 direction above TSR, changes spontaneously below TSR and becomes aligned along the low symmetry angular 〈u u w〉 phase. The results are analyzed taking into account those reported earlier, such as the negative magnetodielectric property for Hex

Cavity optomechanics of topological spin textures in magnetic insulators

Collective dynamics of topological magnetic textures can be thought of as a massive particle moving in a magnetic pinning potential. We demonstrate that inside a cavity resonator this effective mechanical system can feel the electromagnetic radiation pressure from cavity photons through the magneto-optical inverse Faraday and Cotton-Mouton effects. We estimate values for the effective parameters of the optomechanical coupling for two spin textures -- a Bloch domain wall and a chiral magnetic soliton lattice. The soliton lattice has magnetic chirality, so that in circularly polarized light it behaves like a chiral particle with the sign of the optomechanical coupling determined by the helicity of the light and chirality of the lattice. Most interestingly, we find a level attraction regime for the soliton lattice, which is tunable through an applied magnetic field.

Anisotropic Magnetoelectric Coupling and Cotton-Mouton Effects in the Organic Magnetic Charge-Transfer Complex Pyrene-F4TCNQ.

Magnetoelectric coupling is of high current interest because of its potential applications in multiferroic memory devices. Although magnetoelectric coupling has been widely investigated in inorganic materials, such observations in organic materials are extremely rare. Here, we report our discovery that organic charge-transfer (CT) complex pyrene-2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (pyrene-F4TCNQ) can display anisotropic magnetoelectric coupling. Investigation of the crystal structure of pyrene-F4TCNQ complex demonstrates that the magnetoelectric coupling coefficient along the π-π interaction direction is much larger than the value along other directions. Furthermore, magnetoelectric coupling and magnetization can be tuned by changing the fluorine content in complexes. Besides, the Cotton-Mouton effect in pyrene-F4TCNQ is observed, enabling the control of optomagnetic devices. These results can pave the way for a new method for the future development of organic CT complexes and their applications in perpendicular memory devices and energy-transfer-related multiferroics.

Magneto-optic effects of the cosmic microwave background

Generation of magneto-optic effects by the interaction of the CMB with cosmic magnetic fields is studied. Effects which generate polarization such as the Cotton–Mouton effect, vacuum polarization and photon–pseudoscalar mixing in external magnetic field are studied. Considering the CMB linearly polarized at decoupling time, it is shown that photon–pseudoscalar mixing in external magnetic field, the Cotton–Mouton effect in plasma and the vacuum polarization in cosmic magnetic field, would generate elliptic polarization of the CMB depending on the photon frequency and magnetic field strength. Among standard magneto-optic effects, the Cotton–Mouton effect in plasma turns out to be the dominant effect in the generation of CMB elliptic polarization in the low frequency part ν0∼108–109Hz with degree of circular polarization PC(T0)≃10−10–10−6 for magnetic field amplitude Be0∼1nG–100nG. The vacuum polarization in magnetic field is the dominant process in the high frequency part ν0≥1010Hz where the degree of circular polarization at present is PC(T0)≲10−11 in the best scenario. The effect of pseudoscalar particles on the CMB polarization is also studied. It is shown that photon–pseudoscalar particle mixing in cosmic magnetic field generates elliptic polarization of the CMB as well and even in the case of initially unpolarized CMB. New limits/constraints on the pseudoscalar parameter space are found. By using current limit on the degree of circular polarization of the CMB, the upper limit of |gϕγ|<4.29×10−19(G/Be0)GeV−1 for mϕ<1.6×10−14eV in the weak mixing case is found. If |gϕγ|<1.17×10−24(G/Be0)GeV−1, a value of the order |gϕγ|≃10−26(G/Be0)GeV−1 for mϕ≃1.6×10−14eV in the resonant case, from large scale temperature anisotropy is obtained. Prior decoupling CMB polarization due to pseudoscalar particles is also discussed.

A Faraday-effect polarimeter for fast magnetic dynamics measurement on DIII-D.

A Faraday-effect-based radial-interferometer-polarimeter diagnostic has been developed to explore fast magnetic dynamics in high-performance DIII-D plasmas. The instrument measures radial magnetic field perturbations using three chords positioned near the magnetic axis. Newly developed solid-state sources operating at 650 GHz provide phase noise down to 0.01°/ and tunable bandwidth up to 10 MHz. Various systematic errors which can contaminate the polarimetric measurement have been investigated in detail. Distortion of circular polarization due to non-ideal optical components is calibrated using a rotating quarter wave plate technique. The impact of perpendicular magnetic field, i.e., the Cotton-Mouton effect, is evaluated. The error due to non-collinearity of probe beams is minimized to less than 0.5° for electron density up to 7 × 1019 m-3 by alignment optimization. Optical feedback, due to multiple reflections induced by the double-pass configuration, is identified and reduced. Coherent and broadband high-frequency magnetic fluctuations for DIII-D H-mode plasmas are observed.

Intrinsic mirror noise in Fabry\u2013Perot based polarimeters: the case for the measurement of vacuum magnetic birefringence

Although experimental efforts have been active for about 30 years, a direct laboratory observation of vacuum magnetic birefringence, due to vacuum fluctuations, still needs confirmation: the predicted birefringence of vacuum is Delta n = 4.0times 10^{-24} @ 1 T. Key ingredients of a polarimeter for detecting such a small birefringence are a long optical path within the magnetic field and a time dependent effect. To lengthen the optical path a Fabry–Perot is generally used with a finesse ranging from {{mathscr {F}}} approx 10^4 to {{mathscr {F}}} approx 7times 10^5. Interestingly, there is a difficulty in reaching the predicted shot noise limit of such polarimeters. We have measured the ellipticity and rotation noises along with Cotton-Mouton and Faraday effects as a function of the finesse of the cavity of the PVLAS polarimeter. The observations are consistent with the idea that the cavity mirrors generate a birefringence-dominated noise whose ellipticity is amplified by the cavity itself. The optical path difference sensitivity at 10;hbox {Hz} is S_{Delta {{mathscr {D}}}}=6times 10^{-19};hbox {m}/sqrt{mathrm{Hz}}, a value which we believe is consistent with an intrinsic thermal noise in the mirror coatings. Our findings prove that the continuous efforts to increase the finesse of the cavity to improve the sensitivity has reached a limit.

Dominant role of inverse Cotton-Mouton effect in ultrafast stimulation of magnetization precession in undoped yttrium iron garnet films by 400-nm laser pulses

Magnetization ($\mathbit{M}$) precessions driven by ultrafast laser-induced nonthermal effects are observed in undoped yttrium iron garnet (YIG) films of (100) and (111) orientations using pump-probe time-resolved magneto-optical Kerr effect. The $\mathbit{M}$ precessions show a strong dependence on the polarization direction of linearly polarized pump pulses of 400 nm. In contrast, we can barely observe any $\mathbit{M}$ precession using circularly polarized pump pulses, which indicates that the inverse Faraday effect is negligible. For the case of linear pump polarization, a phenomenological model is introduced, based on the modulation of $\mathbit{M}$ via a modulation of fourth-rank susceptibility tensors by a laser pulse. This allows one to distinguish the contributions of the inverse Cotton-Mouton effect (ICME) from those of the photoinduced magnetic anisotropy (PMA). Using the formula derived from the phenomenological model, we perform the fitting of the polarization-direction-dependent precession phase and amplitude in (100)- and (111)-oriented YIG films. The fitting results reveal that the $\mathbit{M}$-precession excitation originates from a combination effect of ICME and PMA, but the ICME plays the dominant role.

Impact of the Cotton–Mouton effect on Faraday polarimetry measurements using circular polarization

A comprehensive understanding of the impact of the Cotton–Mouton effect on Faraday polarimetry measurements using counter-rotating circular polarization (CP) probe beams has been developed. By using the Jones theory, an analytic study shows that the Cotton–Mouton effect cancels to first order with coupling into the Faraday measurement only at higher orders. A Jones-based numerical study shows the coupling effect strongly depends on the Cotton–Mouton effect, Faraday effect, and wavelength chosen for the measurement. For realistic DIII-D plasma conditions and far-infrared wavelength, numerical calculation suggests the measurement is dominated by the Faraday effect while the coupling effect leads to a small but finite correction. By statistical comparison between the experimental measurement and the Jones-based numerical calculation under various plasma parameters, the impact of the Cotton–Mouton effect has been verified. Proper treatment of the coupling effect is essential in the data analysis under certain conditions for polarimetric measurement using CP in present devices and beyond.

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M is retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M, based on linear response theory and the Green's function method; the results are used to study the system optical properties. First, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Second, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α×q). In the presence of M, which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M. For α∥M, these components yield the Faraday effect for the Faraday configuration q∥M and the Cotton-Mouton effect for the Voigt configuration (q⊥M). When α and M are noncollinear, M- and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the Voigt configuration. In these nonreciprocal optical phenomena, a “toroidal moment,” α×M, and a “quadrupole moment,” αiMj+Miαj, play central roles. These phenomena are strongly enhanced at the spin-split transition edge in the electron band.

Dispersions of Goethite Nanorods in Aprotic Polar Solvents.

Colloidal suspensions of anisotropic nanoparticles can spontaneously self-organize in liquid-crystalline phases beyond some concentration threshold. These phases often respond to electric and magnetic fields. At lower concentrations, usual isotropic liquids are observed but they can display very strong Kerr and Cotton-Mouton effects (i.e., field-induced particle orientation). For many examples of these colloidal suspensions, the solvent is water, which hinders most electro-optic applications. Here, for goethite (α-FeOOH) nanorod dispersions, we show that water can be replaced by polar aprotic solvents, such as N-methyl-2-pyrrolidone (NMP) and dimethylsulfoxide (DMSO), without loss of colloidal stability. By polarized-light microscopy, small-angle X-ray scattering and electro-optic measurements, we found that the nematic phase, with its field-response properties, is retained. Moreover, a strong Kerr effect was also observed with isotropic goethite suspensions in these polar aprotic solvents. Furthermore, we found no significant difference in the behavior of both the nematic and isotropic phases between the aqueous and non-aqueous dispersions. Our work shows that goethite nanorod suspensions in polar aprotic solvents, suitable for electro-optic applications, can easily be produced and that they keep all their outstanding properties. It also suggests that this solvent replacement method could be extended to the aqueous colloidal suspensions of other kinds of charged anisotropic nanoparticles.

Influence of the geometry system on the effectiveness of polarimetric measurements in thermonuclear plasma diagnostics

Simulations are undertaken using the angle variable technique (AVT) to study changes of the polarimetry state of an electromagnetic wave passing through a thermonuclear plasma in the poloidal plane. The first section analyses the changes in polarization state depending on the angle at which a test beam is sent for a set of fixed plasma parameters Subsequently, for a given geometry, numerical calculations are used to verify the influence of changes in various parameters of plasma (plasma density, current density, the safety factor profile) on the state of polarization of the test beam. All numerical calculations were being performed for ITER relevant plasma parameters. It should be emphasized that due to the different geometries in the present work both Faraday and Cotton-Mouton effect are taken into account.

Ultrafast optical excitation of coherent magnons in antiferromagnetic NiO

In experiment and theory, we resolve the mechanism of ultrafast optical magnon excitation in antiferromagnetic NiO. We employ time-resolved optical two-color pump-probe measurements to study the coherent non-thermal spin dynamics. Optical pumping and probing with linearly and circularly polarized light along the optic axis of the NiO crystal scrutinizes the mechanism behind the ultrafast optical magnon excitation. A phenomenological symmetry-based theory links these experimental results to expressions for the optically induced magnetization via the inverse Faraday effect and the inverse Cotton-Mouton effect. We obtain striking agreement between experiment and theory that, furthermore, allows us to extract information about the spin domain distribution. We also find that in NiO the energy transfer into the magnon mode via the inverse Cotton-Mouton effect is about three orders of magnitude more efficient than via the inverse Faraday effect.