Gyration Vector Research Articles

Experimental and Theoretical Studies of Magnetic Circular Dichroism for Chiral Lead Halide Perovskites

Chiral lead halide perovskites (LHPs) exhibit pronounced absorption or transmission circular dichroism (CD), which can be efficiently tuned by externally applied magnetic fields, giving rise to magnetic circular dichroism (MCD). To date, a systematic understanding of natural optical activities (NOAs) and magneto-optical activities (MOAs) in LHPs on an equal footing is still lacking. In this work, a joint experimental and theoretical study is carried out systematically in order to establish a unified picture of CD and MCD via a gyration vector for highly crystalline and solution-processable chiral LHPs. Experimentally, MCD strengths that appear near photoabsorption band edges of the chiral LHPs can be enhanced remarkably with increasing fields up to ±1.6 T. The experimental results can be well accounted for by a theory based on excitonic states, material chirality, and field dependence of the gyration vector. Importantly, numerical values of the exciton’s g-factor and chirality-induced spin–orbit coupling (SOC) strength can be extracted. Our work suggests that the magnetic field can be an important tool to elucidate the microscopic origin of NOA in chiral LHPs.

Spatial dynamics of light quasispin vector in an anisotropic medium with twisting

On the Poincar's sphere the spatial evolution of the light's polarization state has been studied quantitatively in the smoothly inhomogeneous anisotropic media with gyrotropy. The main features of the dependence on the sample?s thickness, the gyration vector and the azimuth of the polarization of the incident linearly polarized wave were revealed. An analytical solution of the system of coupled equations relative to Cartesian components of light's wave electric component obtained by transition to rotating coordinate system has been used for analysis. Keywords: Poincar' sphere, polarization evolution, medium with gyrotropy, rotating coordinate system.

Пространственная динамика вектора квазиспина света в анизотропной среде с кручением

On the Poincaré sphere the spatial evolution of the light’s polarization state has been studied quantitatively in the smoothly inhomogeneous anisotropic media with gyrotropy. The main features of the dependence on the sample’s thickness, the gyration vector and the azimuth of the polarization of the incident linearly polarized wave were revealed. An analytical solution of the system of coupled equations relative to Cartesian components of light's wave electric component obtained by transition to rotating coordinate system has been used for analysis.

Chiral filtration of light by Weyl-semimetal medium

Recently discussed topological materials Weyl-semimetals (WSs) combine both: high electron mobility comparable with graphene and unique topological protection of Dirac points. We present novel results related to electromagnetic field propagation through WSs. It is predicted that transmission of the normally incident polarized electromagnetic wave (EMW) through the magnetic WS strongly depends on the orientation of polarization with respect to a gyration vector g. The latter is related to the vector-parameter b, which represents the separation between the Weyl nodes of opposite chirality in the first Brillouin zone. By changing the polarization of the incident EMW with respect to the gyration vector g the system undergoes the transition from the isotropic dielectric to the medium with Kerr- or Faraday-like rotation of polarization and finally to the system with chiral selective electromagnetic field. It is shown that WSs can be applied as the polarization filters.

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.

Time dependent Faraday rotation

Faraday rotation in a magnetoactive medium with time dependent dielectric permittivity tensor is analyzed through both its diagonal and non-diagonal elements. Continuous and pulse incident laser field cases are considered. In a continuous case linear increasing of Faraday rotation angle with time is obtained. In the continuous laser field case Faraday angle of rotation in both time dependent diagonal and non-diagonal element cases shows an increase with periodic oscillations as either positive (time-dependent dielectric permittivity case) or negative (time dependent gyration vector case) and follows a general pattern. Ultrashort pulse can scan the time dependent dielectric permittivity through the Faraday rotation angle.

The linearized problem of magneto-photoelasticity

The equations of magneto-photoelasticity are derived for a nonhomogeneous background isotropic medium and for a variable gyration vector. They coincide with Aben's equations in the case of a homogeneous background medium and of a constant gyration vector. We obtain an explicit linearized formula for the fundamental solution under the assumption that variable coefficients of equations are sufficiently small. Then we consider the inverse problem of recovering the variable coefficients from the results of polarization measurements known for several values of the gyration vector. We demonstrate that the data can be easily transformed to a family of Fourier coefficients of the unknown function if the modulus of the gyration vector is agreed with the ray length.

Nonreciprocal photonic surface states in periodic structures of magnetized plasma nanospheres

We report on the occurrence and properties of photonic surface states in periodic structures of magnetized plasma nanospheres by means of rigorous calculations using the full-electrodynamic layer-multiple-scattering method, properly extended to treat gyrotropic spheres with arbitrarily oriented gyration vector. More specifically, dispersion diagrams of Tamm states at the (001) surface of a semi-infinite fcc crystal of plasma nanospheres and of guided modes of a square array of such spheres supported by a quartz substrate, without and under the action of an in-plane static uniform magnetic field, are analyzed and nonreciprocal optical response, which emerges as a result of the simultaneous lack of space-inversion and time-reversal symmetries, is demonstrated in the Voigt geometry.

Calculation Equation of Tooth Face of Shaping Gear for Logarithmic Spiral Bevel Gear

According to the processing principle of the spiral bevel gear, analyzed the relative motion of cutter and workpiece in process. Combing the feature of logarithmic spiral bevel gear, this paper took the advantage of the gyration vector expansion to derivate the tooth surface equation of logarithmic spiral bevel gear shaping gear and deduced the meshing equation.

Gyration effect of the large-scale turbulence in the upper ocean

A new quantity, gyration vector, measuring the gyration effect in turbulent flow field is suggested. While the formerly introduced spin characterizes the trajectories of fluid particles within the Lagrangian stochastic turbulence models, then the suggested gyration vector is defined as an average Eulerian characteristic of the turbulent flow field. The relation between the gyration vector and the average spin is analyzed. The meridional distributions of the gyration vector and of the average spin estimated from the global ocean surface drifter data in the Pacific Ocean are presented. Although the estimates of values of both quantities differ substantially for certain latitude intervals, their meridional distributions exhibit extensive qualitative similarities. The gyration vector as well as the average spin estimated for the unaltered original data on the velocity of drifters display the anticyclonic orientation of rotation at all latitudes, while for the low-pass filtered velocity data with the cut-off frequency value corresponding to 1.5 inertial periods the both quantities show a cyclonic orientation of rotation in narrow zonal bands around 10–20°N and S. The estimates of meridional distribution of two other quantities related to the gyration vector are presented and some aspects of theoretical context of the gyration vector are discussed.

Boundary Layer Flow Due to a Moving Flat Plate in Micropolar Fluid

Pemodelan matematik bagi aliran lapisan sempadan terhadap plat rata bergerak telah dibincangkan. Satu plat bergerak berterusan dalam arah positif paksi–x dengan halaju tetap. Persamaan lapisan sempadan yang dihasilkan telah diselesaikan secara berangka dengan menggunakan skema beza terhingga tersirat. Keputusan berangka telah diberikan, ini termasuk profil halaju, profile komponen legaran dan perubahan tegasan ricih permukaan. Kajian ini menunjukkan bahawa keputusan bagi masalah dalam bendalir mikropolar berbanding dengan bendalir likat adalah sangat memuaskan apabila parameter bahan K = 0 (bendalir Newtonan). Seterusoya tegasan ricih permukaan meningkat dengan peningkatan nilai K. Untuk nilai K yang ditetapkan, didapati tegasan ricih permukaan menyusut dan kompenan legaran meningkat dengan peningkatan nilai n, dalam selang O

An additive theory for finite elastic–plastic deformations of the micropolar continuous media

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, the micropolar hypo-elastic constitutive equations for isotropic micropolar materials are considered. Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic–plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying the developed elastic–plastic constitutive equations are investigated. It is shown that in the proposed formulation, the rate of skew-symmetric part of the stress tensor does not exhibit any jump across the singular surface. As an example, a generalization of the Drucker–Prager yield criterion to the micropolar continuum through a generalized form of the J2-flow theory incorporating isotropic and kinematic hardenings is introduced.

A new type of surface polaritons at the interface of the magnetic gyrotropic media

A new type of surface electromagnetic waves localized near the interface of the halves of the same transparent uniaxial magnetic gyrotropic medium is theoretically predicted. The gyration vectors of the halves are perpendicular to the interface and are oppositely directed to each other. Existence of such waves is due to both anisotropy of the medium and non-coincidence of the gyration vector directions on different sides of the interface. Distribution of intensity and variation of polarization of the surface polaritons as a function of the distance from the interface are studied. It is shown that the surface waves under consideration can be excited in uniformly magnetized ferromagnetics with axis of easy magnetization if their frequency does not exceed the magnetic resonance frequency.

Laminar flow of micropolar fluid in rectangular microchannels

Compared with the classic flow on macroscale, flows in microchannels have some new phenomena such as the friction increase and the flow rate reduction. Papautsky and co-workers explained these phenomena by using a micropolar fluid model where the effects of micro-rotation of fluid molecules were taken into account. But both the curl of velocity vector and the curl of micro-rotation gyration vector were given incorrectly in the Cartesian coordinates and then the micro-rotation gyration vector had only one component in the z-direction. Besides, the gradient term of the divergence of micro-rotation gyration vector was missed improperly in the angular moment equation. In this paper, the governing equations for laminar flows of micropolar fluid in rectangular microchannels are reconstructed. The numerical results of velocity profiles and micro-rotation gyrations are obtained by a procedure based on the Chebyshev collocation method. The micropolar effects on velocity and micro-rotation gyration are discussed in detail.

Handedness of magnetic-dipolar modes in ferrite disks

For magnetic-dipolar modes in a ferrite, components of the magnetic flux density in a helical coordinate system are dependent on both an orientation of a gyration vector and a sign of a pitch. It gives four types of helical harmonics for magnetostatic-potential wave functions in a ferrite disk. Because of the reflection symmetry breaking, coupling between certain types of helical harmonics takes place in the reflection points. The reflection feature leads to exhibition of two types of resonances: the “right” and “left” resonances. These resonances become coupled for a ferrite disk placed in a homogeneous tangential RF magnetic field. One also observes such resonance coupling for a ferrite disk with a symmetrically oriented linear surface electrode, when this ferrite particle is placed in a homogeneous tangential RF electric field. In a cylindrical coordinate system handedness of magnetic-dipolar modes in a ferrite disk is described by spinor wave functions.

Propagation of a Gaussian beam in a gyrotropic medium

Propagation of a slightly diverging Gaussian beam in a gyrotropic medium [constitutive equation (1.1)] across the gyration vector g is considered. The polarization, phase, and geometrical features of the beams are elucidated. For a sufficiently small gyrotropy, the medium deflects the beams like a wedge while for a sufficiently large gyrotropy the medium focuses them like a cylindrical lens. For the field polarized along g, focusing automatically and completely eliminates the diffraction broadening of the beam along this direction.

COLLINEAR ACOUSTO-OPTIC INTERACTION OF LIGHT BEAMS NEAR THE OPTICAL AXES OF BIAXIAL CRYSTALS

Collinear acousto–optic interaction of light beams near the optical axes of biaxial crystals, including gyrotropic ones, is considered. Efficient acousto–optic transformation of fast and slow light beams under the conditions of internal conical refraction has been revealed. It is shown that the width of the transmission band and the central frequency of ultrasound in collinear acousto–optic filtration in a nongyrotropic crystal are determined by the angle at the apex of the cone of wave vectors (by the anisotropy of the crystal) and in a gyrotropic one by the projection of the gyration vector onto the direction of the optical axis.

Mixed convection flow of a micropolar fluid over a stretching sheet

The mixed convective flow of a steady, incompressible micropolar fluid over a stretching sheet has been studied. This situation may arise in polymer technology involving the stretching of plastics sheets. The resulting system of non-linear ordinary coupled differential equations has been solved by the finite element method, using the variational Ritz model. Numerical results obtained for velocity, microrotation and temperature distributions are shown graphically. It was found that an increase in the micropolar parameter leads to a faster rate of cooling of the sheet. Also the velocity increases with an increase in micropolar effects. Microrotation effects are much smaller for the no-spin boundary condition as compared to the other boundary condition which assumes that the gyration vector is identical to the angular velocity of the fluid.

Dynamo-optical effects and hidden anisotropy of the medium

We study the electrodynamics of macroscopically isotropic media with temporal dispersion moving inhomogeneously. The dynamo-optical effects are shown to depend considerably on the hidden anisotropy of the medium (i.e., on the anisotropy at the microscopic level). A general expression is found for the dielectric tensor of an inhomogeneously moving medium without hidden anisotropy. It is shown that when this medium is rotated the gyration vector is determined completely by the kinematic contribution.

Influence of alloy composition and local environment on the magneto-optical properties ofCoxPd1−xalloys

Results of ab initio calculations performed to investigate the dependence of magneto-optical properties of ${\mathrm{Co}}_{x}{\mathrm{Pd}}_{1\ensuremath{-}x}$ alloys on chemical ordering and alloy composition are presented. A procedure of averaging the calculated spectra for compounds with respect to the orientation dependence of the gyration vector is proposed that makes it possible to account for the effects of random orientation of microcrystals in polycrystalline samples. Good agreement between theoretical and experimental spectra for varying alloy composition is found demonstrating the applicability of the theoretical approach.