Radiation properties of a uniaxial chiral quadratic inhomogeneous slab under oblique incidence

In this paper, the focussing of the transmitted electromagnetic field through a quadric inhomogeneous slab of lossless uniaxial chiral medium is derived using transmission coefficient under oblique incidence. The inhomogeneity in the uniaxial chiral slab has been incorporated through permittivity parameter. Asymptotic ray theory provides valid field everywhere except at focal point where it gives infinite value. Singularity of the field at focal point is addressed using Maslov's method. The derived analytical field expressions at caustic or focal point of uniaxial quadratic inhomogeneous slab have been solved numerically using MATHEMATICA. The effects of chirality parameter, axial permittivity, transvers permittivity, angle of incidence on the refracted field are discussed and the effects of Brewster angle on the focussed field are also discussed. The results obtained using Maslov's method are compared with Huygens–Kirchhoff's integral which are in good agreement.     

Resonant shielding of an inhomogeneous gyrotropic plasma slab

Conclusions The problem of the incidence of a plane TM electromagnetic wave on an isotropic, symmetric, resonance plasma slab (n=2, 4, 6, ...), discussed in [1], was solved by an iteration method in a recent paper [6]. The physical results found there are the same as those of [1]. Zhivulin and Makarov [6] then applied the iteration method to the analogous problem of a gyrotropic resonance plasma slab [7]. The analysis in these papers furnishes a clearer mathematical justification of the results of [1] and the present paper and thus of the method used there. The present method, which satisfies only a physical condition of rigor, is preferable to the mathematically more rigorous methods (in particular, the iteration method) because of its simplicity, its graphic nature, and its clear physical meaning. It also answers many questions which cannot be answered in the more rigorous approach because of the serious difficulties which arise (and which have not yet been overcome).N. G. Denisov has called our attention to the fact that complete shielding was actually found previously by Rytov and Yudkevich [8], who treated the problem of the incidence of a plane TE electromagnetic wave on a slab with a dielectric constant (x)=₁ – A₁/(a – x)² for x<0. (x)=₂ – A₂/(b + x)² for x>0, and ₁ – A₁/(a² = ₂ – A₂/b² in the plane x=0. In the limita0, b0, they found results corresponding to a slab with a dielectric constant having a first-order pole; it is in this case that complete shielding is achieved. This method for obtaining the corresponding results is analogous to the method used in [1] and the present paper. We also note that the distribution of the effective dielectric constant (6) in the immediate vicinity of the pole—where the contribution of the last term. (1–u)x², can be neglected—is the same as the distribution adopted in [8] if we seta-b-0, ₁ = ₂, A₁=A₂=u.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 19, No. 8, pp. 1130–1141, August, 1976.     

Kinetics of a phase transition into an inhomogeneous state in a ferroelectric plate

The kinetics of the emergence of a polarization vector field after a ferroelectric sample is rapidly cooled is investigated in two cases, in which the rate of growth of the polarization vector is determined by viscous forces of phonon origin or by the diffusion of charged particles. Analytic expressions are obtained for the rate of growth of the polarization vector and the period of the inhomogeneous phase as a function of the degree of supercooling of the sample. The existence of a slow relaxation process in the domain structure is established and the time dependence of this process is found. Zh. éksp. Teor. Fiz. 114, 2238–2245 (December 1998)     

Analysis of an inhomogeneous symmetric cladded slab optical waveguide

A detailed analysis of a symmetric cladded slab waveguide having a parabolic refractive-index profile in the core is carried out. Two techniques, one based on the step-index approximation and the other on the WKB approximation, are used to obtain the dispersion curves and the field plots for both the even and odd TE and TM-modes. An example of the practical relevance of the structure studied is given.     

Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics, mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles, arbitrary-shaped liquid-like scatterers, and range-dependent environments. In all cases, the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative), by projecting the Helmholtz equation on a constructed orthogonal and complete local basis. The admittance matrix, which is the modal representation of Direchlet-to-Neumann operator, is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes. The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation. The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed. Besides, the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method. It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles, liquid-like scatterers, and range-dependent environments. The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.     

Resonant interaction of an electromagnetic wave with an inhomogeneous plasma slab

Resonant interaction at oblique incidence of an electromagnetic wave on an inhomogeneous plasma slab is studied. The time evolution of this interaction is solved numerically from two-fluid equations, adiabatic equation for electron pressure and from Maxwell equations. It is shown that the electromagnetic energy of an incident wave is transformed both into the heat energy and into the energy of plasma oscillations in the direction of density gradient. The distribution of the transformed energy between the heat energy and the energy of plasma oscillations is strongly dependent on the plasma temperature. The ratio of heat energy to the energy of plasma oscillations is growing with growing temperature. The plasma oscillations are generated by magnetic induction of the penetrating wave. In a cold plasma they are generated especially in the overdense region and their frequency is equal to local plasma frequency. The electric field in the direction of plasma gradient has a form of a wave packet whose envelope reaches a maximum at resonance. The characteristic wavelength in the wave packet decreases and the amplitude of the packet increases with the time.     

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model. In this newly developed model, modifications to the chemical μ and chiral chemical \begin{document}$\mu_5$\end{document} potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian. In the proper-time scheme, the chiral phase transition is a crossover in the \begin{document}$T-\mu$\end{document} plane. However, when \begin{document}$\mu_5$\end{document} is incorporated, our study demonstrates that a first order phase transition may emerge. Furthermore, the chiral imbalance will soften the equation of state of quark matter. The mass-radius relationship and tidal deformability of quark stars are calculated. The maximum mass and radius decrease as \begin{document}$\mu_5$\end{document} increases. Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.     

Modelling of transmission through a chiral slab using fractional curl operator

Transmission of electromagnetic plane wave through a slab of reciprocal chiral medium has been modelled using fractional curl operator. It is noted that when order of the fractional curl operator becomes zero, the equivalent situation may correspond to absence of the chiral slab. Variation of the order of fractional curl operator may explore situations which may be regarded as intermediate step of a situation dealing with no chiral slab and a situation dealing with a chiral slab. It is noted that real order of the fractional curl operator may model the optical rotation while complex order of the fractional curl operator may model optical rotation as well as circular dichroism.     

Corner transfer matrix study of an inhomogeneous Ising model

We consider a planar Ising model with an extended defect described by couplings of the form K(r) = K·(1 + A/r). We determine the spectrum of the corner transfer matrix numerically and analytically and use it to calculate the local magnetization at the defect and the corresponding, non-universal critical exponent.     

Characterization of continuously inhomogeneous media with arbitrary thermophysical profiles using photothermal technique

A numerical method of determining depth profile of thermo-physical parameters of an inhomogeneous sample is presented. By dividing the inhomogeneous material into number of sublayers in which each single layer can be treated as homogeneous, the thermal-wave field of the material is obtained based on recurrence relations of thermophysical parameters of each divided layer. A numerical algorithm of determining the depth profile of thermophysical parameters in the continuously inhomogeneous material under excitation of arbitrary beam size has been demonstrated by a polynomial fitting process for three arbitrary generated thermophysical profiles.     

Symmetry properties of the polarizability matrix of an inhomogeneous electron gas

The properties of the polarizability matrix of an inhomogeneous electron gas in nonconducting crystals, are subjected to group-theoretical analysis. The analytical properties of the eigenvalues and eigenvectors of the polarization operator (intrinsic polarizabilities and intrinsic densities) are discussed. It is shown that intrinsic densities transformed with respect to the vector representation of the point symmetry group of the crystal are excited in an external homogeneous electrical field. The acoustic sum rule for a dielectric matrix is obtained as a consequence of invariance relative to an infinitely small shift of space.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 84–89, June, 1989.     

Polarization spectroscopy of an excited state transition

We demonstrate polarization spectroscopy of an excited state transition in room-temperature cesium vapor. An anisotropy induced by a circularly polarized pump beam on the D2 transition is observed using a weak probe on the 6P(3/2)→7S(1/2) transition. At high pump power, a subfeature due to Autler-Townes splitting is observed that theoretical modeling shows is enhanced by Doppler averaging. Polarization spectroscopy provides a simple modulation-free signal suitable for laser frequency stabilization to excited state transitions.     

First-order phase transition through an intermediate state

The theory of first-order phase transitions in systems where the direct formation of nuclei of a new phase is inhibited for any reason, for example, because of the extremely high elastic energy, has been constructed using the example of the silicon-silicon carbide phase transition due to the chemical reaction with carbon monoxide. It has been shown that, in this case, the phase transition occurs through an intermediate state, which significantly promotes the formation of new-phase nuclei. For the silicon-silicon carbide phase transition, such an intermediate state is the “pre-carbide” state of silicon saturated with dilatation dipoles, i.e., pairs formed by a carbon atom and a silicon vacancy that are strongly attracted to each other. The model dependence of the potential energy of systems with an intermediate phase on the reaction coordinates has been investigated. The kinetics of transformation of the intermediate state into a new phase has been described.     

Steady state self-focusing, self-modulation of laser beam in an inhomogeneous plasma

Laboratory as well as PIC simulation experiments reveal strong flow of energetic electrons co-moving with laser beam in laser plasma interaction. Equation governing the evolution of complex envelope in slowly varying envelope approximation is nonlinear parabolic equation. Variational approach is used to solve this problem and a Lagrangian for the problem is set up. Assuming a trial Gaussian profile, authors solve the reduced Lagrangian problem for beam width and curvature. Two scale lengths for inhomogenity along the direction of propagation, one for nonlinearity and other for diffraction management are introduced. Self-focusing, self-modulation as well as self-trapping of the laser-electron-beam plasma system is studied under variety of parameters.     

Continuous spin-reorientation phase transition in the surface region of an inhomogeneous magnetic film

A continuous spin-reorientation transition from a uniform magnetic state with the in-plane orientation of the moments of all atomic layers to a nonuniform canted state in the surface region is considered. This transition was discovered in experiments on the divergence of magnetic susceptibility in a perpendicular magnetic field at a temperature of about 240 K, which is lower than the Curie point of gadolinium, equal to 292.5 K. These experiments were carried out on an ultrathin iron magnetic film deposited on the (0001) surface of a thin gadolinium film. It is shown that, in the vicinity of the spin-reorientation transition, the thermodynamic potential has a form characteristic of the Landau theory of second-order phase transitions. The orientation angle of the moment of the surface atomic layer with respect to the plane of the film, which is chosen as an order parameter, exhibits anomalous behavior and increases with temperature. Expressions are derived for the magnetic susceptibility of each atomic layer. It is shown that, in the vicinity of the transition, the irregular part of the magnetic susceptibility of each atomic layer exhibits behavior characteristic of the susceptibility in the Landau theory: it is less by a factor of two in the low-symmetry phase and diverges at the transition point. The regular part of the magnetic susceptibility of each atomic layer makes an additional contribution to the asymmetry of the total susceptibility in the vicinity of the transition point; this result follows from the fact that the inhomogeneous magnetic system considered is semi-infinite.     

Crossover of polaron conductivity and the inhomogeneous state of lanthanum manganites in the magnetic phase transition region

The transport properties of lanthanum manganites over a wide range of temperatures below the magnetic phase transition point are discussed within the model of a two-phase composite whose phases differ in the magnetic order and charge carrier concentration. The volume ratio of the phases depends on the temperature and the magnetic field. The magnetoelastic polarons are charge carriers in both phases, and the metal-dielectric transition occurs as a percolation transition accompanied by the crossover of the polaron conductivity. The results obtained by numerical simulation of the resistivity, magnetoresistance, and thermopower are compared with the experimental data for La_0.7Mn_1.3O_3?δ thin films. The theoretical and experimental data are in good agreement.     

Tuning density profiles and mobility of inhomogeneous fluids

Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends.     

Boundary-induced nonequilibrium phase transition into an absorbing state

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example, we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.