广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射

在实验室坐标系下由Maxwell旋度方程出发构造了横向场的状态矢量和耦合矩阵,讨论了各 向异性介质中的特征波.通过引入横向场的传播矩阵,进而得到分层各向异性介质的反射系数和透射系数的解析表达式.该式可以适用于一般情况,包括分层单轴各向异性材料和回旋介质,以及半空间各向异性介质的反射和透射问题. 关键词： 广义传播矩阵 各向异性介质 反射与透射     

Interaction of a surface magnetostatic wave with an inhomogeneous granular HTSC medium

In the present paper the dispersion properties of surface magnetostatic waves (SMSWs) propagating in a stratified structure, ferrite film—high-temperature superconducting layer, have been investigated. The problem of SMSW propagation in an inhomogeneous stratified medium has been solved and the dispersion equation has been obtained. In the solution of this problem, the granular nature of the high-temperature superconducting (HTSC) medium and the exposure to a constant magnetization field have been taken into account. Upon exposure to the constant magnetic field the HTSC film becomes an inhomogeneous anisotropic medium with respect to a variable magnetic field. The nonhomogeneous wave equation describing the SMSW field in a granular HTSC medium has been solved by the method of sequential iterations. Corrections for the SMSW velocity and attenuation, calculated with the use of the exact dispersion equation, are significant in comparison with previously obtained approximate values and exceed 20 and 40%, respectively. The method of analyzing electromagnetic fields in inhomogeneous granular high-temperature media can be used to solve some other problems, where spatially inhomogeneous HTSC media are used. Tomsk State University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 45–48, April, 1999.     

A note on scalar Hertz potentials for gyrotropic media

The scalar Hertz potentials are generalized to the case of electromagnetic fields in gyrotropic media. Expressions for electromagnetic fields in terms of two potentials are presented and the system of differential equations for the potentials is derived. The result are summarized in the form of a theorem. The case of a stratified gyrotropic medium with parameters varying along the distinguished axis has been considered also. Scalar “superpotentials” satisfying a fourth-order partial differential equation are introduced. They allow expressions for electromagnetic fields to be found in terms of one scalar superpotential only. Basic results on scalar Hertz potentials in isotropic media are recalled. The research reported in this paper was carried out during S. Przeździecki's leave of absence from the Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokryzyska 21, PL-00-049 Warszawa, Poland.     

Wave nonreciprocity in inhomogeneous gyrotropic media and multilayer systems: I. Inhomogeneous gyrotropic media

The propagation of electromagnetic waves in naturally (or structurally) gyrotropic inhomogeneous media is considered. A new mechanism of wave nonreciprocity is found, which is caused by the simultaneous presence of a gradient of one of the parameters of a medium and natural (or structural) gyrotropy. The problem of light transmission through a layer of a naturally gyrotropic inhomogeneous medium of finite thickness is solved by the method of addition of layers. Specific features of this nonreciprocity are considered. It is shown that such a system can operate as a one-sided reflector at certain angles of incidence of light. The mechanisms of enhancement of the nonreciprocity effects are investigated. It is shown that multiple reflections in a layer of finite thickness and diffraction of light by periodic inhomogeneities of a medium increase the nonreciprocity effects by several (from 2 to 5) orders of magnitude. This phenomenon, in turn, opens new fields of application of the nonreciprocity effects. Another interesting manifestation of wave nonreciprocity is revealed, which consists in asymmetry of the curve R(?):R(?)≠R(??) (R is the reflectance and ? is the angle of incidence).     

Intermediate regime for the diffraction of light on ultrasound in gyrotropic anisotropic crystals

An intermediate regime for the diffraction of light on ultrasound in gyrotropic anisotropic and cubic crystals in an external electric field is considered. A system of equations of the coupled waves, which describes acoustooptic diffraction in gyrotropic anisotropic crystals with consideration of the electrically induced optical anisotropy for a strong interaction between light and ultrasound, is presented. An intermediate regime for the diffraction of light on ultrasound in gyrotropic anisotropic crystals which is close to the Bragg regime for a weak acoustooptic interaction is studied. It is shown that the diffracted light is elliptically polarized and that the ellipticity and polarization azimuth of the diffracted wave depend on the anisotropy of the photoelasticity, the electrically induced anisotropy of the crystal in the external electric field, the gyrotropy, and the asymmetry of the diffraction structure. Zh. Tekh. Fiz. 67, 80–82 (September 1997)     

Anisotropy of inhomogeneous resonant media during transient interaction with optical pulses

This study predicts the manifestation of anisotropic properties in linearly isotropic inhomogeneous resonant media during the propagation of optical pulses through them with pulse durations comparable to the phase memory of the medium. For examples, the energy of an obliquely incident pulse propagating through a layered inhomogeneous medium, varies with inversion of the propagation direction. This effect results from phase modulation of the pulse duse to variation in refraction in a region of transient coherent processes in the medium. This study analyzes the most favorable conditions for observing anisotropic effects.V. D. Kuznetsov Siberian Physical — Technical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 96–99, August, 1994.     

A note on debye potentials for spherically gyrotropic media

The Debye potentials are generalized to the case of electromagnetic fields in spherically gyrotropic media. A medium is called spherically gyrotropic if it is locally gyrotropic with the distinguished axis having a radial direction determined by a central point. Expressions for electromagnetic fields in terms of the generalized potentials are presented and the system of differential equations for the potentials is derived. The results are summarized in the form of a theorem. Basic facts about the Debye potentials in isotropic media are recalled.     

Natural electromagnetic waves in round inhomogeneous layered waveguides

A general theory of gyrotropic waveguide is considered. The theory allows the entire spectrum of natural electromagnetic waves and oscillations in regular waveguide structures discretely inhomogeneous in their cross sections to be obtained. A mathematical model is discussed that enables the propagation constants to be calculated for an arbitrary number of bigyrotropic layers of the structure based on an informal algorithmic formulation of the dispersion equation. Examples of numerical analysis of electrodynamic structures are given. They provide the basis for the development of gyromagnetic microwave devices and measuring cutoff converters intended for monitoring of the electrophysical characteristics of various materials and fluid media. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 15–19, September, 2006.     

Eigenwaves in an inhomogeneous azimuthally bigyrotropic medium

The problem of natural electromagnetic waves in an azimuthally magnetized bigyrotropic medium which is inhomogeneous in the radial direction is solved analytically. A system of generalized wave equations is obtained in the longitudinal components of the electrical and magnetic fields. Particular solutions of the system are represented in the form of generalized power series. The series exponents are determined and recursion formulas are built up for calculating their coefficients. The passage to particular cases of a homogeneous gyrotropic and inhomogeneous isotropic medium is realized, and the results are compared with known data from the literature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 46–49, November, 1982.     

Differential matrix formalism for depolarizing anisotropic media

Azzam's differential matrix formalism [J. Opt. Soc. Am. 68, 1756 (1978)], originally developed for longitudinally inhomogeneous anisotropic nondepolarizing media, is extended to include depolarizing media. The generalization is physically interpreted in terms of means and uncertainties of the elementary optical properties of the medium, as well as of three anisotropy absorption parameters introduced to describe the depolarization. The formalism results in a particularly simple mathematical procedure for the retrieval of the elementary properties of a generally depolarizing anisotropic medium, assumed to be globally homogeneous, from its experimental Mueller matrix. The approach is illustrated on literature data and the conditions of its validity are identified and discussed.     

Novel properties of wave propagation in biaxially anisotropic left‐handed materials

Some physically interesting properties and effects (including the quantum effects) of wave propagation in biaxially anisotropic left‐handed materials are investigated in this paper: (i) we show that in the biaxially gyrotropic left‐handed material, the left‐right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media; (ii) it is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left‐handed media we will present a different geometric phase that is independent of the cone angles; (iii) the extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left‐ and right‐handed (LRH) media is also studied in detail by using the Lewis‐Riesenfeld invariant theory. Some interesting applications (e.g., controllable position‐dependent frequency shift, detection of quantum‐vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left‐handed media is briefly discussed.     

Calculation of transmission characteristics of smoothly inhomogeneous anisotropic media in the approximation of negligible smallness of the bulk reflection: III. Analytical solutions

The situations are considered in which the differential equation for calculating the transmission 2×2 matrix of a smoothly inhomogeneous anisotropic medium in the approximation of negligible smallness of the bulk reflection (NSBR) can be solved analytically. The general expression for this matrix is obtained for the case of normal incidence of light on an arbitrary ideally twisted optically locally centrosymmetric medium. It is shown that, under certain conditions of normalization of the eigenwave basis, the solutions obtained in the NSBR approximation are as simple as those obtained in the approximation of a small anisotropy, but the accuracy of the former solutions is significantly greater. It was shown that, generally, the determinant of the transmission 2×2 matrix of a smoothly inhomogeneous anisotropic medium can be expressed in terms of the parameters of the eigenwave basis, while, in the case of a locally inhomogeneous anisotropic medium, this value is expressed in terms of the parameters of the medium. This circumstance can be used in solving inverse problems.     

Photonic Crystals Based on Media with Arbitrary Anisotropy of Permittivity and Permeability

Technical Physics - A general approach to analyzing eigenmodes in anisotropic and gyrotropic 3D photonic crystals based on dielectric and magnetic media is proposed. This approach is based on the...     

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Generalization of a scattering theorem for plane-stratified gyrotropic media

A previously derived eigenmode scattering theorem for plane-stratified gyrotropic media established that the scattering matricesS andS′, defined, respectively, in terms of a given and a conjugate set of eigenmode amplitudes, are mutually transposed, i.e. , the theorem being valid specifically for the incoming and outgoing eigenmodes ofgyrotropic bounding media. In this paper the theorem is extended to include linearly and circularly polarized base-modes in theisotropic media which may bound the multilayered, gyrotropic structure. Transformation of the eigenmode scattering matrix leads to a generalization of the scattering theorem to include base modes which are not necessarily eigenmodes of the medium. In the important special case in which the ambient magnetic field is parallel to the plane of the stratification, the scattering matrix is shown to have a special symmetry whose form depends on the base modes chosen (eigenmodes, linear modes or circular modes).     

Volume Fresnel reflection of electromagnetic waves in three-dimensionally inhomogeneous media

Eikonal approximation is used to derive equations describing propagation of monochromatic electromagnetic waves in a three-dimensionally inhomogeneous medium, including volume Fresnel reflection from inhomogeneities. The analysis is based on a locality principle. Separation into reflection and transmission effects is performed. The former effects are found to be isotropic, whereas the latter are anisotropic and depend on interference phenomena. Interference effects lead to violation of the Rytov law of polarization rotation. Brewster phenomena in layered and three-dimensionally inhomogeneous media are shown to occur under different conditions.