Amplitudenverhältnisse bei der Reflexion und Brechung des Lichtes an der Grenzebene zwischen isotropen und anisotropen Medien

Relations for the Amplitudes in Case of Reflection and Refraction of Light at the Boundary Plane between Isotropic and Anisotropic Media Relations for the amplitudes of the electric fields of plane monochromatic waves reflected and refracted at the boundary plane between isotropic and arbitrarily anisotropic media are derived from the Maxwell theory both for incidence from the isotropic or from the anisotropic medium. Furthermore, the vectorial amplitudes of the uniradial oscillations are determined. The following special cases of the general formulae are considered: 1. normal incidence, 2. optic axis in direction of the reflected respectively refracted wave in the anisotropic medium, 3. normal and parallel polarization of the partial waves in the anisotropic medium with respect to the plane of incidence.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

Propagation of an arbitrary incident light in a uniaxially planar slab

Similarly to the Jones calculus, a propagation formulation of an arbitrary incident light in a uniaxially planar slab with any orientation of the optic axis is derived, where both the multi-reflections and multi-refractions and the phase difference between the ordinary and extraordinary waves arising at the interface are considered. Unlike the case of propagation in the stratified isotropic media, the elements of the reflection and transmission matrices not only include the reflection and transmission coefficients, but also comprise phase differences caused by the mutual couples between ordinary (O) and extraordinary (E) waves. At this point, the propagation of an arbitrary light in a stratified uniaxially anisotropic media may be viewed as the multi-reflections and multi-refractions of a compound wave composed of one O wave and one E wave.     

Reflexion und Brechung des Lichtes an optisch einachsigen Medien

Reflection and Refraction of Light in Uniaxial Media The formulae for the amplitude relations for the reflection and refraction of plane monochromatic light waves at a plane interface between an isotropic and an arbitrarily anisotropic medium, derived in an earlier paper by the author, are specialized here to the case of uniaxial media. The incidence both from the isotropic and from the uniaxial medium is dealt with. A series of special cases (normal incidence, optical axis parallel or normal to the plane of incidence, transition from uniaxial to isotropic media a.o.) are considered.     

各向同性介质界面本征模分析

分析了两个各向同性材料界面处的本征模,从另一个角度来分析解释了布儒斯特定律.当入射光与界面处的表面模匹配时,入射光的能量就会全部转移到界面的本征场上,如果电磁波在折射介质中为行波,界面的本征场又会在折射介质中激发新的电磁波,形成透射波,也就是布儒斯特定律描述的横电波或者横磁波的全透射现象,这也可以看作是一种光学共振现象.横磁波的全透射现象往往出现在两个具有相同磁导率的介质的界面处,而横电波的全透射现象则往往出现在两个具有相同介电常数的介质的界面处.     

Reflection and refraction of elastic wave at VTI-TTI media interface

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media.Specifically,one medium is a transversely isotropic medium with a vertical axis of symmetry(VTI medium)and the other one is a transversely isotropic medium with a tilt axis of symmetry(TTI medium).By solving the Kelvin-Christoffel equation,an eighth-order polynomial is established for reflection and refraction angles,which is confirmed from SnelFs law.Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions.An effective algorithm has been developed for numerical analysis of the polarization coefficients.Applying characteristic anisotropic parameters reported in the literature,the influencing factors on reflection and refraction coefficients are analyzed,e.g.,the anisotropy,the tilt-angle of rock-layer,and the incident-angle.The calculated reflection and refraction coefficients have been rechecked for energy conservation.     

Reflected and transmitted powers from a planar isotropic chiral–uniaxial anisotropic chiral interface

In this paper, analysis and theoretical investigations are carried out to find the reflected and transmitted powers for a planar isotropic chiral–uniaxially anisotropic chiral interface with optical axis parallel to interface. The expressions of the reflected and transmitted powers for right-circularly polarized (RCP) and left-circularly polarized (LCP) incident waves are derived. Results of the reflected and transmitted powers for the RCP and LCP incident waves from materials with different isotropic chirality and uniaxial chirality values are presented. The effect of the uniaxial chirality on three other cases of dielectric constant combinations is also studied. The numerical results derived from the presented analytical expressions are found to be in good agreement with those obtained by computational techniques elsewhere.     

Reflexion und Brechung des Lichtes an einer anisotropen Schicht

Reflection and Refraction of Light by an Anisotropic Layer The linear problem of reflection and refraction of plane monochromatic electromagnetic waves by a plane-parallel homogeneous anisotropic layer between (in general different) homogeneous optically isotropic semiinfinite media is treated on the basis of MAXWELL 's equations and the boundary conditions following from them. The permittivity tensor of the anisotropic layer is assumed to be widely arbitrary and therefore asymmetric, neglecting only the spatial dispersion, i. e., the dependence on the wave vector. The electrical fields of reflected, refracted, and transmitted waves are calculated in dependence on the electric field of the incident wave. The conditions for waveguide modes of the layer in the absence of incident waves are obtained from the vanishing of a determinant. The general formulae are specialized to the cases of normal incidence and also of perpendicular and parallel polarisation, relatively to the plane of incidence, of the refracted partial waves in the anisotropic layer thus obtaining simplifications in these cases. The interesting cases of uniaxial layers, when the optic axis lies either parallel or perpendicular to the plane of incidence, belong to the last mentioned special cases of perpendicular and parallel polarisation relatively to the plane of incidence.     

Anisotropic gratings recorded from two circularly polarized coherent waves

A constant intensity, rectilinear light vibration, with spatially varying orientation, is obtained from superposition of two orthogonal circularly polarized waves propagating, in slightly different directions. Such an exposure on a photoanisotropic medium, prints a grating characterized only by spatial variations in the orientation of the induced optic axis. The diffraction properties of such a grating are investigated. It behaves as a uniformly transparent isotropic medium when illuminated by the same waves as during the recording process. Illumination by a circular wave, generates a transmitted and a single diffracted beam, while an incident elliptically polarized one would produce, apart from the central order, two diffracted beams with orthogonal circular polarizations.     

Reflexion und Brechung des Lichtes an der Grenzebene zwischen zwei anisotropen Medien

Reflection and Refraction of Light at the Boundary Plane between Two Anisotropic Media Relations for the amplitudes in the case of reflection and refraction of plane monochromatic waves at the boundary plane between two arbitrarily anisotropic media are derived from Maxwell equations with invariant methods. Solutions are represented with use of the refraction vectors and of the polarization vectors for the electric field. From the general solution of the problem the following essentially more simple special cases are obtained: 1. normal incidence, 2. optic axis in direction of the incident or reflected wave, 3. parallel and normal polarization of the partial waves in both media relatively to the plane of incidence.     

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.     

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.     

Network characterization of acoustic boundary-value problems

By utilizing an analogy with electromagnetic theory, a transmission-line representation is derived for acoustic waves in a lossless, isotropic medium. The results are used to construct a general network for a planar welded interface that tightly binds two different media. Equivalent networks for a large class of boundary conditions at a planar interface are then obtained by means of straightforward simplifications of the general equivalent network.     

Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves

New formulae for the angles of refraction at the interface of the absorbing/transparent isotropic media are derived from Maxwell's equations. Using the time-averaged Poynting vector for the direction of the beam of light, the noncoincidence of incidence and refraction planes is predicted for the mixed polarization of incident wave. The angle between the refracted beam and incidence plane is especially large for the condition of non-resonant excitation of surface electromagnetic waves at a flat interface of absorptive-transparent media.     

Magneto-optical effects in crystals at the normal incidence

We consider the interaction of a polarized electromagnetic wave in a magnetically ordered crystal plate surrounded by an isotropic ambient at the normal incidence. The crystalline medium of the plate is specified by the general non-symmetric permittivity tensor. The results are expressed in terms of the transmission and reflection matrices which relate the electric fields of the incident wave to those of transmitted and reflected waves. Their applications are illustrated by examples of an isotropic plate magnetized normal to the interface, a cubic crystal magnetized parallel to the interface and an orthorhombic crystal magnetized along the axis normal to the interface. The effect of the reflection from the interfaces and the interference effect are included. The paper treats the reflection at an interface between an isotropic ambient and an absorbing magnetic crystal at small non-zero angles of incidence. The general reflection matrix is applied to the determination of the magneto-optical effects quadratic in magnetization.     

Bragg diffraction of surface magnetostatic waves from magnetic lattices

We present a theoretical and experimental investigation of Bragg scattering of surface magnetostatic waves (SMSW) by a time-independent, spatially periodic magnetic field when the wave orientation is arbitrary with respect to the magnetization field. In the theoretical section the theory of single-mode Bragg diffraction is generalized to the case of waves with arbitrary dispersion propagating through an anisotropic medium. The calculated results are, on the whole, supported by experimental measurements on SMSW. We demonstrate that a geometry which in isotropic media leads to a sinusoidal distribution of diffraction order amplitudes as a function of penetration into the differing lattice, can lead to a nearly exponential distribution of such amplitudes in anisotropic media. The anisotropy of the interaction between SMSW and the magnetic diffracting lattice is manifested by anomalously high scattering efficiencies for certain cases of relative orientation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 76–85, November, 1988.     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

Reciprocity and the concept of the brewster wavenumber

Reflection of planewaves at the planar interface of two biisotropic media has been examined in order to obtain the Brewster wavenumber. This examination shows that the Brewster wavenumber is, at least, not necessarily affected by the reciprocity or the non-reciprocity of the media on either side of the planarinterface.     

Operator of Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Fluctuations

The majority of known works on the theory of multiple scattering of electromagnetic waves in media with strong fluctuations are constrained by the assumption of statistical homogeneity of a medium. In this paper, we consider an isotropic lossy random medium, for which the principle value and multipole moments of the permittivity are invariant with respect to arbitrary rotations about a fixed symmetry axis and translations along the axis and are inhomogeneous in the radial direction. This paper is aimed at calculating the effective permittivity operator (EPO) for such a medium for the case of strong permittivity fluctuations.