The electromagnetic-wave propagation through a medium consisting of two dielectric half-spaces with a plate in between, has been investigated. The half-spaces are isotropic with their dielectric permittivity depending only on the z coordinate. The plate is anisotropic, and the components of its dielectric permittivity tensor are also z-dependent. For the first time, the sufficient conditions allowing the transformation of the system of Maxwell's equations into two independent equations, are ascertained. For an arbitrary z-dependence of the dielectric permittivity, the plate's reflectance and transmittance coefficients are obtained, this result being a generalization of the Fresnel formulas. We have considered both determinate and random dependences of the dielectric permittivity on the z-coordinate, and the plate's full-transparency conditions are specified. For a statistically inhomogeneous plate, the conditions of its full opacity are formulated. The Faraday effect in such a medium is studied. The influence of the medium's inhomogeneity on the temporal rotation of the polarization plane of a propagating wave has been demonstrated.
1. Bass, F. and L. Resnick, "Spatial and temporal rotation of the polarization plane of electromagnetic waves reflected from and transmitted through a gyrotropic plate," J. of Electromagn. Waves and Appl., Vol. 17, 1131-1137, 2003. doi:10.1163/156939303322519739
2. Brekhovskikh, L. M., Waves in Layered Media, Academia, New York, 1980; Tsang, L., J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing, Wiley-Interscience, New York, 1985.
3. Bilotti, F., A. Toscano, and V. Vegni, "Design of inhomogeneous slabs for filtering applications via closed form solutions of the reflection coefficient," J. of Electromagn. Waves and Appl., Vol. 16, 1233-1254, 2002.
4. Hashish, E. A., "Forward and inverse scattering from an inhomogeneous dielectric slab," J. of Electromagn. Waves and Appl., Vol. 17, 719-736, 2003. doi:10.1163/156939303322226374
5. Landau, L. D. and E. M. Lifshits, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1984.
6. Cheng, P. (ed.), Scattering and Localization of Classical Waves in Random Media, World Scientific, Singapore, 1990.