Laws of reflection and refraction of TE and TM polarization waves on the border of rhombic crystals

Abstract

The article analytically solves the problem of reflection and refraction of electromagnetic plane waves of different polarization at the boundary of anisotropic half-spaces of rhombic symmetry. Based on the matrix method, the angles of refraction of electromagnetic waves of different polarization, the amplitudes of the reflected and refracted waves, the angles that determine the direction of the group velocities and vectors of the flow of electromagnetic energy, the magnitudes of the flows of electromagnetic energy and their components depending on the direction of the wave vector of the incident wave are determined. The determination of the angles of total internal reflection and the refractive index of electromagnetic waves of different polarization is considered. A significantly different dependence of the kinematic and energy characteristics of electromagnetic waves of different polarization on the anisotropy of the magnetic and dielectric tensors is shown. For electromagnetic waves, the polarization of which is determined by the component of the electric tension vector perpendicular to the wave propagation plane (TE wave), the characteristics of the reflected and refracted waves, the velocity indicatrix, the propagation angles, etc. determined primarily by the components of the magnetic permeability tensor. In the case of electromagnetic waves, when the polarization is determined by the component of the magnetic field (TM wave), perpendicular to the plane of wave propagation, all characteristics depend mainly on the components of the dielectric constant. The validity of the Fresnel formulas for determining the coefficients of reflected and refracted waves at the boundary of anisotropic media of rhombic symmetry is shown. However, in this case, the components of the wave vectors included in the Fresnel formulas are determined by their indicatrices. In addition, it is necessary to take into account the dependence of these components on the angle of refraction in the second medium.