Indicatrix of TE and TM- polarized wave velocities in crystal of classes 4mm, 3m, 6mm with magneto-electric effect

This work is devoted to the theoretical study of the laws of propagation of electromagnetic waves of TE and TM polarization in anisotropic media belonging to classes 4mm, 3m, 6mm, etc. having a magnetoelectric effect. The directions of the vectors of the phase and group velocities of the polarization waves TE and TM at the boundary of a uniaxial crystal with magnetoelectric properties are considered. In the analytical form, the values of the directions of the phase and group velocities of the TE and TM waves are indicated, depending on the direction of the wave vector of the incident wave. The consequences of the obtained results for uniaxial crystals in the absence of magnetoelectric properties are discussed. The solution of the tasks set in this paper is based on the use of the matrix method. On its basis, various problems of wave processes in an isotropic elastic medium, electromagnetic waves in crystals, the distribution of coupled elastic and electromagnetic waves in piezoelectric and piezomagnetic media with a magnetoelectric effect were previously considered. In the presence of a magnetoelectric effect for electromagnetic waves propagating through uniaxial crystals, the parameters of the wave vector, phase and group velocities are determined. The obtained results are analyzed for electromagnetic waves propagating through uniaxial crystals in the absence of a magnetoelectric effect. The indicatrices of the wave vectors propagating in the plane and the phase velocities of the TM polarization waves are limited ( 0 ) x z . Based on the Rayleigh equation, the values of the group velocity are obtained. The density of electromagnetic energy fluxes and their components are determined for TE and TM waves. The energy transfer rate and its direction are determined. It is shown that the group velocities and directions obtained from the Rayleigh equation and the Umov-Poynting vector do not coincide.