Propagation of electromagnetic waves in anisotropic magnetoelectric medium

In the article we consider porpagation and interaction of electromagnetic waves of different polarization, in anisotropic medium that is inhomogeneous along the Z axis with magnetoelectric effect of tetragonal, trigonal, and hexagonal symmetries are described by the structure of the matrix coefficients. The matricant structure of the original system of equations follows from the structure of coefficient matrix. In unlimited periodic structures, dispersion relations of electromagnetic waves are determined from the new modified conditions for the existence of non-trivial solutions which are the consequence of the matricant structure. Obvious analitical form of the matricants for the homogeneous anisotropic dielectric medium with magnetoelectric effects follows from the matricant structure. Analytical equations for homogeneous anisotropic medium with magnetoelectric effects allow one, in matrix setting, to obtain analytical solutions for the problem of reflection and refraction on the border of isotropic and anisotropic medium with magnetoelectric effect based on the matricant method. Initial relationships that describe electromagnetic wave propagation in anisotropic magnetoelectric medium are reduced to the system of linear homogeneous first order differential equations. The structure of the matricant is obtained. Dispersion equations of electromagnetic waves in periodic inhomogeneous medium with magnetoelectric effects are constructed. Averaged matricant describing the propagation of electromagnetic waves in homogeneous anisotropic medium with magnetoelectric medium are also constructed. Besides, the graphs of energy reflection coefficient of TE and TM electromagnetic waves and incident angle are plotted.