Matrix solution 4x4 by the Wentzel-Kramers-Brillouin method for electromagnetic waves reflected on the boundary of inhomogeneous chiral layer

The propagation of a plane electromagnetic wave in a plane inhomogeneous chiral medium with oblique incidence is considered. The chirality parameter varies with the distance from the boundary. The problem reduces to solving a system of the ordinary differential equations (ODE) with variable coefficients 4x4. The solution was obtained by the Wentzel-Kramers-Brillouin method in the matrix form. We found a fundamental solution matrix and a Cauchy matrix for a chiral inhomogeneous medium with continuously varying properties along one of the coordinates. The dependence of the absolute values of the matrix coefficients of reflection and cross-polarization components on the reflection from the profile of the chirality parameter and the angle of incidence is shown.