Analytical modelling of semi-infinite electromagnetic crystal's excitation by plane electromagnetic wave

We introduce analytical theory for the excitation of a semi-infinite electromagnetic crystal by a plane electromagnetic wave. We consider a three-dimensional crystal with an orthorhombic elementary cell formed by scatterers which can be substituted by point dipoles with known polarizability and fixed orientation. The reflection coefficient, amplitudes of excited modes and Floquet harmonics of the diffracted field for the semi-infinite electromagnetic crystal are derived through solutions of the dispersion equation for an infinite electromagnetic crystal.