Floquet-Bloch Theory for Semiconductor Bragg Structure

The problem of Floquet-Bloch waves propagation in a semiconductor magnetophotonic crystal with a transverse magnetic field was solved. The fundamental solutions of the Hill equation in layers that based on the Floquet theory were obtained in an analytical form. The dispersion equation and its roots are found explicitly. The analysis of the dispersion properties of the structures depending on the material parameters of the layers was carried out. The parameters of gyrotropic layers for the full transmission and reflection of a plane wave for different frequencies through a limited magnetophotonic crystal in modes of surface and bulk waves are determined.