Electrodynamic properties of a magnetic fine-stratified structures

Let us consider an infinite periodic structure where semiconductor layers of thickness d1 and dielectric layers of thickness d2 alternate. We ignore the collision frequency in the semiconductor layers and losses in dielectric. We introduce a coordinate system such that the x axis is parallel to the boundaries of the layers and z axis is perpendicular to the layers. We will assume that the structure is homogeneous in the x and y directions and put ∂/∂y = 0 , omitting the dependence on the coordinate y in the equations. Let the structure be exposed to an external magnetic field parallel to the y axis (see Fig.1). Then, Maxwell's equations split into independent equations for two modes with different polarization. External magnetic field doesn't affect the properties of H-waves therefore we will consider E-waves with components Ex, Ez, Ey.