Exact analytical solution for the electromagnetic wave propagation in a photonic band gaps material with sinusoidal periodicity of dielectric permittivity

Abstract We used an exact analytical approach to investigate the propagation of the electromagnetic wave through a photonic band gaps material with sinusoidal periodicity of a dielectric permittivity. Mathieu's functions are used to obtain the solution of Maxwell equations in the structure for the nonzero angle of incidence wave. The analytical expression of the transmittance and the distribution of the electric field inside the structure are given.