Estruturas de bandas e propriedades de simetria dos modos eletromagnéticos em um cristal fotônico unidimensional

Abstract

We perform in this work, through the techniques of transfer matrix, an analytical study of the photonic band structure and the density of states of a one dimensional photonic crystal consisting of a super-lattice composed by two alternating layers of air and GaAs of thicknesses a and the b, respectively. We find photonic band gaps, as expected, and also null gap points. We study the reflectivity and the transmissivity of the electromagnetic field through the structure. We further analyze the symmetry properties of the solutions for the electromagnetic field and find that, in general, these solutions have a well defined parity except at the null gap points where there are degeneracies. At these points we show that the phase difference between the various waves, reflected at all interfaces, interfere destructively so that, in contrast with the Bragg mirrors, the incident wave is efficiently transmitted through the structure.