Band structure and reflectivity of omnidirectional Si-based mirrors with a Gaussian profile refractive index

Abstract

Using the transfer matrix method we calculate the band structure for a one-dimensional photonic crystal consisting of alternating layers of two dielectric materials A and B with refractive indices nA and nB, respectively. The refractive index of layer A is constant and the refractive index for layer B varies according to the envelope of a Gaussian function. We find that under certain circumstances it is possible to obtain a 100% reflectivity for both polarizations (TE and TM) and any value of the incident angle of the electromagnetic waves. The interval of maximum reflectivity coincides with the photonic band gap of the structure. By an adequate selection of the parameters forming the structure, it is possible to tune the interval of frequencies with maximum reflectivity. This could be used in the fabrication of the so-called omnidirectional mirrors.