<title>Exact numerical technique for the analysis of Bragg reflectors in integrated optical filters</title>

Abstract

We present an exact numerical technique for analyzing Bragg reflectors. Bragg reflectors can be used as narrow-band distributed feedback reflectors that reflect at the center of the grating stopband and transmit at frequencies to either side. THese reflectors can be sued as highly selective pass-band filters. These reflectors can be also used as highly selective pass-band filters. Our structure that is realized by the LEAME consists of microcavities inserted in a waveguide suspended in air. These cavities ar air voids placed periodically in a high-refractive index semiconductor material. Recently Zhang et al. realized a broad-band Bragg reflector by placing a 1D array of air holes in a dielectric waveguide without taking into account the power loss in their simulation. Power loss due to radiation at abrupt discontinuities limits the performance of these microcavities.Unlike the other analytical methods no physical approximations are made throughout the entire analysis, so it may be used to analyze any periodic dielectric structure regardless of the geometry or strong discontinuities. Our exact technique uses the local normal modes of the structure to form a transfer matrix for the whole structure. For this reason our method can be used to evaluate exactly the transmitted, reflected and radiated power. We will present later the result of the numerical simulations for a Bragg reflector with few steps.