Bloch analysis of finite periodic microring chains

Abstract

We apply Bloch analysis to the study of finite periodic cascading of microring resonators. Diagonalization of the standard transfer matrix approach not only allows one to find an exact analytic expression for transmission and reflection, but also to derive a closed form solution for the field in every point of the structure. To gain more physical insight we have analyzed the main features of the transmission resonances in a finite chain and we have given some hints for their experimental verification.