Analysis on transmission characteristics of nested ring resonators

Abstract

The transmission characteristics of the nested ring resonator are analyzed. The intensity transmission of the resonator is obtained. Based on this, the critical coupling and coupled-resonator-induced transparency conditions are derived as length ratio of the U-shaped loop and the inner circle ring is an integer or half-integer. Accurate expressions of these two conditions are provided. Numerical calculation at some specific parameters verifies the conditions and demonstrates their variations vs. parameters of the resonator.