Integral equation analysis of microring and microdisk coupled-resonator optical waveguides

We present a rigorous integral equation (IE) method for analyzing propagation in microring and microdisk coupled-resonator optical waveguides (MR/MD-CROWs). The approach is based on Green's theorem to formulate the IE for the axial field component and the Galerkin technique to obtain a homogeneous linear system between the expansion coefficients of the resonator field in terms of cylindrical wave functions. The CROW propagation constants are determined by the nontrivial solutions of the system. TE and TM polarizations are treated in parallel. Examples for single-mode MR and whispering gallery mode (WGM) MD-CROWs are presented, including coupling with WGMs of higher radial order