Accuracy of coupled-mode theory and mode-matching method in the analysis of photonic crystal waveguide perturbations

In this paper, the accuracy of coupled-mode theory (CMT) and mode-matching (MM) method in estimating the scattering due to geometric perturbations in photonic crystal waveguides (PCWs) is examined. Two CMT formulations are considered: 1) the instantaneous virtual grating and 2) the conventional CMT. The two CMT formulations and the MM method are compared against the finite-difference frequency-domain (FDFD) method combined with the adjoint variable (AV) method. The results obtained with the AV/FDFD and MM methods agree very well, proving the validity of the latter for the sensitivity analysis of PCW structures. It is also deduced that although both CMT formulations lead to almost identical results, they can provide only a first approximation to the perturbation-induced scattering.