On the Effectiveness of Coupled Mode Theory in the Analysis of Photonic Crystal Coupled Resonator Devices

Coupled resonator photonic crystal devices may find important applications in future integrated nanophotonic circuits. These devices are well suited for coupling of mode analysis, which usually requires much less computational resources compared with finite-difference time domain (FDTD) schemes. Coupled mode models also provide a useful physical insight in the device operation. In this paper, we present a general coupled mode theoretic model for the treatment of coupled cavity devices incorporating various phenomena such as dispersion, frequency variation of the coupling coefficients, nonadjacent cavity coupling, and waveguide mode self coupling. The model is validated comparing its results against the FDTD method and the strength of the underlying assumptions is highlighted. Various approximations that can lead to further simplification of the coupled mode model are also discussed. It is shown that, unless the device transfer function possesses very sharp resonances, coupled mode analysis can provide an accurate device description.