“Transfer matrix” method for direct and indirect coupling of cascaded cavities in resonator-waveguide systems

Using formalism similar to the transfer matrix, we analyze the problem of direct and indirect coupling of cascaded cavities in resonator-waveguide systems based on the temporal coupled-mode theory. The recurrence relations between modes supported by the cascaded cavities are established by using transfer matrix technique. By setting two auxiliary cavities as the start and termination conditions, the optical properties of the cascaded cavity system can be obtained, especially convenient to get the transmission properties. We validate our method by comparing its prediction with the finite-difference time-domain method in a channel drop filter system in photonic crystals and obtaining excellent agreement between the two. The new analytical method provides a powerful tool to design and analyze complex cavity-waveguide systems.