In this paper, a general methodology for the design of higher order coupled resonator filters in photonic crystals (PCs) is presented. In the proposed approach, the coupling between resonators is treated as though it occurs through a waveguide with an arbitrary phase shift. The coupling through the waveguide is analyzed theoretically, based on the coupled-mode theory in time. The derived theoretical model suggests a way to extend an equivalent circuit approach, previously demonstrated with a certain value of a phase shift, to the higher order filter design with an arbitrary phase shift. The validity of the proposed approach is confirmed by the design of a third-order Chebyshev filter having a center frequency of 193.55 THz, a flat bandwidth of 50 GHz, and ripples of 0.3 dB in the passband. The characteristics of the designed filter are suitable for wavelength-division-multiplexed (WDM) optical communication systems with a 100-GHz channel spacing. The performance of the designed filter is numerically calculated using the two-dimensional (2-D) finite-difference time-domain (FDTD) method.
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