FULL-WAVE ANALYSIS OF COUPLED WAVEGUIDES IN A TWO-DIMENSIONAL PHOTONIC CRYSTAL

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Abstract
It is shown that the modal analysis of coupled waveguides in a two-dimensional photonic crystal can be reduced to the evaluation of natural frequencies of an equivalent network. This network is constituted of ideal transmission lines and transformers and is directly derived from Maxwell's equations without any simplifying assumptions. The natural frequencies of the proposed equivalent network are computed after its subdivision into a series of cascaded sub-networks. These sub-networks are then described by their multi- port impedance matrices so that the entire network can be described by the cascaded connection of these matrices. Resonance conditions of this cascaded connection yield the natural frequencies and consequently the propagation constants of various modes of the original coupled photonic-crystal waveguides. Under the resonance condition, the voltages and currents of the equivalent network are nonzero, and they can be used to determine all the field components of the corresponding mode. The obtained numerical results verify the fact that the coupling length of photonic-crystal directional couplers can be reduced considerably.