Abstract
The application of the mode-matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, and the modes of each cell are calculated by an alternative formulation of the plane-wave expansion (PWE) method. This formulation allows the calculation of both guided and evanescent modes at a given frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and the end of the structure. The accuracy of the MM method is compared to the finite-difference frequency-domain (FDFD) method and the finite-difference time-domain (FDTD) method, and good agreement is observed. The MM method requires far fewer resources than the FDFD and the FDTD methods while providing a useful physical insight to the calculation of the frequency response of waveguide discontinuities. The method is also applied to the calculation of power loss due to structural fabrication-induced variations.
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