Modeling of discontinuities in photonic crystal waveguides with the multiple multipole method

A method for the simulation of discontinuities in photonic crystal defect waveguides is presented. This frequency domain technique is based on the multiple multipole method. In contrast with other known techniques, spurious reflections (due to the impedance mismatch at the waveguide terminations) are avoided. The absence of spurious reflections allows one to characterize precisely the intrinsic behavior of the sole discontinuity, reducing at the same time the size of the simulation domain. To achieve a perfect impedance matching, the guided modes of infinitely long waveguides corresponding to the input and output channels of the discontinuity are first computed using a supercell approach. Then, the discontinuity is fed with one of the previously computed modes, and the fields transmitted or reflected towards the discontinuity arms are matched to the modal fields corresponding to each output waveguide. This method allows one to compute the intrinsic transmission and reflection coefficients of the discontinuity (i.e., coefficients not altered by additional effects such as finite crystal size, etc.). The procedure is presented in detail using some simple discontinuities as test cases. Then, it is applied to the computation of the coupling from a waveguide to free space and for the analysis of a filtering T junction.