Fast-multipole analysis of electromagnetic scattering by photonic crystal slabs

In this paper, a multilevel fast-multipole algorithm (MLFMA) for simulating electromagnetic-wave propagation in photonic-crystal (PhC)-slab devices is presented. The scheme accelerates the 3-D multiple-scattering technique (MST) for characterizing open PhC-slab devices comprising air holes in multilayered stacks proposed in a recent work by Boscolo and Midrio. This 3-D MST 1) truncates open PhC-slab devices by conductor-backed perfectly matched layers, 2) expands total fields in the resulting closed structures in terms of discrete radial modes of the associated closed slab waveguides, and 3) uses scattering tensors to evaluate air-hole interactions. Here, this last step is accelerated using a hybrid MLFMA that leverages low- and high-frequency fast-multipole constructs in conjunction with a mode-trimming feature. The computational complexity of the resulting hybrid MLFMA-MST scales almost linearly in the number of air holes, thereby enabling the analysis of electromagnetically large PhCslab devices on readily available computer hardware. The scheme is applied to the analysis of a variety of practical PhC-slab devices, including a straight PhC-slab waveguide, a couple of bended PhC-slab waveguides, and a large PhC-slab coupler.