High-quality cavities in hybrid material systems have various interesting applications. We perform a comprehensive modeling comparison on such a design, where confinemen in the III-V material is provided by gradual photonic crystal tuning, a recently proposed method offering strong resonances. The III-V cavity couples to an underlying silicon waveguide. We report on the device properties using four simulation methods: finite-di ference time-domain (FDTD), finite-elemen method (FEM),

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... l eigenmode propagation (BEP) and aperiodic rigorous coupled wave analysis (aRCWA). We explain the major confinemen and coupling effects, consistent with the simulation results. E.g. for strong waveguide coupling, we fin quantitative discrepancies between the methods, which establishes the proposed high-index-contrast, lossy, 3D structure as a challenging modeling benchmark. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001),