Reflectivity calculated for a 3D silicon photonic band gap crystal with finite support

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TitleReflectivity calculated for a 3D silicon photonic band gap crystal with finite support
Publication TypeJournal Article
Year of PublicationIn Press
List number


AuthorsD. Devashish, S. B. Hasan, J. J. W. van der Vegt, and W. L. Vos
JournalPhys. Rev. B
Keywordsfinite element method, finite size effects, photonic band gap, photonic crystal, photovoltaics, polarization



We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap, with the aim to interpret recent experiments. We employ the finite element method to study crystals with the cubic diamond-like inverse woodpile structure. The high-index
backbone has a dielectric function similar to silicon. We study crystals with a range of thicknesses up to ten unit cells (L.le.10c). The crystals are surrounded by vacuum, and have a finite support as in experiments. The polarization-resolved reflectivity spectra reveal Fabry-Perot fringes related to standing waves in the finite crystal, as well as broad stop bands with nearly 100 % reflectivity, even for thin crystals. From the strong reflectivity peaks, it is inferred that the maximum reflectivity observed in experiments is not limited by finite size. The frequency ranges of the stop bands are in excellent agreement with stop gaps in the photonic band structure, that pertain to infinite and perfect crystals. The frequency ranges of the observed stop bands hardly change with angle of incidence, which is plausible since the stop bands are part of the 3D band gap. Moreover, this result supports the previous assertion that intense reflection peaks measured with a large numerical aperture provide a faithful signature of the 3D photonic band gap. The Bragg attenuation lengths
L_B exceed the earlier estimates based on the width of the stop band by a factor 6 to 9. Hence crystals with a thickness of 12 unit cells studied in experiments are in the thick crystal limit (L >> L_B). In our calculations for p-polarized waves, we also observe an intriguing hybridization of the
zero reflection of Fabry-Perot fringes and the Brewster angle, which has not yet been observed in experiments.

z_arxiv2016devashish1609-01112FEM_reflectivity_3D_xtal.pdf4.04 MB