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30 September 2003 Modeling of 2-D photonic crystals using the layer-by-layer method and 'fast Fourier factorization' rules
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Abstract
A method for calculating the transmission of a two-dimensional (2D) photonic crystal (PhC) of finite extent is presented. The 2D PhC is regarded as a collection of identical quasi-1D diffraction gratings stacked in the propagation direction. The dielectric permittivity profile of a grating is arbitrary in general and can be approximated with a staircase, by dividing it in slices. For each slice, a 1D eigenvalue problem is solved, using Fourier expansions and 'fast Fourier factorization' rules. A fixed frequency is considered at a time, and propagation constants are calculated. Wave propagation from one slice to the next one is described by a scattering matrix algorithm that emerges from continuity of field tangential components at interfaces. The method described has the following advantages: dimension of the eigenvalue problem is reduced, convergence is improved, and material dispersion can be taken into account. Results for 2D photonic crystals composed of square and circular shaped rods are shown and discussed.
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Cazimir-Gabriel Bostan and Rene M. de Ridder "Modeling of 2-D photonic crystals using the layer-by-layer method and 'fast Fourier factorization' rules", Proc. SPIE 5227, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies, (30 September 2003); https://doi.org/10.1117/12.519894
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