Progress In Electromagnetics Research B · 2008 · 13 citations · 9 references
Natural SciencesElectrical EngineeringMaterials ScienceComputational ElectromagneticsOptical MaterialsPhotonicsDielectricsPeriodic Structure AnalysisPhotonic CrystalsPhotonic Device SimulationPhotonic MaterialsPropagation In Dielectric MediaBand GapBand Gap DeterminationBand Structure In Dielectric MediaPhotonic Band StructurePhotonic Crystal AnalysisPhotonic Crystal ModelingPhotonic Crystal SimulationQr Decomposition
An effective computational method based on a conven- tional modal expansion approach is presented for handling a multilay- ered dielectric grating whose profiles are multilayered and sinusoidally modulated. This structure fabricated by dielectric material is one of the useful photonic crystals. The method is based on Yasuura's modal expansion, which is known as a least-squares boundary residual method or a modified Rayleigh method. In the extended method, each layer is divided into shallow horizontal layers. The Floquet modal func- tions and approximate solutions are defined in each shallow layer, and the latter are matched with boundary conditions in the least-squares sense. A huge-sized least-squares problem that appears in finding the modal coefficients is solved by the QR decomposition accompanied by sequential accumulation. This procedure makes it possible to treat the case where the groove depths are the same as or a little more than the grating period. As numerical example, we calculate a diffractive char- acteristic by a multilayered deep dielectric grating and confirm that a common band gap occurs for both polarizations.
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