Abstract
We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics, the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority of this method over plane wave based techniques.
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D’yerville, M.L.V., Monge, D., Cassagne, D. et al. Tight-binding method modelling of photonic crystal waveguides. Opt Quant Electron 34, 445–454 (2002). https://doi.org/10.1007/BF02892609
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DOI: https://doi.org/10.1007/BF02892609