Tight-binding method modelling of photonic crystal waveguides
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.
Key wordsphotonic band gap photonic crystal tight-binding Wannier function waveguide
- Soukoulis, C. M., (ed.)Photonic BandGaps and Localization. Plenum, New York, 1993;Photonic Band Gap Materials, ed. CM. Soukoulis. Kluwer, Dordrecht, 1996.Google Scholar