Tight-Binding Wannier Function Method for Photonic Band Gap Materials
Using the concept of generalized Wannier functions, adapted form the electronic theory of solids, we demonstrate for two-dimensional photonic crystals the existence of a localized state basis and we establish an efficient computational method allowing a tight-binding-like parameter free modelization of any dielectric structure deviating from periodicity. Examples of numerical simulations using this formalism, including modal analysis of microcavities and waveguides and calculations of the transmission coefficients are presented to prove the ability of this approach to deal accurately with large scale systems and complex structures.
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- 3.See for example Photonic Band Gaps and Localization, edited by C. M. Soukoulis (Plenum, New York, 1993); Photonic Band Gap Materials, edited by C. M. Soukoulis (Kluwer, Dordrecht, 1996).Google Scholar
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- 6.Generalized Wannier functions which are referred in the text as Wannier functions for simplicity constitute for a group of interlacing bands the equivalent of the elementary Wannier functions defined in the case of isolated bands. These site centered functions span the same space as the Bloch functions and are symmetry adapted to the point group of the crystal. For their definition and properties see Des Cloiseaux7 and Kohn.8 Google Scholar
- 13.We refer here to the difficulties associated with the evaluation of matrix elements at the interface between two materials where, in the empirical TB method, ad hoc weighting rules have to be considered.Google Scholar