Berlin 2008 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 27: Photonic crystals III

HL 27.3: Talk

Tuesday, February 26, 2008, 16:30–16:45, EW 203

Efficiency optimization for constructing maximally localized Wannier functions — •Tobias Stollenwerk, Dmitry N. Chigrin, and Johann Kroha — Physikalisches Institut, Universität Bonn, Nussallee 12, 53115 Bonn, Germany

The Wannier function approach is well suited for the description of photonic crystal based structures. The efficiency of this approach crucially depends on the degree of localization of the Wannier functions in real space. Due to the phase indeterminacy of the Bloch functions the problem of obtaining maximally localized Wannier functions is reduced to the problem of finding an optimal set of phases and is an optimization problem in parameter space of large dimensionality. In that respect, questions like, definition of the locality criterion or the choice of the optimization method, are of great importance.

We have systematically analyzed maximally localized Wannier functions of two-dimensional square and triangular lattice photonic crystals for both fundamental polarizations. Two definitions of the locality criterion have been introduced, namely the integrated modulus in the first unit cell and the second moment of the Wannier function. We have used the standard conjugate gradient optimization scheme as well as a genetic algorithm based stochastic algorithm to solve the optimization problem. We report on "pros-and-cons" of the different locality criteria and optimization methods applied to the problem of constructing maximally localized Wannier functions in photonic crystals.