Mr. Matthias H. Schillinger Profile

Matthias H. Schillinger

PhD Student at Univ Karlsruhe

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Proceedings Article | 13 April 2005 Paper

Highly localized Wannier functions for the efficient modeling of photonic crystal circuits

Matthias Schillinger, Sergei Mingaleev, Daniel Hermann, Kurt Busch

Proceedings Volume 5733, (2005) https://doi.org/10.1117/12.591137

KEYWORDS: Waveguides, Systems modeling, Photonic crystals, Dispersion, Dielectrics, Waveguide modes, Liquid crystals, Beam splitters, Matrices, Refractive index

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We present a novel approach for the accurate and efficient modeling of photonic crystal-based integrated optical circuits. Within this approach, the electromagnetic field is expanded into an orthogonal basis of highly localized Wannier functions, which reduces Maxwell's equations to low-rank eigenvalue problems (for defect mode and waveguide dispersion calculations) or to sparse systems of linear equations (for transmission/reflection calculations through/from functional elements). We illustrate the construction of Wannier functions as well as the subsequent determination of defect modes, waveguide dispersion relations, and the characterization of functional elements for realistic two-dimensional photonic crystal structures consisting of square and triangular lattices of air pores in a high-index matrix. Moreover, on the basis of our Wannier function calculations we suggest a novel type of broad-band integrated photonic crystal circuits based on the infiltration of low-index materials such as liquid crystals or polymers into individual pores of these systems. We illustrate this concept through the design of several functional elements such as bends, beam splitters, and waveguide crossings.

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