Photonic bandgap calculations with Dirichlet-to-Neumann maps
A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wav...
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| Published in | Journal of the Optical Society of America. A, Optics, image science, and vision Vol. 23; no. 12; p. 3217 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
01.12.2006
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| Online Access | Get more information |
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| Summary: | A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wave vector. A linear matrix eigenvalue problem is obtained even when the medium is dispersive. For photonic crystals composed of a square lattice of parallel cylinders, the DtN map is obtained by a cylindrical wave expansion. This leads to eigenvalue problems for relatively small matrices. Unlike other methods based on cylindrical wave expansions, sophisticated lattice sums techniques are not needed. |
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| ISSN: | 1084-7529 1520-8532 |
| DOI: | 10.1364/JOSAA.23.003217 |