Photonic band gap phenomenon in a metal–dielectric periodic structure
| Autor: | Hai Zhang, Fadil Santosa |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Permittivity
Spectral theory Applied Mathematics 010102 general mathematics Eigenfunction 01 natural sciences Drude model Theoretical Computer Science 010101 applied mathematics Computational Mathematics Mathematics (miscellaneous) Quantum mechanics Group velocity 0101 mathematics Eigenvalues and eigenvectors Photonic crystal Mathematics Bloch wave |
| Zdroj: | Research in the Mathematical Sciences. 7 |
| ISSN: | 2197-9847 2522-0144 |
| DOI: | 10.1007/s40687-020-00211-w |
| Popis: | We study the photonic band structure of a metal–dielectric periodic structure. The metallic component is described by the Drude model; therefore, the electric permittivity is frequency dependent, i.e., dispersive. Rather than solving a nonlinear eigenvalue problem for the band structure of the material, we follow a time-dependent formulation described in Raman and Fan (Phys Rev Lett 104:087401, 2010) which leads to a linear eigenvalue problem. At issue is the question of completeness of the eigenfunctions, which is claimed but not proven in Raman and Fan (2010). We establish completeness in one dimension. We further describe the existence of accumulation points in the spectrum that lead to an infinite family of ‘zero group velocity’ waves. Numerical calculations illustrate some of the main ideas of this work. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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