Abstract
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.
Original language | English (US) |
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Article number | 15 |
Journal | Research in Mathematical Sciences |
Volume | 7 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2020 |
Bibliographical note
Publisher Copyright:© 2020, Springer Nature Switzerland AG.
Keywords
- Bloch waves
- Eigenfunction expansions
- Metallic optical material
- Photonic band gaps
- Spectral theory