Band structure of absorptive photonic crystals

Citation
A. Tip et al., Band structure of absorptive photonic crystals, J PHYS A, 33(35), 2000, pp. 6223-6252
Citations number
34
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
33
Issue
35
Year of publication
2000
Pages
6223 - 6252
Database
ISI
SICI code
0305-4470(20000908)33:35<6223:BSOAPC>2.0.ZU;2-D
Abstract
The band structure of absorptive dielectric photonic crystals is investigat ed. Provided the frequency-dependent electric permeability epsilon(x, omega ) satisfies certain analyticity requirements as a function of frequency, we show that no bandgaps exist in frequency regions where absorption takes pl ace, i.e. where epsilon(x, omega) has a non-zero imaginary part. In this ca se real eigenvalues of the Helmholtz operator in the Bloch-decomposed forma lism are absent. Using a suitable analytic continuation procedure, we find that the former change into resonances, i.e. complex numbers depending on k , the wavevector from the first Brillouin zone, thus leading to complex ban ds in the lower half plane. This is confirmed numerically for a simple, one -dimensional example.