On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals
(2010) In Mathematical Models and Methods in Applied Sciences 20(8). p.1319-1341- Abstract
We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational operator-valued function in terms of a polynomial... (More)
We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational operator-valued function in terms of a polynomial operator pencil and study two-component dispersive and absorptive crystals in detail.
(Less)
- author
- EngstrÖm, Christian LU
- publishing date
- 2010-08
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bloch wave, Floquet theory, Maxwell's equations, nonlinear eigenvalue problem, operator pencil, photonic crystal
- in
- Mathematical Models and Methods in Applied Sciences
- volume
- 20
- issue
- 8
- pages
- 23 pages
- publisher
- World Scientific Publishing
- external identifiers
-
- scopus:77956611203
- ISSN
- 0218-2025
- DOI
- 10.1142/S0218202510004611
- language
- English
- LU publication?
- no
- id
- 650b29b7-9abd-4d47-af15-134173482132
- date added to LUP
- 2023-03-24 11:16:15
- date last changed
- 2023-03-24 15:09:14
@article{650b29b7-9abd-4d47-af15-134173482132,
abstract = {{<p>We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational operator-valued function in terms of a polynomial operator pencil and study two-component dispersive and absorptive crystals in detail.</p>}},
author = {{EngstrÖm, Christian}},
issn = {{0218-2025}},
keywords = {{Bloch wave; Floquet theory; Maxwell's equations; nonlinear eigenvalue problem; operator pencil; photonic crystal}},
language = {{eng}},
number = {{8}},
pages = {{1319--1341}},
publisher = {{World Scientific Publishing}},
series = {{Mathematical Models and Methods in Applied Sciences}},
title = {{On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals}},
url = {{http://dx.doi.org/10.1142/S0218202510004611}},
doi = {{10.1142/S0218202510004611}},
volume = {{20}},
year = {{2010}},
}