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On the spectrum of ...
On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals
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- Engström, Christian (författare)
- ETH Zurich, Switzerland,ETH Zurich, Seminar for Applied Mathematics
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(creator_code:org_t)
- World Scientific, 2010
- 2010
- Engelska.
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 20:8, s. 1319-1341
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Annan matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Other Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Bloch wave
- Floquet theory
- operator pencil
- nonlinear eigenvalue problem
- Maxwell's equations
- photonic crystal
- Matematik
- Mathematics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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