On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals
2010 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 20, no 8, 1319-1341 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 20, no 8, 1319-1341 p.
Bloch wave, Floquet theory, operator pencil, nonlinear eigenvalue problem, Maxwell's equations, photonic crystal
IdentifiersURN: urn:nbn:se:umu:diva-51434DOI: 10.1142/S0218202510004611OAI: oai:DiVA.org:umu-51434DiVA: diva2:481876