Počet záznamů: 1
Spectral analysis of photonic crystals made of thin rods
- 1.0494798 - ÚJF 2019 RIV NL eng J - Článek v odborném periodiku
Holzmann, M. - Lotoreichik, Vladimir
Spectral analysis of photonic crystals made of thin rods.
Asymptotic Analysis. Roč. 110, 1-2 (2018), s. 83-112. ISSN 0921-7134. E-ISSN 1875-8576
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: Photonic crystals * spectral gaps * inverse problem * thin rods * electromagnetic waves * TE- and TM-modes * periodic differential operators * perturbation theory * Floquet-Bloch analysis * point interactions
Obor OECD: Pure mathematics
Impakt faktor: 0.808, rok: 2018
In this paper we address the question how to design photonic crystals that have photonic band gaps around a finite number of given frequencies. In such materials electromagnetic waves with these frequencies can not propagate. This makes them interesting for a large number of applications. We focus on crystals made of periodically ordered thin rods with high contrast dielectric properties. We show that the material parameters can be chosen in such a way that transverse magnetic modes with given frequencies can not propagate in the crystal. At the same time, for any frequency belonging to a predefined range there exists a transverse electric mode that can propagate in the medium. These results are related to the spectral properties of a weighted Laplacian and of an elliptic operator of divergence type both acting in L-2 (R-2). The proofs rely on perturbation theory of linear operators, Floquet-Bloch analysis, and properties of Schrodinger operators with point interactions.
Trvalý link: http://hdl.handle.net/11104/0287858
Počet záznamů: 1