Spectral analysis of photonic crystals made of thin rods

0494798 - ÚJF 2019 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Photonic crystals * spectral gaps * inverse problem * thin rods * electromagnetic waves * TE- and TM-modes * periodic differential operators * perturbation theory * Floquet-Bloch analysis * point interactions
OECD category: Pure mathematics
Impact factor: 0.808, year: 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.
Permanent Link: http://hdl.handle.net/11104/0287858