Spectral analysis of metamaterials in curved manifolds
Year: 2024
Type: article
Abstract: Negative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with operators encountered in an operator-theoretic description of metamaterials. First, we introduce an indefinite Laplacian and consider it on a compact tubular neighbourhood in constantly curved compact two-dimensional Riemannian ambient manifolds, with Euclidean rectangle in R 2 being present as a special case. As this operator is not semi-bounded, standard form-theoretic methods cannot be applied. We show that this operator is (essentially) self-adjoint via separation of variables and find its spectral characteristics. We also provide a new method for obtaining alternative definition of the self-adjoint operator in non-critical case via a generalized form representation theorem. The main motivation is existence of essential spectrum in bounded domains.
Author: Tomáš Faikl
Institution: Czech Technical University in Prague
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
OpenAlex ID: W4405269557