Spectral and scattering theory of one-dimensional coupled photonic crystals

Abstract

We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods in a two-Hilbert spaces setting, we determine the nature of the spectrum and prove the existence and completeness of the wave operators of the system.

31 pages, 1 figure. Keywords: Spectral theory, scattering theory, Maxwell operators, commutator methods. [v3] revised version to appear in Reviews in Mathematical Physics