# Spectral and scattering theory of one-dimensional coupled photonic crystals

## TL;DR

This paper investigates the spectral and scattering properties of light in coupled one-dimensional photonic crystals, providing a rigorous mathematical framework for understanding wave transmission and the system's spectral characteristics.

## Contribution

It introduces a novel analytical approach using commutator methods in a two-Hilbert space setting to analyze coupled photonic crystal systems.

## Key findings

- Determines the nature of the spectrum for coupled photonic crystals.
- Proves the existence and completeness of wave operators in the system.
- Provides a rigorous mathematical foundation for light transmission analysis.

## 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.