Resonances of a finite one-dimensional photonic crystal with a defect (Q2841013)

This work studies the resonances of a bounded one-dimensional dielectric medium that is modelled using the scalar wave equation. The medium is assumed to consist of layers with constant material properties that are periodically arranged with the exception of a defect layer around the origin. The main result is that for each element of the point spectrum of an infinite layered structure there exists a resonance of the bounded structure in close distance. This distance is also shown to decay exponentially as a function of the number of the periodic layers. Furthermore, the result motivates a numerical method to approximate these resonances.