Resonances of a finite one-dimensional photonic crystal with a defect

This paper is concerned with the scattering resonances of a layered dielectric medium of finite extent. The photonic structure consists of a finite number of periodic layers and some defect embedded in the interior. It is proved that there exist resonances that are close to the point spectrum of an infinite layered structure. Moreover, the distance between such near bound-state resonances and the point spectrum decays exponentially as a function of the number of the periodic layers. A simple numerical method is also presented to calculate the near bound-state resonances accurately.