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A perturbation approach for near bound-state resonances of photonic crystal with defect

Published online by Cambridge University Press:  09 July 2015

J. LIN
J. LIN*
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA email: jzl0097@auburn.edu
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Abstract

This paper is concerned with scattering resonances of a 1D photonic crystal of finite extent. We propose a general perturbation approach to study the resonances that are close to the bound-state frequency of the infinite structure when some defect is embedded in the interior. It is shown that near bound-state resonances exist on the complex plane and the distance between the resonance and the associated bound-state frequency decays exponentially as a function of the number of periodic cells. A numerical approach based upon the perturbation theory is also proposed to calculate the near bound-state resonances accurately.

Keywords

photonic crystalscattering resonancesHelmholtz equation

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 66 - 86
Copyright
Copyright © Cambridge University Press 2015 

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