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scattering resonances

European Journal of Applied Mathematics (1)

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A perturbation approach for near bound-state resonances of photonic crystal with defect
J. LIN
Journal:

European Journal of Applied Mathematics / Volume 27 / Issue 1 / February 2016

Published online by Cambridge University Press:

09 July 2015, pp. 66-86
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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.