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.
