Localized modes in one-dimensional nonlinear periodic photonic structures

We study the generation of localized second-harmonic modes in a one-dimensional photonic crystal with a defect in the form of a phase slip. Due to the presence of the defect the photonic crystal has localized in-gap modes. We consider the case when the fundamental mode is localized in the first bandgap and because of its nonlinear properties it generates a localized second-harmonic mode. As a function of the parameters of the photonic crystal and the defect the intensity of the second-harmonic mode has sharp maxima, which correspond to the resonance condition, i.e. the frequency of the second-harmonic mode is equal to the frequency of the localized mode in the second bandgap. We find the conditions when such resonance can be achieved. We also determine the optimal parameters of the photonic crystal at which the generation of the second-harmonic mode becomes less sensitive to violation of the resonance condition.