Localized modes in one-dimensional nonlinear periodic photonic structures

Abstract

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