Localization of light and second-order nonlinearity enhancement in weakly disordered one-dimensional photonic crystals

We show how one-dimensional photonic crystal structures which suffer from a weak random disorder in the layer lengths may give rise to strong localization of light. Using the transfer matrix method we numerically study the effects of this localization in media with a second-order nonlinearity. Localization has a deep impact on the second-harmonic generation efficiency and may give rise to very strong enhancement in correspondence to the localized wavelengths.