Role of a localized modulation of χ(2) in Cerenkov second-harmonic generation in nonlinear bulk medium

We study the second-harmonic generation in quadratic nonlinear media with localized spatial modulation of chi((2)) response. We demonstrate that the emission of Cerenkov second-harmonic takes place only when the fundamental beam illuminates the region of chi((2)) variation. This proves that the sharp modulation of the chi((2)) nonlinearity constitutes a sufficient condition for the emission of Cerenkov second harmonic in bulk materials. Our calculations are in excellent agreement with simple analytical approach utilizing the concept of reciprocal vectors representing the Fourier spectrum of the modulation of chi((2)). (C) 2012 Optical Society of America