Cascaded Second Harmonic Generation with a Half-Order Periodical Orientation

Abstract

We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.