Theory of noncollinear frequency doubling of transform limited pulses in non-steady-state regime

Abstract

We consider non-collinear second harmonic generation from two ultrashort pulses intersecting in a nonlinear medium in spectral and time domains. We derive analytical expressions for the second harmonic amplitude in crystals of finite thickness and obtain a refined phase-matching condition. The contribution from characteristics of the fundamental radiation and interaction geometry to the process is analyzed. We find that the spectral bandwidth is determined by the intersection angle and can be enlarged. The SH pulse duration can be optimized by varying the fundamental beam size and the intersection angle. It is shown that the fundamental pulse duration can be readily characterized with single pulses by means of measuring the second harmonic beam profile. The approach developed can potentially be used to calculate parametric interactions in one-and two-dimensional nonlinear photonic crystals.