Accurate switching intensities and length scales in quasi-phase-matched materials

We consider unseeded type I second-harmonic generation in quasi-phase-match ed quadratic nonlinear materials and derive an accurate analytical expressi on for the evolution of the average intensity. The intensity dependent nonl inear phase mismatch that is due to the cubic nonlinearity induced by quasi phase matching is found. The equivalent formula for the intensity of maxim um conversion, the crossing of which changes the one-period nonlinear phase shift of the fundamental abruptly by rr, corrects earlier estimates [Opt. Lett. 23, 506 (1998)] by a factor of 5.3. We find the crystal lengths that are necessary to obtain an optimal flat phase versus intensity response on either side of this separatrix intensity. (C) 2001 Optical Society of Ameri ca.