Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media

We analyze frequency conversion and its control among three light waves usi ng a geometric approach that enables the dynamics of the waves to be visual ized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understa nd the fully nonlinear dynamics. The Poincare sphere has been used in the s ame way to visualize polarization dynamics. A geometric understanding of co ntrol strategies that enhance energy transfer among interacting waves is in troduced, and the quasi-phase-matching strategy that uses microstructured q uadratic materials is illustrated in this setting for both type I and II se cond-harmonic generation and for parametric three-wave interactions. (C) 20 00 Optical Society of America [S0740-3224(00)02006-3].