We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions.
© 2000 Optical Society of America
(000.3860) General : Mathematical methods in physics
(190.0190) Nonlinear optics : Nonlinear optics
(190.2640) Nonlinear optics : Stimulated scattering, modulation, etc.
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, "Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media," J. Opt. Soc. Am. B 17, 932-941 (2000)