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Geometric Analysis of Optical Frequency Conversion and its Control in Quadratic Nonlinear Media
Luther, G.G.; Alber, M.S.; Marsden, J.E.; Robbins, J.M.
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Abstract: Frequency conversion and its control among three light waves is analyzed using a geometric approach that enables the dynamics of the waves to be visualised 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 Poincare sphere has been used in the same way to visualise 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. Notes: M.S. Alber, Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556.J.E. Marsden, Control and Dynamical Systems 107- 81, Caltech, Pasadena, CA 91125
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