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

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 Poincare 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.

[1]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[2]  N. Bloembergen,et al.  Interactions between light waves in a nonlinear dielectric , 1962 .

[3]  A. Bloom.  Quantum Electronics , 1972, Nature.

[4]  S. Meenakshi,et al.  Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals , 1982 .

[5]  C. McKinstrie,et al.  Solitary-wave solutions of the generalised three-wave and four-wave equations , 1988 .

[6]  Darryl D. Holm,et al.  Integrable and chaotic polarization dynamics in nonlinear optical beams , 1989 .

[7]  C. McKinstrie,et al.  Signal enhancement in collinear four-wave mixing , 1990 .

[8]  M. Fejer,et al.  Quasi-phase-matched second harmonic generation: tuning and tolerances , 1992 .

[9]  S. Wabnitz,et al.  Two-wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos. , 1992, Optics letters.

[10]  C. McKinstrie,et al.  Nonlinear detuning of three-wave interactions , 1993 .

[11]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[12]  Martin M. Fejer,et al.  Quasi-phasematched optical parametric oscillators using bulk periodically poled LiNbO3 , 1995, Photonics West.

[13]  M. Fejer,et al.  Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO 3 , 1995 .

[14]  Andrey Kobyakov,et al.  Vectorial type-II interaction in cascaded quadratic nonlinearities — an analytical approach , 1996 .

[15]  Lederer,et al.  Cascading of quadratic nonlinearities: An analytical study. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[16]  Jerrold E. Marsden,et al.  Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction , 1998 .