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

Luther, G. G. and Alber, M. S. and Marsden, J. E. and Robbins, J. M. (2000) Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media. Journal of the Optical Society of America B, 17 (6). pp. 932-941. ISSN 0740-3224. http://resolver.caltech.edu/CaltechAUTHORS:LUTjosab00

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Abstract

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.


Item Type:Article
Additional Information:© Copyright 2000 Optical Society of America Received June 1, 1999; revised manuscript received February 2, 2000 M.S. Alber was partially supported by National Science Foundation (NSF) grants DMS 9626672 and 9508711. G.G. Luther gratefully acknowledges support from The Basic Research Institute in the Mathematical Sciences, Hewlett-Packard Labs, and from NSF under grants DMS 9626672 and 9508711. J.E. Marsden was partially supported by the California Institute of Technology and NSF grant DMS-9802106. J.M. Robbins was partially supported by NSF grant DMS 9508711, by North Atlantic Treaty Organization grant CRG 950897, and by the Department of Mathematics and the Center for Applied Mathematics, University of Notre Dame.
Record Number:CaltechAUTHORS:LUTjosab00
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LUTjosab00
Alternative URL:http://www.opticsinfobase.org/abstract.cfm?URI=josab-17-6-932
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6105
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:17 Nov 2006
Last Modified:29 Aug 2014 17:13

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