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Diffractive optics in nonlinear media with periodic structure

Published online by Cambridge University Press:  26 September 2008

Gang Bao  and
David C. Dobson
Gang Bao
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
David C. Dobson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
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Abstract

The diffraction of time-harmonic waves in a nonlinear medium with periodic structure is studied in this paper. In particular second harmonic generation – an important phenomenon in nonlinear optics-is modelled. The model, derived from a general nonlinear system of Maxwell's equations, is shown to have a unique solution for all but a discrete number of frequencies. The problem is solved numerically by combining a method of finite elements and a fixed-point iteration scheme. Numerical experiments for some simple grating structures are presented and discussed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 6 , December 1995 , pp. 573 - 590
Copyright
Copyright © Cambridge University Press 1995

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