Abstract

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			This paper concerns the scattering problem for a nonlinear medium of compact support, D, with second-harmonic generation. Such a medium, when probed with monochromatic light beams at frequency omega, generates additional waves at frequency 2omega. The response of the medium is governed by a system of two coupled semilinear partial differential equations for the electric fields at frequency omega and 2omega. We investigate whether there are situations in which the generated 2*omega wave is localized inside D, that is, the nonlinear interaction of the medium with the probing wave is invisible to an outside observer. This leads to the analysis of a semilinear elliptic system formulated in D with non-standard boundary conditions. The analysis presented here sets up a mathematical framework needed to investigate a multitude of questions related to nonlinear scattering with second-harmonic generation. View/Download Publication in pdf format Back to Preprint list Michael Vogelius 2-13-98