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arXiv · 2401.00998

On the lack of external response of a nonlinear medium in the second-harmonic generation process

Fioralba Cakoni·Narek Hovsepyan·Matti Lassas·Michael S. Vogelius
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Abstract

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 $2\omega$. 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 $2\omega$. 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.

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Fioralba Cakoni, Narek Hovsepyan, Matti Lassas, Michael S. Vogelius. 2024-01-02. On the lack of external response of a nonlinear medium in the second-harmonic generation process. https://arxiv.org/abs/2401.00998

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