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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00998 |
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| _version_ | 1866910285597507584 |
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| author | Cakoni, Fioralba Hovsepyan, Narek Lassas, Matti Vogelius, Michael S. |
| author_facet | Cakoni, Fioralba Hovsepyan, Narek Lassas, Matti Vogelius, Michael S. |
| contents | 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 $ω$, generates additional waves at frequency $2ω$. The response of the medium is governed by a system of two coupled semilinear partial differential equations for the electric fields at frequency $ω$ and $2ω$. We investigate whether there are situations in which the generated $2ω$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the lack of external response of a nonlinear medium in the second-harmonic generation process Cakoni, Fioralba Hovsepyan, Narek Lassas, Matti Vogelius, Michael S. Analysis of PDEs 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 $ω$, generates additional waves at frequency $2ω$. The response of the medium is governed by a system of two coupled semilinear partial differential equations for the electric fields at frequency $ω$ and $2ω$. We investigate whether there are situations in which the generated $2ω$ 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. |
| title | On the lack of external response of a nonlinear medium in the second-harmonic generation process |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.00998 |