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Justification of a nonlinear Schrödinger model for laser beams in photopolymers

Abstract : A nonstationary model that relies on the spatial nonlinear Schrödinger (NLS) equation with the time-dependent refractive index describes laser beams in photopolymers. We consider a toy problem, when the rate of change of refractive index is proportional to the squared amplitude of the electric field and the spatial domain is a plane. After formal derivation of the NLS approximation from a two-dimensional quasilinear wave equation, we establish local well-posedness of the original and reduced models and perform rigorous justification analysis to control smallness of the approximation error for appropriately small times.
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https://hal.inria.fr/hal-00917025
Contributor : Dmitry Ponomarev <>
Submitted on : Wednesday, December 11, 2013 - 10:40:35 AM
Last modification on : Thursday, February 7, 2019 - 4:59:20 PM

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Dmitry Pelinovsky, Dmitry Ponomarev. Justification of a nonlinear Schrödinger model for laser beams in photopolymers. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2013, ⟨10.1007/s00033-013-0338-9⟩. ⟨hal-00917025⟩

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