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Rapport (Rapport De Recherche) Année : 2021

Modeling optical Kerr effect in Fabry-Perot resonators

Résumé

In a recent paper, see reference [3] in the bibliography Section, the authors have proposed a model for light-wave propagation in a fiber Fabry-Perot resonator containing a Kerr medium. They provide a set of two coupled non-linear partial differential equations for the forward and backward propagating electric field by exploiting connections between the physics in a medium with general Kerr non-linearity and the physics of a two-level atomic medium. Exploiting such an analogy has the advantage of the conciseness but it hides the underlying assumptions of the model. In this document, we propound a detailed justification of the way the coupled equations that describe light-wave propagation in a fiber Fabry-Perot resonator containing a Kerr medium can be deduced from Maxwell's equations. The main advantage of this presentation is to spotlight the various assumptions that must be made to reach this two coupled equations. In a second part of the document, following [3] again, we deduce from this set of two coupled equations an other non-linear partial differential equation, referred to as the Lugiato-Lefever equation for Fabry-Perot resonators, that allows to compute the forward and backward propagating electric field in the Kerr cavity by solving a single equation for a scalar unknown function rather than a set of two coupled non-linear equations.
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Dates et versions

hal-04481700 , version 1 (28-02-2024)

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  • HAL Id : hal-04481700 , version 1

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Stéphane Balac. Modeling optical Kerr effect in Fabry-Perot resonators. IRMAR - Université Rennes 1. 2021. ⟨hal-04481700⟩
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