Non-linéarité Kerr dans les Fibres Optiques Microstructurées

Abstract : We want to find spatial solitons in optical bres with a nonlinear optical Kerr effect. That's why we propose a new numerical approach using the Finite Element Method, very efficient for a natural treatment of inhomogeneous media in complex structures. A nonlinear scalar model of the electric eld in the bre is used to implement and to validate our method and to understand the physical meaning of the new solutions in a simple case. The field is supposed to be harmonic in time and along the direction of invariance of the bre but inhomogeneous in the cross section. Several examples dealing with step-index fibres and solid core microstructured optical bres (MOFs) with a nite size cross section are described. In each geometry, a complete study is achieved to obtain and to prove with numeric tests the existence of a single self-coherent nonlinear solution (spatial soliton) with the highest reachable energy avoiding the self-focusing instability. The spatial soliton depends on the nite trans- verse prole of the structure, corresponds to the Townes soliton in the nonlinear homogeneous medium but it is different in optical bres. Our new approach of the numerical study of the optical Kerr effect in optical bres permits us to generalize the Townes soliton. However, the refractive index prole induced by the optical Kerr effect shows that the weak guidance approximation is not respected and thus, the characteristics of the nonlinear solution are misvalued in the scalar model. Therefore, the implementation of the full-vector case without approximation is realized. The same study as for the scalar case is performed to take into account all electric eld components. Finally, to extend the eld of investigation of our numerical method, the nonlinear solutions in MOFs with a central hollow defect are studied. By analogy with Solid State Physics, donor/acceptor configurations are defined and nonlinear solutions are analyzed according to the size of the defect. The study of the focusing and defocusing case through these congurations allows us to discover new nonlinear behaviors in these fibres.
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F. Drouart. Non-linéarité Kerr dans les Fibres Optiques Microstructurées. Physique [physics]. Université Paul Cézanne - Aix-Marseille III, 2008. Français. ⟨tel-00438491⟩

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