PhD defense of Martin DUFOUR

DUFOUR Martin, Laboratoire PhLAM - UMR8523 - Equipe DYSCO

Title: Interaction of solitons : Collective and Perturbative effects

Jury: P. SURET (PhLAM), S. RANDOUX (PhLAM), S. BARBAY (Laboratoire C2N Paris), C. FINOT (Université de Bourgogne), C. FOCSA (PhLAM), G. FANJOUX (Université de France Comté)

Abstract:

Solitons are nonlinear waves resulting from the delicate balance between dispersive and nonlinear effects during their evolution. These entities possess the unique ability to propagate without ever altering their shape, speed, or Fourier spectrum. Moreover, in a certain class of onedimensional nonlinear partial differential equations known as "integrable" through the inverse scattering transform (IST) method, these waves have the distinct property of interacting solely in pairs and elastically. When two solitons collide, they emerge from the interaction process unchanged in shape, speed, or spectrum. The only noticeable change is a shift in their trajectories. In 1971, V.E. Zakharov introduced the concept of a "soliton gas." It comprises solitons randomly distributed in amplitudes, speeds, and positions that interact with one another, giving rise to complex dynamics necessitating a statistical description: the kinetic theory of soliton gases. In this thesis, we will experimentally investigate soliton interactions in optical fibers. Indeed, at the first level of approximation, the propagation of the slowly varying temporal envelope of an optical signal in a single-mode optical fiber can be described by the one-dimensional nonlinear Schrödinger equation (NLS), which is among the equations solvable through the inverse scattering transform. The objective of the work presented in this thesis is to provide experimental validation of the results obtained through the IST method and the kinetic theory of soliton gases.