Thesis of Martin Dufour

Defense of thesis  Martin Dufour - laboratory PhLAM

Interaction de solitons : effets collectifs et effets perturbatifs

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, velocity nor Fourier spectrum. Moreover, in a certain class of one-dimensional 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.

keywords : nonlinear dynamics,nonlinear optics,soliton gas,Optical fiber,Integrable turbulence,solitons