טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentPigier Claude
SubjectAspects of Optical Spatial Solitons in (2+1)D
DepartmentDepartment of Applied Mathematics
Supervisor ? 18? Mordechai Segev


Abstract

Solitons are one of the most fascinating phenomena in nonlinear sciences: localized wave-packets that exhibit properties associated with real particles. They have been discovered in a wide range of physical systems, from experimental to theoretical physics, and from macroscopic to microscopic media, and have universal features.

In this thesis, we explore the properties of a novel type of composite soliton: the “propeller” soliton. According to the self-consistency principle, a soliton induces a potential of which it is a bound state. From this concept rose the idea of creating a soliton composed of different “modes”, which populate different bound states of the potential they induce together. The propeller soliton is composed of two modes, of which the second one carries transverse angular momentum. It is trapped in both transverse dimensions (x,y), and propagates in the z direction. The main feature of the propeller is its rotation around its propagation axis. This is the first composite soliton possessing angular momentum that was both predicted theoretically and observed experimentally.

We first demonstrate the existence of the propeller soliton in a self-focusing saturable nonlinearity. This nonlinearity leads to equations that are not integrable through the Inverse Scattering Transform. Consequently, we find solutions through asymptotical analysis and through numerical calculations.

We then study interactions between propeller solitons, in which we find fascinating exchanges of angular momentum. We also find that those interactions demonstrate the propeller soliton to be very robust, and surely more so than any previously known (2+1)D composite soliton.

The last part of the thesis is dedicated to a short study of quasi self-trapped ring beams in self-focusing saturable medium. These beams are not actually solitons or even truly self-trapped beams, even though they are bound state solutions of the equation. They evolve dynamically during propagation, and eventually completely decay.