|Ph.D Thesis||Department of Electrical Engineering|
|Supervisor:||Prof. Orenstein Meir|
Spontaneous pattern formation in nonlinear complex media is an interesting and important research area that expands over a wide range of disciplines. Despite the basic differences between the distinct disciplines, much similarity is found between patterns that evolve spontaneously in the different systems. The fundamental principles that govern the evolution of the patterns are of extreme importance for understanding basic processes in the natural sciences, physics and engineering.
The research here was focused on spontaneously formed optical patterns in two types of nonlinear media: Kerr medium and a complex nonlinear medium of the semiconductor laser.
In Kerr medium we studied the interactions of coherent/incoherent solitons and soliton arrays in the vicinity of nonlinear interfaces. We found that soliton arrays are stabilized if they are propagating in laterally bounded media (a wide nonlinear waveguide). The array exhibits oscillation modes around the equilibrium - some similar to those of a mechanical system composed of springs and masses and some novel phase oscillation modes. The interaction of incoherent solitons in the vicinity of an interface was analyzed and shown to enable all-optical soliton switching.
In semiconductor laser medium we studied the evolution of pattern in broad area and ring shaped VCSELs. Broad area VCSELs were found to emit regular arrays of optical vortices. These field distributions were generated by transverse mode locking of Gauss-Laguerre (GL) modes. The origin of the GL modes was the thermally induced parabolic index (thermal lensing) while the locking of specific combinations is brought about by the nonlinear mechanisms of the laser. Ring shaped VCSELs exhibited regular arrays of intensity lobes distributed uniformly around the ring perimeter. The number of lobes increased as the injection current was increased. The pattern switching was found to stem from a dynamical mechanism (modulation instability) within the complex nonlinear medium. Predictions of our analytical model had an excellent agreement with our experimental results.