Spatial Optical Solitons

When very narrow optical beams propagate in linear isotropic media, they undergo natural diffraction and broaden with distance. The narrower the beam is, the faster it diverges (diffracts). Such phenomenon is disadvantageous for light as the information carrier. In nonlinear materials, when self-focusing effect induced by the nonlinear response of the media to the light balances the diffraction, the beam becomes self-trapped at a very narrow width (~um) and does not spread in the transverse direction with the propagation distance, and is called a spatial optical soliton (SOS). SOS has been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. They exhibit a richness of phenomena such as fusion, fission, annihilation, and stable orbiting etc. Their well-defined shape and robustness makes them attractive as fundamental bits in future data transmission and processing schemes, and on the other hand, SOS may provide a powerful means for creating reconfigurable all-optical circuits where light is guided and controlled by light itself.The work of this thesis mainly concentrates on spatial optical solitons, and the primary achievements obtained are as the following:1. More universal algorithm—Frequency Domain Runger-Kutta method for solving the initial problem of partial differential equationThe dynamical equation of spatial optical solitons is Nonlinear Schrodinger equation (NLS). In chapter 2, we gave the detailed process of how to derive the NLS equation, including the discrete nonlinear Schrodinger equation. Generally speaking, NLS equation is non-integral, therefore, it must be solved numerically. Some numerical methods including our new method—Frequency Domain Runger-Kutta method for solving NLS equation and the stationary soliton solution were introduced in chapter 5 and in the appendix. By comparing with Split-step Fourier...