Chapter 1 - Introduction

Abstract

This chapter provides an overview of optical solitons by emphasizing on the physical principles and the simplest theoretical model based on the cubic nonlinear SchröSdinger (NLS) equation and its generalizations. The term “solitary wave” or “solitons” is used to reflect the particle-like nature of solitary waves that remained intact even after mutual collisions. In the context of nonlinear optics, solitons are classified as being either temporal or spatial, depending on whether the confinement of light occurs in time or space during wave propagation. Temporal solitons represent optical pulses that maintain their shape, whereas spatial solitons represent self-guided beams that remain confined in the transverse directions orthogonal to the direction of propagation. Both types of solitons evolve from a nonlinear change in the refractive index of an optical material induced by the light intensity — a phenomenon known as the optical Kerr effect in the field of nonlinear optics. The intensity dependence of the refractive index leads to spatial self-focusing (or self-defocusing) and temporal self-phase modulation (SPM)- the two major nonlinear effects that are responsible for the formation of optical solitons. The scalar NLS equation applies for both temporal and spatial aspects of wave Propagation It is derived on the basis of quite general assumptions about the dispersive (and diffractive) effects and the nonlinear properties of physical systems.