Chapter 11 - Discrete Solitons

Abstract

A periodic array of optical waveguides creates a novel kind of device in which new types of spatial solitons can be generated and studied experimentally. The properties of spatially localized modes in a waveguide array are usually analyzed in the framework of a set of coupled-mode equations, each equation representing the soliton amplitude in a specific waveguide, but coupled to the neighboring waveguides. Such a coupled set of equations is referred to as the discrete nonlinear Schrödinger (NLS) equation, and its localized solutions are known as discrete solitons. A similar approach for studying discrete spatial solitons in solid-state physics is known as the tight-binding approximation. In the context of an optical waveguide array, this approximation corresponds to the assumption that the fundamental modes in all waveguides are only weakly coupled. The solitoncentered inside a single waveguide is stable because it corresponds to the minimum of the Hamiltonian. If the discrete soliton is forced to move sideways, it has to jumpfrom one waveguide to the next, passing from a stable to an unstable configuration. Thedifference between the Hamiltonians in the two cases—the so-called Peierls-Nabarropotential—accounts for the resistance that the soliton has to overcome during transverse propagation. This potential increases as the input power level increases. As a result, the soliton becomes localized to a single waveguide and is effectively decoupled from the rest of the array.