Self-Interaction Effects in One-Dimensional Wave Propagation: Solitons in Optical Fibers and in Periodic Structures

Abstract

In Chap. 6, we discussed phenomena which, in the language introduced at the end of Chap. 3, fall into the regime of strong nonlinearities. The electronic structure of the physical system exposed to the electromagnetic field is perturbed far from equilibrium in the course of its evolution. In the soliton pulses encountered in the theory of self-induced transparency, for example, the resonant atoms are moved from their ground state, to the first excited state, at the midpoint of the pulse. We now return to the regime of weak nonlinearities, where the nonlinear polarization P^(NL) may be expanded in powers of the electric field.