ABSTRACT
This chapter outlines how nonlinear propagation in the guided modes of optical waveguides can be described efficiently in a so-called 1+1D propagation formalism. This terminology implies that the transverse degrees of freedom in the waveguide cross section are integrated out and a first-order differential equation describing the evolution of the temporal, or spectral, profile of an optical pulse along the length of the waveguide is obtained. The two dimensions involved in the calculation are therefore the spatial coordinate along the length axis of the waveguide, and the time, or equivalently the frequency, coordinate. Efficient modelling tools for nonlinear propagation are therefore increasingly important for waveguide designers. Many texts on nonlinear propagation modelling start out by deriving the simplest reasonable propagation equation, which is then gradually extended to take various physical effects into account. The nonlinear processes described by Equation include elastic photon-photon scattering and inelastic photon-phonon scattering.
