Spectral approach to pulse propagation in a dispersive nonlinear medium

The nonlinear physical processes influencing pulse propagation are emphasized by analyzing equations for the pulse spectrum amplitude and phase. A constant pulse is maintained when it has the correct form necessary to suppress the four-photon mixing processes, so that the amplitude is constant and the total optical Kerr effect counterbalances the frequency dependence of the linear dispersion, thus preventing variable frequency-dependent terms in the phase. The effects are demonstrated explicitly and offer an alternative to the self-phase-modulation picture based on the equivalent nonlinear Schrödinger equation. The fundamental soliton is immediately obtained. Constants associated with pulse propagation in a nonlinear medium are related to moments of the pulse spectrum. The constraints on pulse shape and magnitude are discussed, and the effects of power absorption are examined.