The Nonlinear Schrödinger Equation (NLSE) is ubiquitous as a description of weakly nonlinear dispersive behavior in diverse physical systems. In nonlinear optics it can be obtained from Maxwell’s equations as an envelope description of optical pulse propagation through an asymptotic expansion in powers of an appropriate small parameter. Additional correction terms that become important for shorter pulse durations can be systematically obtained in a similar fashion. However, it has been critically important to obtain a mathematical model of ultrashort high power pulse propagation in situations where the NLS description fails and yet, Maxwell’s equations remain untenable as a computationally feasible model.

We have recently derived a “carrier-resolved” unidirectional propagation model that allows us to accurately propagate high-power, few-cycle femtosecond laser pulses over meter distances. Moreover, this model explicitly incorporates the full material dielectric response allowing one to evaluate the role of white light supercontinumm generation in the presence of real material transparency windows and absorption bands. The NLS model with its various correction terms and other recent pulse propagation models in the literature can be derived as approximations in a physically transparent fashion.