Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides

We describe generalized nonlinear envelope equation modeling of sub-cycle dynamics on the underlying electric field carrier during one-dimensional propagation in fused silica. Generalized envelope equation simulations are shown to be in excellent quantitative agreement with the numerical integration of Maxwell's equations, even in the presence of shock dynamics and carrier steepening on a sub-50 attosecond timescale. In addition, by separating the effects of self-phase modulation and third harmonic generation, we examine the relative contribution of these effects in supercontinuum generation in fused silica nanowire waveguides.