Laser pulses propagating through plasma undergo spectral broadening through local energy exchange with driven plasma waves. During propagation, a high power laser pulse drives large amplitude plasma waves, depleting the pulse energy. At the same time, the large amplitude plasma wave provides a dynamic dielectric response that leads to spectral shifting. The loss of laser pulse energy and the approximate conservation of laser pulse action imply that spectral red-shifts accompany the depletion. Here we examine the spectral shift and broadening, energy depletion, and action conservation of nonlinear laser pulses using the modified paraxial solver in WAKE. For pulses causing complete cavitation, large wavenumber shifts and action decay are observed at the distance where 40-50% of the pulse energy is depleted, consistent with theoretical prediction.

A tenuous plasma, enveloped, full wave solver was further implemented and compared to the modified paraxial solver through studying the University of Maryland laser-plasma system. The full wave solver has the advantage of better predicting the dispersion relation and eliminating the problematic divergence in the dispersion of the modified paraxial solver as wavenumber approaches zero, which is important especially when considering long wavelength generation.

Numerical analysis of the two propagation algorithms has been conducted via monitoring conservation laws. For large spectral shifts, numerical damping and convection of radiation out of the simulation domain result in action decay. Implementing a higher order evaluation of numerical derivatives and smaller spatial step have reduced numerical damping.

Spectral red-shifting of high power laser pulses propagating through underdensed plasma channel can be a source of ultrashort mid-infrared (MIR) radiation. Parametric dependence of MIR generation on laser pulse power, initial pulse duration, and plasma density is investigated through characteristic wavenubmer estimates and simulations.