Quasi-matched propagation of ultra-short, intense laser pulses in plasma channels

The propagation of an ultrashort and relativistically intense laser pulse in a preformed plasma channel is investigated. The nonlinear paraxial wave equation describing the laser propagation in the plasma is solved both analytically and numerically. For any arbitrary temporal laser pulse profile with a given power (less then the critical power for self-focusing) and any prescribed transverse density profile in the channel, we determine the laser intensity distribution along the pulse ensuring quasi-matched propagation, neglecting non-paraxial effects. For the case of a Gaussian laser with an initially uniform spot throughout the pulse, we determine the optimal channel depth that minimizes laser evolution (e.g., minimizes spot size oscillations). The analytical and semi-analytical results obtained for both cases in the weakly relativistic regime are presented and validated through comparison with numerical simulations.