Nonlinear laser energy depletion in laser-plasma accelerators

Energy depletion of intense, short-pulse lasers via excitation of plasma waves is investigated numerically and analytically. The evolution of a resonant laser pulse proceeds in two phases. In the first phase, the pulse steepens, compresses, and frequency redshifts as energy is deposited in the plasma. The second phase of evolution occurs after the pulse reaches a minimum length at which point the pulse rapidly lengthens, losing resonance with the plasma. Expressions for the rate of laser energy loss and rate of laser redshifting are derived and are found to be in excellent agreement with the direct numerical solution of the laser field evolution coupled to the plasma response. Both processes are shown to have the same characteristic length scale. In the high intensity limit, for nearly resonant Gaussian laser pulses, this scale length is shown to be independent of laser intensity.