Group velocity and pulse lengthening of mismatched laser pulses in plasma channels

Analytic solutions are presented to the non-paraxial wave equation describing an ultra-short, low-power, laser pulse propagating in a plasma channel. Expressions for the laser pulse centroid motion and laser group velocity are derived, valid for matched and mismatched propagation in a parabolic plasma channel, as well as in vacuum, for an arbitrary Laguerre-Gaussian laser mode. The group velocity of a mismatched laser pulse, for which the laser spot size is strongly oscillating, is found to be independent of propagation distance and significantly less than that of a matched pulse. Laser pulse lengthening of a mismatched pulse owing to laser mode slippage is examined and found to dominate over that due to dispersive pulse spreading for sufficiently long pulses. Analytic results are shown to be in excellent agreement with numerical solutions of the full Maxwell equations coupled to the plasma response. Implications for plasma channel diagnostics are discussed