Nonparaxial propagation of ultrashort laser pulses in plasma channels

The propagation characteristics of an ultrashort laser pulse in a preformed plasma channel are analyzed. The plasma channel is assumed to be parabolic and unperturbed by the laser pulse. Solutions to the wave equation beyond the paraxial approximation are derived that include finite pulse length effects and group velocity dispersion. When the laser pulse is mismatched within the channel, betatron oscillations arise in the laser pulse envelope. A finite pulse length leads to a spread in the laser wave number and consequently a spread in betatron wave number. This results in phase mixing and damping of the betatron oscillation. The damping distance characterizing the phase mixing of the betatron oscillation is derived, as is the dispersion distance characterizing the longitudinal spreading of the pulse.