Dynamics of short laser pulses propagating in plasma channels

We present an extension of the paraxial wave equation, taking finite-pulse- length effects into account. A pair of coupled envelope-power equations hav ing finite pulse length as well as nonlinear focusing effects is derived an d analyzed in a plasma channel. In plasma channels, pulses can undergo an e nvelope modulation which is damped in the front and initially grows in the back of the pulse. Finite-pulse-length effects also significantly increase the nonlinear focusing. [S0031-9007(99)08439-2].