Possibility of pulse compression of a short-pulse laser in a plasma

On account of nonlinear refraction, arising through the relativistic mass effect, a short intense laser pulse tends to accumulate its energy around the intensity maximum, leading to pulse compression over a length Z(c) approximate to tau(0)c(2) omega(2)/omega(2) nu, where tau(0) and omega are the pulse duration and frequency of the laser, nu is the oscillatory electron velocity and omega(p) is the plasma frequency. When the transverse extent of the laser is finite, nonlinear self-focusing interferes strongly with this process. The self-focusing occurs in a periodic manner on a shorter scale length. However, over long lengths of pulse propagation, pulse compression could be significant.