DYNAMICS OF THE SPECTRUM OF A SELF-MODULATED POWERFUL LASER-PULSE IN AN UNDERDENSE PLASMA

The evolution of the spectrum of a powerful laser pulse during its sel f-modulation in an underdense plasma is studied analytically and numer ically. It is shown that, in the early stages of the self-modulation i nstability. the linear theory gives a qualitatively correct descriptio n of the dynamics of the pulse spectrum in most cases. Depending on th e parameters of the laser pulse and of the plasma, this spectrum conta ins either Stocks satellites (downshifted from the fundamental frequen cy to a value equal to the plasma frequency), or both Stocks and anti- Stocks satellites of the fundamental frequency. When the three-dimensi onal mechanism for the instability is dominant and the pulse power is close to the critical power for relativistic self-focusing, the numeri cal calculations show that the intensity of the blue satellite exceeds the intensity of the red one. This specific feature of the spectrum, which does not arise when the instability is one-dimensional, cannot b e explained in terms of the linear para-axial theory, and can be used to identify the three-dimensional mechanism for the instability in exp eriments on the self-modulation of powerful laser pulses. It is shown that the transition to the nonlinear stage of the instability is accom panied by the occurrence of cascades (at frequencies separated from th e laser carrier frequency by intervals equal to an integer number of p lasma frequencies) in the spectrum of the laser pulse.