Envelope analysis of intense laser pulse self-modulation in plasmas

An envelope equation describing laser pulse self-focusing and optical guiding in plasmas is derived and is used to analyze self-modulation. Included is the plasma wave generated by the pulse front, which leads to periodic focusing, radial energy transport, and laser envelope modulation. The onset criterion and growth rates are calculated and compared to simulations using the envelope equation and a nonlinear fluid code. For a long square pulse, onset of strong self-modulation occurs at one-half the power needed for optical guiding.