An intense ultrafast laser pulse propagating through a plasma undergoes self-focusing and self-phase-modulation as a result of relativistic mass nonlinearity. The inclusion of a quartic (r<sup>4</sup>) term in the expansion of the eikonal in the radial coordinate <i>r</i> allows the modification of the shape of the radial intensity profile. The front of the pulse, under the combined effects of time-dependent self-focusing and frequency downshifting, acquires a severely distorted temporal shape. The radial profile for Iλ<sub>μ</sub><sup>2</sup><2.8×10<sup>18</sup> W/cm<sup>2</sup>, where <i>I</i> is the axial laser intensity and λ<sub>μ</sub> is the laser wavelength in micrometers, is transformed from a Gaussian to a super-Gaussian because of the faster convergence of the marginal rays than the paraxial rays. In the opposite case of Iλ<sub>μ</sub><sup>2</sup>>2.8×10<sup>18</sup> W/cm<sup>2</sup> when nonlinear plasma permittivity approaches saturation, the radial profile in the axial region becomes broader than the Gaussian.
© 2001 Optical Society of America
(060.5060) Fiber optics and optical communications : Phase modulation
(140.7090) Lasers and laser optics : Ultrafast lasers
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(260.5950) Physical optics : Self-focusing
Chuan Sheng Liu and Vipin K. Tripathi, "Self-focusing and frequency broadening of an intense short-pulse laser in plasmas," J. Opt. Soc. Am. A 18, 1714-1718 (2001)