Self-focusing and frequency broadening of an intense short-pulse laser in plasmas

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 (r4) term in the expansion of the eikonal in the radial coordinate r 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 I(lambda)2(mu) < 2.8 x 1018 W/cm2, where I is the axial laser intensity and lambda(mu), 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 I(lambda)(2)(mu) > 2.8 x 10(18) W/cm2 when nonlinear plasma permittivity approaches saturation, the radial profile in the axial region becomes broader than the Gaussian.