Self-phase modulation of a laser in self created plasma channel

Summary form only given. An analytical formalism of self focusing and self-phase modulation of an intense short pulse laser in a plasma due to relativistic and ponderomotive nonlinearities is developed. In the paraxial ray approximation, the pulse retains its Gaussian radial profile, however, its spot size varies with the distance of propagation in a periodic manner. It is influenced by self focusing. The frequency of the laser undergoes red shift. For a tan-hyperbolic temporal profile of pulse the red shift is maximum at the foot of the pulse and decreases slowly as one goes to portions of higher and higher intensity. The effect of ponderomotive nonlinearity is very significant in this respect. The maximum downshift occurs at a distance at which the laser acquires a minimum spot size. With retarded time normalized axial intensity increases more at Z ~ R_d and the radial intensity is also more narrowly peaked at z ~ R_d, where R_d = 2pir₀ ²/lambda is the Rayleigh length, r₀ and lambda are the spot size and wavelength of the laser pulse respectively.