Analysis of propagation of an intense and short laser pulse in inhomogeneous plasmas

The effect of plasma inhomogeneity on propagation of an intense and short laser pulse is examined analytically, especially in the case of a plasma with a constant density gradient. An envelope equation describing the laser pulse propagating through inhomogeneous plasmas is derived and solved analytically by using operator calculus. As a result, it is found that propagation of a laser pulse through a plasma with a constant density gradient is characterized by a unique parameter alpha = 57 kappa lambda x P[TW] which depends on the plasma gradient kappa, the laser wavelength lambda, and the laser power P. With this parameter, we discuss self-focusing of laser pulses for realistic parameters. Necessary power to propagate the laser pulse for a desired distance without diffraction becomes clear by using our result.