Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp

Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp is studied. The differential equation for beam width parameter is derived by parabolic wave equation approach under paraxial approximation. For different values of plasma density, laser intensity and initial beam width, the behavior of beam width parameter with the normalized propagation distance is examined. It is found that the beam width parameter decreases with a higher rate. The frequency of the oscillations increases while amplitude decreases and the laser beam focuses up to long distance. Further, increase in relative plasma density causes reduction in the amplitude of spot size of laser beam near the propagation axis.