Stationary self-focusing of intense laser beam in cold quantum plasma using ramp density profile

By using a transient density profile, we have demonstrated stationary self-focusing of an electromagnetic Gaussian beam in cold quantum plasma. The paper is devoted to the prospects of using upward increasing ramp density profile of an inhomogeneous nonlinear medium with quantum effects in self-focusing mechanism of high intense laser beam. We have found that the upward ramp density profile in addition to quantum effects causes much higher oscillation and better focusing of laser beam in cold quantum plasma in comparison to that in the classical relativistic case. Our computational results reveal the importance and influence of formation of electron density profiles in enhancing laser self-focusing.