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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.

The authors have investigated the non-stationary self-focusing of Gaussian laser pulse in cold quantum plasma. In case of high dense plasma, the nonlinearity in the dielectric constant is mainly due to relativistic high intense interactions and quantum effects. In this paper, we have introduced a ramp density profile for plasma and presented graphically the behavior of spot size oscillations of pulse at rear and front portions of the pulse. It is observed that the ramp density profile and quantum effects play a vital role in stronger and better focusing at the rear of the pulse than at the front in cold quantum plasmas.

The propagation of a Gaussian beam in underdense plasma with upward increasing density ramp is analyzed. In this work are shown that the spot size oscillations of laser beam increases and its amplitude shrinks with proper plasma density ramp. This causes the laser beam to become more focused and penetrations deep into the plasma by reduction of diffraction effect. The related focusing parameters are optimized to get the best possible focusing at the relativistic threshold intensity of Nd-glass laser and the effect of the laser intensity in the self-focusing parameters is also investigated. The analytical calculations are presented and showed more reliable results in comparison to the previous works.

This paper presents a preliminary study on relativistic self-focusing of cosh-Gaussian (ChG) laser beam and its dependence on the value of decentered parameter b through cold quantum plasma (CQP). In contrast to the earlier work on self-focusing in such a medium, higher order terms in the expansion of the dielectric function and the eikonal have been taken into account. It is seen that the inclusion of such terms (up to r 4 ) in the extended paraxial theory does significantly affect the dependence of the beamwidth parameter ( f ) on the distance of propagation and allows the modification of the shape of the radial intensity distribution. We have also found that ChG in comparison with Gaussian beam has caused better focusing in the CQP, which is very important for some applications in high power laser-dense plasma interactions.Index Terms-Cold quantum plasma (CQP), coshGaussian (ChG), relativistic self-focusing (RSF), the extended paraxial approximation approach.