Self-focusing of Gaussian laser beam has been investigated in quantum plasma under the effect of applied axial magnetic field. The nonlinear differential equation has been derived for studying the variations in the beam-width parameter. The effect of initial plasma electron temperature and the axial magnetic field on self-focusing and normalized intensity are studied. Our investigation reveals that normalized intensity increases to tenfolds where quantum effects are dominant. The normalized intensity further increases to twelvefolds on increasing the magnetic field.

This paper presents an investigation on the self-focusing of a cosh-Gaussian laser beam in the thermal quantum plasma (TQP) by taking into account the effects of relativistic nonlinearity. An appropriate nonlinear Schrödinger equation has been solved analytically by applying the variational approach. The self-focusing and the self-phase modulation are examined under a variety of parameters. The self-trapping of a cosh-Gaussian laser beam is further studied at various values of the decentered parameter, b with different absorption levels, ${k}^{\prime}_i$. Numerical analysis shows that these parameters play a vital role in propagation characteristics. The significant contribution of the quantum effects to enhance the self-focusing and minimize the longitudinal phase has been observed. Further, a comparison has been made with the classical relativistic (CR), the relativistic cold quantum (RCQ), and the thermal quantum (TQ) regimes. The self-focusing is found to occur earlier and is strongest for the case of TQP in the present analysis.

In the present paper, we have investigated self-focusing of the quadruple Gaussian laser beam in underdense cold quantum plasma. The non-linearity chosen is associated with the relativistic mass effect that arises due to quiver motion of electron and electron density perturbation caused by ponderomotive force. The non-linearity modifies the plasma frequency in the dielectric function and hence the refractive index of the medium. The focusing/defocusing of the quadruple laser depends on the refractive index of the medium. We have set up non-linear differential equation that controls the beam width parameter by using well-known paraxial ray approximation and Wentzel–Krammers–Brillouin approximation. The effect of intensity parameter and electron temperature is observed on laser beam self-focusing in the presence of cold quantum plasma. From the results, it is revealed that electron temperature and the initial intensity of the laser beam control the profile dynamics of the laser beam.

The paper presents an investigation on self-focusing of cosh-Gaussian (ChG) laser beam in a relativistic–ponderomotive non-uniform plasma. It is observed numerically that the selection of decentered parameter and initial beam radius determines the focusing/defocusing of ChG laser beam. For given value of these parameters, the plasma density ramp of suitable length can avoid defocusing and enhance focusing effect significantly. Focusing length and extent of focusing may also be controlled by varying slope of the ramp density. A comparison with Gaussian beam has also been attempted for optimized set of parameters. The results establish that ChG beam focuses earlier and sharper relative to Gaussian beam. We have setup the non-linear differential equation for the beam width parameter using Wentzel–Kramers–Brillouin and paraxial ray approximation and solved it numerically using Runge–Kutta method.

A model is presented for the resonant third harmonic generation of short pulse lasers in cluster plasma in the presence of density ripple. Because of ripple in cluster density and plasma electron density outside the cluster, the phase-matching condition for the third harmonic process is satisfied, leading to resonant enhancement of harmonic generation. We explore the impact of laser intensity, cluster size, and collisional frequency of electrons on the efficiency of third harmonic generation. Moreover, since the group velocity of the third harmonic wave is greater than that of the fundamental wave, it causes the slippage of the generated harmonic pulse out of the fundamental laser pulse and its amplitude increases with time.