Self-Focusing of Hermite-Cosh-Gaussian Laser Beams in Plasma under Density Transition

Self-focusing of Hermite-Cosh-Gaussian (HChG) laser beam in plasma under density transition has been discussed here. The field distribution in the medium is expressed in terms of beam-width parameters and decentered parameter. The differential equations for the beam-width parameters are established by a parabolic wave equation approach under paraxial approximation. To overcome the defocusing, localized upward plasma density ramp is considered, so that the laser beam is focused on a small spot size. Plasma density ramp plays an important role in reducing the defocusing effect and maintaining the focal spot size up to several Rayleigh lengths. To discuss the nature of self-focusing, the behaviour of beam-width parameters with dimensionless distance of propagation for various values of decentered parameters is examined by numerical estimates. The results are presented graphically and the effect of plasma density ramp and decentered parameter on self-focusing of the beams has been discussed. 1. Introduction The self-focusing of laser beams in nonlinear optical media is a fascinating topic which has inspired theoretical and experimental interest [1–3]. In self-focusing and self-phase modulation of Cosh-Gaussian laser beam in magnetoplasma using variational approach, it is found that the decentered parameter along with absorption coefficient plays a key role in the nature of self-focusing/defocusing of the beam [4]. However in the propagation of a Cos-Gaussian beam in a kerr medium, it is found that although the RMS beam width broadens, the central parts of the beam give rise to an initial radial compression and a significant redistribution during propagation. The partial collapse of central part of the beam appears while the RMS beam width still increases or remains constant. It is further observed that the Cos-Gaussian beam eventually converts into a Cosh-Gaussian type beam in a kerr medium with low and moderate power [5]. In self-focusing of Cosh-Gaussian laser beam in plasma with weak relativistic and ponderomotive regime, it is observed that a large value of absorption level weakens the self-focusing effect in the absence of decentered parameter. However, oscillatory self-focusing takes place for a higher value of decentered parameter, , and all curves are seen to exhibit sharp self-focusing effect for [6]. In ponderomotive self-focusing of a short laser pulse under plasma density ramp, the pulse acquires a minimum spot size. As the laser propagates through the density ramp region, it sees a slowly narrowing channel. In such a case the oscillation