Self-focusing/defocusing of skew-cosh-Gaussian laser beam for collisional plasma

The inverse relationship between the linear increase in skewness parameter s and the domain’s width of the order of skewness n plays a vital role in both critical beam radius and propagation dynamics of skew-cosh-Gaussian (skew-chG) laser beams. The interplay between the skewness parameter s and the order of skewness n is explored analytically and graphically in the current study to unveil the complexity of the propagation dynamics of the skew-chG laser beam. Naturally, the intensity’s complexity considerably affects the dielectric constant of the medium. Basically, the nonlinearity in the dielectric function of collisional plasma is attributed to the non-uniform heating of energy carriers along the wavefront of the laser beam, which becomes important and is used in the current study. By following Akhmanov’s parabolic wave equation approach under Wentzel–Kramers–Brillouin and paraxial approximations, the nonlinear differential equations are set up for the beam width parameters f ₁ and f ₂ and solved numerically. The present work analytically investigates the domains of the order n of skew-chG laser beams for a given set of skewness parameter s to investigate their effects on the self-focusing and defocusing of skew-chG laser beams. The critical curve also gets affected significantly due to the choice of domains for n. Finally, the numerical results are presented in the form of graphs and discussed in this study.