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In the present paper, an analysis of self-focusing of asymmetric elegant Hermite-cosh-Gaussian laser beams having transverse electromagnetic (TEMmn) modes with mode indices m = 0 and n = 0, 2, and 4 in magnetized plasma has been presented. The nonlinearity in the effective dielectric function of plasma considered herein is mainly due to the ponderomotive mechanism. The nonlinear coupled differential equations for beam width parameters in both x and y dimensions of the beams are established by using Wentzel–Kramers–Brillouin and paraxial approximations through a parabolic equation approach. The behavior of beam width parameters with the dimensionless distance of propagation is presented graphically at different parameters of plasma and those of general beam's family considered. Specifically, complexity in beam width parameters is highlighted through the influence of light absorption, mode index, and decentered parameter. The results show that two unlike decentered parameters in transverse dimensions of the beam change beam-widths considerably at higher order mode indices. Absorption gives an important role in complexity of beam width parameters in transverse dimensions of the beam.

In the present paper, an analytically investigated domain of decentered parameter and its effect on the self-focusing of Hermit-cosh-Gaussian (HChG) laser beams in a collisional plasma have been studied theoretically. The nonlinearity in the dielectric constant of plasma arising due to the nonuniform heating of carriers along the wavefront of the laser beam has been employed in the present investigation. The nonlinear differential equation of beam width parameter for various laser modes of HChG beam is obtained by following the standard Akhamanov's parabolic equation approach under Wentzel-Kramers-Brillouin and paraxial approximations. The analytical treatment has enabled us to define three distinct regions: self-focusing, self-trapping and defocusing, which are presented graphically.