A comparative study of extraordinary and ordinary modes in the presence of external magnetic field in self-focusing of higher-order mode TEM\(_{m,n}\) of elegant Hermite–cosh-Gaussian laser beams in collisionless plasma medium

This work investigates the complexity involved in extraordinary (E-mode) and ordinary (O-mode) mode in the presence of external magnetic field in self-focusing of higher-order mode of elegant Hermite–cosh-Gaussian laser beams within collisionless magnetized plasma medium. Specifically, complexity in beam width parameters is highlighted through the influence of magnetic field, polarization mode, and decentred parameters. In that, transverse electromagnetic mode indices (m, n) of lasers with values (0, 4) have been explored. The ponderomotive force is primarily responsible for the dielectric constant’s nonlinearity in this context. In present study, WKB and paraxial approximations via the parabolic wave equation approach are used to establish the general form of differential equations for beam-width parameters in both transverse dimensions of the beam. At various plasma properties and those of the considered beams family, the behaviour of beam-width parameters with dimensionless distance of propagation is analysed theoretically.