Higher-order nonparaxial approximation for the self-focusing propagation of circular cosine-hyperbolic-Gaussian beams in plasmas

In the present manuscript, the beam width parameter differential equations are developed using standard Wentzel-Kramers-Brillouin (WKB) and higher-order nonparaxial approximations in the spatial dependent irradiance of the circular cosine-hyperbolic-Gaussian laser beams (CiChGB) for collisional, collisionless, and ponderomotive nonlinearities in the plasmas. The authors have examined the impact of the decentered parameter and higher-order nonparaxial spatial irradiance on the higher-order coefficients of dielectric functions and beam width parameters for CiChGB under various plasmas. The investigation suggests that, the higher-order dielectric functions are strongly affected by the nonparaxial irradiance approximations of the beam. It is observed that, there is a certain domain for higher-order coefficients of nonparaxial approximations and the decentered parameter for the self-trapping and self-focusing of the CiChGB beam inside the plasmas. The current work has potential applications in particle trapping.