Non-paraxial theory of self-focusing/defocusing of Hermite cosh Gaussian laser beam in rippled density plasmas

Present research work focuses on study of self-focusing and self-trapping of Hermite cosh Gaussian (HchG) laser beams in rippled density plasma by considering relativistic non-linearity. The coupled non-linear differential equations for the beam width parameters (for modes m = 0, 1, and 2) were derived by employing higher-order correction in comparison to paraxial ray theory by expanding dielectric function and eikonal up to r(4) terms. It is observed that the inclusion of higher-order terms significantly influence the off-axial properties for m >= 1 mode indices. Furthermore, the effect of parameters including beam intensity, ripple factor, depth of density modulation, and decentred parameter on self-focusing and self-trapping is analysed and discussed both analytically and numerically.