In this theoretical work, we study the non-linear propagation of a linearly-polarized laser beam, which is normally incident on the surface of semi-bounded magnetized warm plasma. Inside the plasma, the linearly-polarized laser beam is considered as a combination of system modes, i.e. right- and left-hand circularly-polarized modes that each behave differently. Based on a perturbative method, coupled non-linear wave equations are derived for these modes, and the problem of self-focusing is investigated. It is demonstrated that laser frequency has an essential impact on the non-linear dynamics of modes. At the frequency area where both modes can propagate, the right- and left-hand modes' behavior is different in comparison with the uncoupled propagation of individual modes. In this case, an increase in the external magnetic field improves the focusing property of both modes.
Mode crossing effects at electron beam–plasma interaction and related phenomena