Nonlinear propagation of an intense Laguerre–Gaussian laser pulse in a plasma channel* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61665006 and 61865011) and the Natural Science Foundation of Jiangxi Province of China (Grant Nos. 20171ACB21018, 20161BAB212041, and 20162BCB23012).

Abstract

The nonlinear propagation of an intense Laguerre–Gaussian (LG) laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method. The evolution equation of the spot size is derived including the effects of relativistic self-focusing, preformed channel focusing, and ponderomotive self-channeling. The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size, periodically focusing and defocusing oscillation, catastrophic focusing, and solitary waves are obtained. Compared with the laser pulse with fundamental Gaussian (FG) mode, it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse, while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse. Thus, the matched condition for the intense LG laser pulse with constant spot size is released obviously, while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.