The evolution of the transverse centroid of asymmetric laser field in plasmas with various density distributions

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The propagation of asymmetric relativistic intense laser beams in nonuniform and uniform underdense cold plasmas is studied. After simplifying the wave equation, we obtain the evolution equation of the transverse centroid of laser beams in terms of variational approaches. Theoretical analysis shows that in uniform plasmas a laser beam with an asymmetric initial phase has a constant centroid drift velocity, at which the centroid of the laser beam drifts away from the light axis in a fixed direction; the centroid drift velocity of a laser beam with symmetric initial phase, but either symmetric or asymmetric amplitude, is always zero, i.e., the symmetric features of the laser field is retained. Furthermore, the channel-like symmetric plasma plays a role like a restoring force to confine the laser centroid around the density channel axis so the centroid of the laser beam with asymmetric amplitude or phase is going to oscillate with damp around the channel axis. The nonlinear effect can symmetrize initially asymmetric laser beams and the steeper effective density gradient is more beneficial to the symmetrizing process. Finally, the analytic results are checked and confirmed by numerical simulations with finite difference to the wave equation and two-dimensional particle-in-cell code.