Propagation dynamics of an azimuthally polarized Bessel-Gauss laser beam in a parabolic plasma channel

The propagation dynamics of an azimuthally polarized dark hollow laser beam described by a first-order Bessel-Gauss laser beam in a parabolic plasma channel is investigated by adopting the weakly relativistic limit. By using the variational method, the evolution equation of the ring-beam radius is derived and the ring-beam width is proportional to and synchronous with the radius. It is found that the azimuthal polarization can weaken the vacuum diffraction effect and the propagation dynamics of the dark hollow laser beam may be classified into three types, i.e., propagation with a constant ring-beam radius and width, or synchronous periodic defocusing oscillation, or synchronous periodic focusing oscillation. Their corresponding critical conditions and characteristic quantities, such as the amplitudes and spatial wavelengths, are obtained. Further investigation indicates that, with the increase in the initial laser power or the ratio of initial ring-beam radius to channel radius, the dark hollow beam may experience a process from synchronous periodic defocusing oscillation to constant propagation and then to synchronous periodic focusing oscillation, in which the corresponding amplitudes decrease sharply to zero (constant propagation) and then increase gradually, while the spatial wavelength decreases continuously. The evolution type of this kind of dark hollow beam also depends on its initial amplitude but is insensitive to the initial laser profile which, however, has a large influence on the spatial wavelength. These results are well confirmed by the numerical simulation of the wave equation. A two-dimensional particle-in-cell simulation of an azimuthally polarized laser beam is performed finally and also reveals the main results.