Dynamic evolution of Riemann-Silberstein vortices for Gaussian vortex beams
The dynamic evolution of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=±1 in free space is studied. It is shown that for Gaussian on-axis vortex beams there exist both RS vortex with m=+2 and circular edge dislocation. For Gaussian off-axis vortex beams the circular edge dislocation splits into two RS vortices with opposite topological charges m=±1 and the RS vortex with m=+2 decays into two vortices with same topological charges m=+1. The motion of RS vortices takes place by varying the propagation distance, waist width, off-axis parameter, or topological charge. RS vortices for Gaussian vortex-free beams can be treated as a special case. The results are illustrated analytically and numerically.