Optical phase singularities and superluminal motion in unbounded space

In this paper, we summarize a remarkable result obtained by Soskin et al. in Phys Rev A 56, 4064 (1997). We show that for an on-axis superposition of two different-waist Laguerre-Gauss beams with numbers (0, n) and m), the topological charge equals TC=m up to plane where waist radii become same, given beam m) has greater radius, changing TC=n after plane. This occurs because initial op-tical vortex on different axis-centered circles there are (n – vortices TC= +1 –1. On approaching above-specified plane, -1 "depart" infinity higher-than-light speed, TC total becoming equal TC=n. If, contrary, smaller waist, then n path from said n–m –1 "arrive" speed.