Evolution of a fractional-charge optical vortex upon free-space propagation

Previously, it has been demonstrated theoretically (J. Opt. 6, 259 (2004)) and experimentally (Opt Express 19, 5760 (2011)) that upon the free-space propagation, an initial fractional-charge optical vortex acquires an integer topological charge (TC) equal to the nearest smaller integer if the fractional part is less than 0.5, otherwise becoming equal to the nearest larger integer. In this work, we demonstrate by the numerical modeling that as an initial fractional-charge optical vortex propagates in free space, the TC changes to the nearest smaller or larger integer at a fractional part threshold of 0.12. The fact is that an additional singularity center is born on the beam periphery where the field intensity is near-zero (one millionth part of the maximum), meaning that it cannot be experimentally detected but can be numerically simulated.