Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"

In this work, using the Rayleigh-Sommerfeld integral and Berry formula, topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It shown that for different parts TС, beam contains number screw dislocations, which determine TС entire beam. With small part consists main centered on axis equal to nearest integer (let be n), two edge dislocations located vertical (above below center). increase in TC, "dipole" formed from upper dislocation, consisting vortices TC+1 –1. further part, additional displaced center beam, TC–1 periphery. another lower which, contrary, (to beam), When becomes 1/2, "lower" TC–1, was begins shift periphery, "upper" moves closer merges when approaches 1. Such dynamics whole have (n or n+1) values segment [n, n+1].