Evolution of an optical vortex with an initial fractional topological charge

Abstract

In the general case, upon free-space propagation of a paraxial optical vortex (OV) its topological charge (TC) is not conserved, unlike the orbital angular momentum (OAM), which remains unchanged. In this work, we discuss a Gaussian beam with fractional TC in the source plane, showing theoretically and numerically in which way the TC is changing (but remains integer) upon free-space propagation. There are four evolution scenarios for an original OV with fractional TC that depend on how close the original TC is to an integer even or odd number. If the TC in the initial plane has an arbitrary fractional value, it becomes an odd integer in the Fourier plane. If the initial TC is close to an odd integer number, then, on propagation, an OV with a TC of +1 is born in the Fresnel diffraction zone, while in the far field an OV with a TC of --1 appears. This optical vortex with a TC of --1 is located in the beam periphery where the intensity is almost zero and thus it is difficult to detect it experimentally. Additional vortices with a TC of +1 and \ensuremath{-}1 are generated in the beam with the initial fractional TC due to the interference between a linear source appearing in the area of phase jump and an ordinary optical vortex with an integer TC. An experiment on registering the optical vortices by using the interferograms matches the theory and simulation. For simple OVs (such as Laguerre-Gaussian or Bessel-Gaussian modes), TC is conserved both upon propagation and following weak phase distortions. When scattered from a random phase screen, the integer TC of an OV is experimentally shown to conserve until random path-difference distortion reaches a half wavelength. Because of this, under weak-turbulence conditions, it makes sense to measure a discretely changing TC, rather than measuring the continuously varying OAM.