Composite optical vortices in noncollinear Laguerre--Gaussian beams and their propagation in free space

Taking two Laguerre--Gaussian beams with topological charge l=±1 as an example, this paper studies the composite optical vorticesformed by two noncollinear Laguerre--Gaussian beams with differentphases, amplitudes, waist widths, off-axis distances, and theirpropagation in free space. It is shown by detailed numericalillustrative examples that the number and location of compositevortices at the waist plane are variable by varying the relativephase β, amplitude ratio η, waistwidth ratio textitζ, or off-axis distance ratio μ. The net topological charge l_net is not always equal tothe sum l_sum of charges of the two component beams. Themotion, creation and annihilation of composite vortices take placein the free-space propagation, and the net charge during thepropagation remains unchanged and equals to the net charge at thewaist plane.