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 vortices formed by two noncollinear Laguerre--Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio \textitζ, or off-axis distance ratio μ. The net topological charge l_net is not always equal to the sum l_sum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.