Light-matter transfer of optical orbital angular momentum has been explored and precisely measured for a variety of systems [1]. Here we perform the first experimental demonstration of optical orbital angular momentum exchange between different field polarizations and we quantify the azimuthal optical flow resulting from the nonlinear interaction. Theoretically this exchange has been shown for saturable media [2]. In our studies in Kerr media, we confirm predictions that there exists an intermediate regime of power that optimizes this exchange, such that small changes in the input beam result in orbital angular momentum switching [3]. We vary the input spatial beam profile and power to influence multiple filamentation patterns by azimuthal modulational instability [4] and transmutation [5] and examine the dynamics in the context of orbital angular momentum exchange. This investigation establishes the connections between inhomogeneously polarized beams and helical phase-fronts, as well as the nonequilibrium phase dynamics that underlie multiple filamentation. Our experimental setup is shown in Fig. 1. We co-propagate a right-handed circularly-polarized (RHCP) vortex of topological charge m = 2 with a left-handed circularly-polarized (LHCP) flat-phase ring through BK7 glass. The linear propagation of the output filamentation patterns is imaged at several distances. We utilize the variational method of optical flow [6] to quantify and compare the small-angle rotation of the RHCP and LHCP components. Figures 2(a-d) show CCD images for powers below and above the threshold, where the LHCP undergoes filamention on and off-axis. Figure 2(e) shows the calculated azimuthal optical flow. Below switching, the m = 0 LHCP has one-tenth the azimuthal flow of the m = 2 RHCP. Above switching, the azimuthal flow is comparable for both polarizations.
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