Breakup of Ring Beams Carrying Orbital Angular Momentum in Sodium Vapor

We have observed filamentation due to azimuthal modulational instabilities in spinning ring solitons with orbital angular momentum $m\hslash$ in sodium vapor. We show experimentally that vortex beams with $m$ values of 1, 2, and 3 tend to break into two, four, and six filaments, respectively. Treating the sodium vapor as a Doppler broadened two-level atomic system, we find that we can accurately model the propagation and breakup of these beams with numerical simulations.

Figure 1

The experimental setup used to observe filamentation of ring solitons in sodium vapor.

Figure 2

The experimental output (a) for an $m=1$ beam with a pulse energy of 76 nJ breaking into two filaments at a wavelength of 588.950 nm, and (b) tuned far from resonance. In (c) and (d) we show the equivalent results from our computer simulations with parameters corresponding to our experiment and a random $1.5\%$ amplitude noise added to the input beam.

Figure 3

The experimental output (a) for an $m=2$ beam with a pulse energy of 234 nJ breaking into four filaments at a wavelength of 588.943 nm, and (b) tuned far from resonance. In (c) and (d) we show the equivalent results from our computer simulations.

Figure 4

The experimental output (a) for an $m=3$ beam with a pulse energy of 359 nJ breaking into six filaments at a wavelength of 588.943 nm, and (b) tuned far from resonance. In (c) and (d) we show the equivalent results from our simulations.

Figure 5

The beam profile at the output of the sodium cell at higher powers than those used in Figs. 2, 3, 4. The tendency of the beam to break into filaments is largely suppressed. (a) $m=1$ at $9.1\mu \mathrm{J}$; (b) $m=2$ at $24.1\mu \mathrm{J}$; (c) $m=3$ at $6.63\mu \mathrm{J}$.