Interference patterns of vortex beams based on photonic band gap structure.

We experimentally observe a vortex six-wave mixing (SWM), namely, enhanced four-wave mixing (FWM), signal with its orbital angular momentum transferred from a vortex probe via a photonic band gap (PBG) structure in a hot rubidium vapor cell. By analyzing spatial images and interference patterns, on the one hand, we demonstrate spatial shift and splitting of the images as well as shift of phase singularity for the probe transmission signal under the nonlinear phase of different dressing fields; on the other hand, we observe defocusing and shift of the images as well as shift of phase singularity for the reflected vortex SWM signal by scanning the frequency detuning of a related field. Moreover, we find the interference patterns of the vortex probe can be switched from parallel shape to spiral shape by changing its incident angle. Also, we further research the spiral interference patterns of the transmitted signal by scanning the probe detuning, observing that the number of forks changes with the detuning. We consider the transmitted signal as a combined beam of the linear probe and nonlinear FWM, which are separated under Kerr effect. It is the separation that causes the fork number to change with probe detuning. Our studies are useful for better understanding and manipulation of optical vortices and have wide applications in quantum communication and information processing.