Spatial evolution of coupled-optical vortices

Vortices in electromagnetic field are called optical vortices, which are well quantized and carry a well-defined orbital angular momentum of light (Allen et al., 1992). The main character of optical vortices is their phase distribution of mphi (m; integer), which provides a helical shape for the wavefronts around the beam center with phase singularity. Here, phi is the azimuthal angle and m is the azimuthal index that represents topological charge, that is, the number of 2pi cycles in phase about circumference. The electro-magnetic amplitude at the vortex center becomes zero, because of the phase uncertainty. For coupled vortices, their intensity profile has coupled dark spots corresponding to phase-singular points of constituent vortices in the beam cross section. While a three-dimensional trajectory of the vortex-center position describes straight line for a single vortex, it is expected that trajectories of phase singular points for coupled vortices are deviated from the straight lines, owing to "a vortex-vortex interaction". Quantum vortices appear not only in electro-magnetic wavefronts but also in Bose-Einstein condensates (BECs) (Madison et al., 2001) or a quantum fluid. Vortices affect the physical properties of systems such as BECs and/or a quantum fluid. Optical vortices can be a good simulator in discussing the interaction between vortices, in the context that the laser beam is regarded as one of the coherent condensates. In the present study, we investigated the spatial evolution of phase-singular points in coupled-optical vortices.