Polarization Evolution of a Vector Vortex Optical Field in a Strongly Nonlocal Nonlinear Medium

The evolution of a vector vortex optical field (VVOF) with a spiral phase and azimuthally-variant polarization distributions in the field cross-section in a strongly nonlocal nonlinear (SNN) medium is demonstrated. The dynamics of interplay between the singular points of polarization and vortex during propagation in the SNN medium leads to novel phenomena. When the topological charge number of the polarization is equal to that of the vortex, the singular point in the beam center is annihilated and the energy can accumulate in the beam center due to the self-focus effect. Furthermore, the linear-circular polarization conversion occurs and can be controllable in the beam center or the periphery of VVOF depending on the different topological charge numbers of the vortex and polarization, due to the coherent superposition of the different polarization components during propagation in an SNN medium. The VVOF rotates along the propagation axis in an SNN medium because of the existence of the vortex, and the optical field as well as the distribution of polarization in the field cross-section always evolves reciprocally with cycles of stretch and shrink in an SNN medium. The numerical results confirm the analytical predictions by the moment method for the vector dynamics of the VVOF during propagation in an SNN medium. The underlying physics for the linear circular polarization conversion in a VVOF during propagation in an SNN medium are discussed in detail.