Vectorial manipulation of twisted vector vortex optical fields in strongly nonlocal nonlinear media

We theoretically investigate the propagation properties and vectorial manipulation of twisted vector vortex beams (TVVB) with a cross-phase in a strongly nonlocal nonlinear medium (SNNM). The root mean square beam-width (RMS-BW) and the critical power required to retain the invariant RMS-BM of the TVVB in an SNNM are derived using the coupled nonlocal nonlinear Schrödinger equation. Numerical calculations reveal novel characteristics of the evolution of the state of polarization (SoP) and the optical intensity distributions during the TVVB propagating in an SNNM. It is found that mode conversions between a Laguerre Gaussian and a Hermite Gaussian mode take place during propagation in an SNNM, and the topological charge of the TVVB can be accurately measured by observing the interference intensity structure in the cross-section. Manipulation of the beam shape, SoP, and rotation of the TVVB is achieved by controlling factors such as the initial power, twisting coefficient, initial beam-width, and topological charge. These findings hold promise for applications in optical micro-manipulation, optical communication, and material processing.