Tight focusing properties of vector polarized partially coherent vortex beams

Aiming at tightly focusing vector polarized partially coherent vortex laser beams, this paper introduced a new kind of vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) power-exponent-phase vortex beam (PEPVB). Based on the vectorial diffraction theory, this work theoretically and numerically investigated the tight focusing properties of radially polarized MGSMPEPVB passing through a high numerical aperture objective lens. Thus, we analyzed the impact of topological charge, power exponent, beam index and coherence length on the intensity of focal zone. We discovered that by increasing beam index, the intensity distribution of focal plane gradually changed from Gaussian to flat-top. Especially, when the power exponent was a non-negative fraction close to 1, regardless of whether the topological charge was an integer or not, the circular symmetry of the focused spot at focal plane would be destroyed, showing a non-uniform and asymmetric central dark core optical intensity distribution. Besides, the value of the fractional part of the topological charge would make the hollow structure of the central dark core fully open due to the introduction of power-exponent phase, which is an improvement over the tight focusing properties of radially polarized MGSM vortex beams. This work has clearly demonstrated that by changing the values of topological charge, power exponent, beam index and coherence length, the special focal spot structures with different intensity distributions including flat-top beam and irregular hollow beam can be obtained, which have many potential applications in laser machining and particle capturing such as manipulation of certain irregular microparticles.