Tightly focused properties of a partially coherent radially polarized power-exponent-phase vortex beam

A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then, the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.