The transverse spin and orbital-to-spin angular momentum conversion during strong focusing of light beams have attracted wide interest due to the novel physics behind and their broad potential applications. In this work, we study the effect of incident beam's degree of polarization on the localized spin density of a tightly focused field. By modulating the correlation strength between two orthogonally polarized vortex modes of the incident beam, we find that the magnitude of the focal-plane transverse spin density component changes only slightly, while its spatial shape becomes an isotropic spin vortex with the decrease of the incident degree of polarization. Whereas, the longitudinal spin density, induced by the vortex phase, reduces its magnitude significantly with the decrease of incident beam's degree of polarization. The behavior of the focal-plane spin density is interpreted with the two-dimensional degrees of polarization among the tightly focused field components. Furthermore, we explore the roles of the topological charge on enhancing the longitudinal spin density for unpolarized incident beam. Our results reveal the feasibility of spin-orbit interaction with partially polarized or even completely unpolarized light, such as the thermal light.
Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light–matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards–Wolf’s vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam’s initial polarization state is also discussed.
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