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Focusing properties of a radially polarized double-ring-shaped beam with an annular classical axicon are numerically investigated based on vector Debye theory. Double focal spots and a flat-topped beam can be generated by choosing appropriate values of the pupil to the beam ratio β, numerical aperture, and annular obstruction. The distance between the twin spots, their depth of focus and the depth of the flat-topped beam are considerably affected by numerical aperture and annular obstruction. These focal shapes may find applications in laser printing, multifocal microscopy, and material processing.

Within the framework of inverse diffractive optics, we present a design for diffractive axicons in twisted, spatially partially coherent fields, in particular twisted Gaussian Schell-model (TGSM) fields. The design is based on the method of stationary phase. A general modification is introduced to the inverse diffractive optics approach for improving the synthesized optical element to produce the desired intensity distribution. Both the design and modification are demonstrated with annular-aperture axicons generating uniform-intensity axial line segments in partially coherent TGSM illumination.

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We investigate the propagation characteristics of partially coherent multi-Gaussian Schell-model (MGSM) and modified Bessel-correlated (MBc) vortex beams traveling in a turbulent plasma. Based on the extended Huygens-Fresnel principle, the cross-spectral density expressions for partially coherent MGSM and MBc vortex beams propagating through turbulent plasma were derived. The results show that the dark spot at the center of the partially coherent MGSM beams disappears in the low-coherence states and remains in the high-coherence states only. In contrast, the intensity of partially coherent MBc vortex beams exists in low- and high-coherence states and does not change during propagation in a weak turbulent plasma.