The intensity distribution of a partially coherent beam with a nonconventional correlation function, named the multi-Gaussian Schell-model (MGSM) beam, focused by an axicon was investigated in detail. Our numerical results showed that an optical needle with a flat-topped spatial profile and long focal depth was formed and that we can modulate the focal shift and focal depth of the optical needle by varying the width of the degree of coherence (DOC) and the parameters of the correlation function. The adjustable optical needle can be applied for electron acceleration, particle trapping, fiber coupling and percussion drilling.

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 cross-spectral density matrix of a nonparaxial SCRP beam propagating in free space is derived with the aid of the generalized Rayleigh–Sommerfeld diffraction integral. The statistical properties, such as average intensity, degree of polarization, and spectral degree of coherence, are studied comparatively for the nonparaxial SCRP beam and the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function. It is found that the nonparaxial properties of an SCRP beam are strikingly different from those of a PCRP beam. These nonparaxial properties are closely related to the correlation functions and the beam waist width. Our results may find potential applications in beam shaping and optical trapping in nonparaxial systems.

In [Opt. Lett. 38, 4023-4025 (2013)] the author predicted that the low coherent X-ray is hard to provide a high-resolution diffraction pattern from an object with a spatially periodic structure. This would severely restrict X-ray crystallography and its similar techniques. In this letter, we indicate that the Ghost diffraction technic takes advantage of the low coherence and may thus break through the bottleneck. Analytical formulae for calculating ghost diffraction patterns diffracted by the periodic structured media under any coherent state are derived.