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The intensity distributions and statistics of partially coherent light fields with random fluctuations have proven to be more robust than for coherent light. However, its full potential in practical applications has not been realized due to the lack of four-dimensional optical field measurement. Here, a general incoherent modal decomposition method of partially coherent light field is proposed and demonstrated experimentally. The decomposed random modes can be used to, but not limited to, reconstruct average intensity, cross-spectral density, and orthogonal decomposition properties of the partially coherent light fields. The versatility and flexibility of this method allows it to reveal the invariance of light fields and to retrieve embedded information after propagation through complex media. The Gaussian-shell-model beam and partially coherent Gaussian array are used as examples to demonstrate the reconstruction and even prediction of second-order statistics. This method is expected to pave the way for applications of partially coherent light in optical imaging, optical encryption, and antiturbulence optical communication.

Coherent diffractive imaging (CDI), especially the ptychography, has been widely used in quantitative phase imaging. However, in traditional diffractive imaging schemes, a highly coherent light source is required for a better-posed inverse problem. Considering that the high coherence cannot be guaranteed in all cases and to avoid the multi-mode of low-coherence light sources complicating the iterative modeling of diffractive imaging, we proposed an overlap-scanning self-referencing diffractive imaging. As a non-iterative partially coherent diffractive imaging method, self-referencing diffractive imaging was combined with the procedure of overlap-scanning ptychography. It does not require prior knowledge of light source coherence, and only a coherent inverse problem was needed to be solved in the final stitching. It has been demonstrated to be able to recover the complex amplitude of objects illuminated by various low-coherence light sources. This study presents significant potential for applications in phase imaging with a wide-field of view under incoherent illuminations. [ABSTRACT FROM AUTHOR]

As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro-particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano-optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.

Zero-order and higher-order Bessel beams are well-known nondiffracting beams. Namely, they propagate with invariant profile (intensity) and carry a fixed orbital angular momentum. Here, we propose and experimentally study an anomalous Bessel vortex beam. Unlike the traditional Bessel beams, the anomalous Bessel vortex beam carries decreasing orbital angular momentum along the propagation axis in free space. In other words, the local topological charge is inversely proportional to the propagation distance. Both the intensity and phase patterns of the generated beams are measured experimentally, and the experimental results agree well with the simulations. We demonstrate an easy way to modulate the beam’s topological charge to be an arbitrary value, both integer and fractional, within a continuous range. The simplicity of this geometry encourages its applications in optical trapping and quantum information, and the like.