We extend the work of photon sieves to spiral photon sieves (SPSs) for the generation of a hard-x-ray vortex. A robust digital prolate spheroidal window, which has an optimal energy concentration at low frequencies, was used to adjust the number of pinholes on each ring of the SPS. It was demonstrated that an SPS has better spatial resolution and lower background than a spiral zone plate using the specified smallest structures condition. The intensity at the center of the dark core is difficult to damp to true zero, primarily owing to current limitations of high-aspect-ratio metal nanostructures. The diameter of the dark core increases as the charge value increases. However, the FWHM of the doughnut-shaped ring and background will also increase. Our results pave the way toward the design of high-performance SPSs for the generation of a hard-x-ray vortex.

In recent years, much effort is dedicated to the generation of vectorial optical fields with an arbitrary spatially varying polarization distribution by means of metasurfaces. However, simultaneous and independent control of the amplitude, phase, and polarization is still challenging, especially for the multichannel generation of a vectorial optical field with an angle‐multiplexed functionality. Here, a facile route, called coherent pixel polarization metaholography, is proposed to realize multichannel, angle‐multiplexed, and arbitrary spatially varying polarization fields and demonstrate how to enable a fully independent realization of full Poincaré beams (lemon, start, spider, and web beams), dual‐way switching print images, vectorial print images, and optical polarization knot profiles. Importantly, the demonstrated angle‐multiplexed metasurfaces have an independently controllable handedness and azimuth and can possess up to four channels. Such angle‐multiplexed multichannel arbitrary spatial polarization fields may enable various applications, including optical dynamic displays, information communication, optical encryption, and quantum experiments.

Binary phase square spiral zone plates (BPSSZPs), a special type of binary phase vortex lenses, are introduced to generate focused optical vortices showing square symmetry. The numerical solution and fabrication method, as well as the experimental results are given. Different from conventional vortex lenses, these BPSSZPs produce focused vortices with small topological charge following a modulo-4 transmutation rule. In addition, the central diffracted image rotates in the vicinity of the focal plane. These interesting properties suggest that BPSSZPs might become key components for many potential applications such as optical image processing and quantum computation.