In this Letter, a photonic crystal (PC) flat lens with a scatterer-size gradient is proposed, which simultaneously achieves imaging of the point source and sub-wavelength focusing of the plane wave in the first, second, and fifth bands. The imaging of the point source breaks through the diffraction limit in the second and fifth bands. The PC flat lens with the scatterer-size gradient is expected to be used in a new multifunctional optical imaging and focusing device, which improves the application potential of a PC flat lens.

The full aperture complex amplitude transmittance function of a multi-level diffraction lens with mask-alignment errors was derived based on scalar diffraction theory. The point spread function (PSF) was calculated by the Kirchhoff diffraction integral. It is found that the radius of the Airy disk increases with the increase of the error in the direction of misalignment, and the image center shifts along the direction of misalignment. A four-level diffractive lens with a diameter of 80 mm was fabricated, and its PSF and diffraction efficiency of +1st order were calculated and measured. The distribution of PSF is consistent with the calculated results, and the tested diffraction efficiency is slightly smaller than the calculated value; the relative error is 5.71%.

We propose axial line-focused spiral zone plates (ALFSZPs) for generating tightly focused X-ray vortex beams with ultra-long depth of focus (DOF) along the propagation direction. In this typical design, compared with the conventional spiral zone plates (SZPs) under the same numerical aperture (NA), the DOF of ALFSZPs has been extended to an ultra-length by optimizing the corresponding parameters. Besides, it also exhibits lower side lobes and smaller dark cores in the whole focus volume. The diameters of dark cores increase as the topological charge value increases.

Metasurfaces have become a new photonic structure for providing potential applications to develop integrated devices with small thickness, because they can introduce an abrupt phase change by arrays of scatterers. To be applied more widely, active metasurface devices are highly desired. Here, a tunable terahertz meta-lens whose focal length is able to be electrically tuned by ～4.45λ is demonstrated experimentally. The lens consists of a metallic metasurface and a monolayer graphene. Due to the dependence of the abrupt phase change of the metasurface on the graphene chemical potential, which can be modulated using an applied gate voltage, the focal length is changed from 10.46 to 12.24 mm when the gate voltage increases from 0 to 2.0 V. Experimental results are in good agreement with the theoretical hypothesis. This type of electrically controlled meta-lens could widen the application of terahertz technology.

A liquid crystal Pancharatnam–Berry (PB) axilens is proposed and fabricated via a digital micro-mirror-device-based photo-patterning system. The polarization-dependent device behaves as an axilens for a left-handed circularly polarized incident beam, for which an optical ring is focused with a long focal depth in the transverse direction at the output, and an anti-axilens for a right-handed circularly polarized incident beam, for which an optical ring gradually expands at the output. The modification of the size and the sharpness of the diffracted ring beam is demonstrated by encoding a positive (negative) PB lens term into the director expression of a PB (anti-)axicon.

We design a new kind of phase zone plates (PZPs) to improve the diffraction efficiency of soft x ray zone plates (ZPs). The design replaces blank parts of PZPs with metals of negative phase shift at the working energy, which is called as the positive and negative PZPs (PNPZPs). According to the calculation, PNPZPs have a higher maximum efficiency than conventional ZPs with the same zone width. With the help of a negative phase coefficient, it is much easier to achieve a π phase shift in one period, resulting in a smaller zone height. This design can help fabricate finer PZPs to achieve a better image resolution.

The demand for space-borne telescopes with an aperture of 20 m is forcing the development of large diameter diffractive Fresnel zone lenses (FZLs) on membranes. However, due to the fabrication errors of multi-level microstructures, the real diffraction efficiency is always significantly smaller than the theoretical value. In this Letter, the effects of a set of fabrication errors on the diffraction efficiency for a diffractive membrane are studied. In order to verify the proposed models, a 4-level membrane FZL with a diameter of 320 mm is fabricated. The fabrication errors of the membrane FZL are measured, and its diffraction efficiency in the +1 order is also tested. The results show that the tested diffraction efficiency is very close to the calculated value based on the proposed models. It is expected that the present work could play a theoretical guiding role in the future development of space-borne diffractive telescopes.