Control over the dispersion of the refractive index is essential to the performance of most modern optical systems. These range from laboratory microscopes to optical fibres and even consumer products, such as photography cameras. Conventional methods of engineering optical dispersion are based on altering material composition, but this process is time-consuming and difficult, and the resulting optical performance is often limited to a certain bandwidth. Recent advances in nanofabrication have led to high-quality metasurfaces with the potential to perform at a level comparable to their state-of-the-art refractive counterparts. In this Review, we introduce the underlying physical principles of metasurface optical elements (with a focus on metalenses) and, drawing on various works in the literature, discuss how their constituent nanostructures can be designed with a highly customizable effective index of refraction that incorporates both phase and dispersion engineering. These metasurfaces can serve as an essential component for achromatic optics with unprecedented levels of performance across a broad bandwidth or provide highly customized, engineered chromatic behaviour in instruments such as miniature aberration-corrected spectrometers. We identify some key areas in which these achromatic or dispersion-engineered metasurface optical elements could be useful and highlight some future challenges, as well as promising ways to overcome them. Flat metasurface optics provides an emerging platform for combining semiconductor foundry methods of manufacturing and assembling with nanophotonics to produce high-end and multifunctional optical elements. This Review highlights the design of metasurfaces, recent advances in the field and initial promising applications.

Flat optics with dispersion-engineered metasurfaces

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.

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Roadmap on superoscillations

Graphene is a 2D sheet of sp2 bonded carbon atoms and tends to aggregate together, due to the strong π-π stacking and van der Waals attraction between different layers. Its unique properties such as a high specific surface area and a fast mass transport rate are severely blocked. To address these issues, various kinds of 2D holey graphene and 3D porous graphene are either self-assembled from graphene layers or fabricated using graphene related materials such as graphene oxide and reduced graphene oxide. Porous graphene not only possesses unique pore structures, but also introduces abundant exposed edges and accelerates mass transfer. The properties and applications of these porous graphenes and their composites/hybrids have been extensively studied in recent years. Herein, recent progress and achievements in synthesis and functionalization of various 2D holey graphene and 3D porous graphene are reviewed. Of special interest, electrochemical applications of porous graphene and its hybrids in the fields of electrochemical sensing, electrocatalysis, and electrochemical energy storage, are highlighted. As the closing remarks, the challenges and opportunities for the future research of porous graphene and its composites are discussed and outlined.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/smll.201903780

Recent Advances of Porous Graphene: Synthesis, Functionalization, and Electrochemical Applications.

Traditional objective lenses in modern microscopy, based on the refraction of light, are restricted by the Rayleigh diffraction limit. The existing methods to overcome this limit can be categorized into near-field (e.g., scanning near-field optical microscopy, superlens, microsphere lens) and far-field (e.g., stimulated emission depletion microscopy, photoactivated localization microscopy, stochastic optical reconstruction microscopy) approaches. However, they either operate in the challenging near-field mode or there is the need to label samples in biology. Recently, through manipulation of the diffraction of light with binary masks or gradient metasurfaces, some miniaturized and planar lenses have been reported with intriguing functionalities such as ultrahigh numerical aperture, large depth of focus, and subdiffraction-limit focusing in far-field, which provides a viable solution for the label-free superresolution imaging. Here, the recent advances in planar diffractive lenses (PDLs) are reviewed from a united theoretical account on diffraction-based focusing optics, and the underlying physics of nanofocusing via constructive or destructive interference is revealed. Various approaches of realizing PDLs are introduced in terms of their unique performances and interpreted by using optical aberration theory. Furthermore, a detailed tutorial about applying these planar lenses in nanoimaging is provided, followed by an outlook regarding future development toward practical applications.

Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications.

The resolution of conventional optical elements and systems has long been perceived to satisfy the classic Rayleigh criterion. Paramount efforts have been made to develop different types of superresolution techniques to achieve optical resolution down to several nanometres, such as by using evanescent waves, fluorescence labelling, and postprocessing. Superresolution imaging techniques, which are noncontact, far field and label free, are highly desirable but challenging to implement. The concept of superoscillation offers an alternative route to optical superresolution and enables the engineering of focal spots and point-spread functions of arbitrarily small size without theoretical limitations. This paper reviews recent developments in optical superoscillation technologies, design approaches, methods of characterizing superoscillatory optical fields, and applications in noncontact, far-field and label-free superresolution microscopy. This work may promote the wider adoption and application of optical superresolution across different wave types and application domains.

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Superoscillation: from physics to optical applications.

The generation of a sub-diffraction longitudinally polarized spot is of great interest in various applications, such as optical tweezers, super-resolution microscopy, high-resolution Raman spectroscopy, and high-density optical data storage. Many theoretical investigations have been conducted into the tight focusing of a longitudinally polarized spot with high-numerical-aperture aplanatic lenses in combination with optical filters. Optical super-oscillation provides a new approach to focusing light beyond the diffraction limit. Here, we propose a planar binary phase lens and experimentally demonstrate the generation of a longitudinally polarized sub-diffraction focal spot by focusing radially polarized light. The lens has a numerical aperture of 0.93 and a long focal length of 200λ for wavelength λ = 632.8 nm, and the generated focal spot has a full-width-at-half-maximum of about 0.456λ, which is smaller than the diffraction limit, 0.54λ. A 5λ-long longitudinally polarized optical needle with sub-diffraction size is also observed near the designed focal point.

Creation of Sub-diffraction Longitudinally Polarized Spot by Focusing Radially Polarized Light with Binary Phase Lens.

Terahertz wave imaging offers promising properties for non-destructive testing applications in the areas of homeland security, medicine, and industrial inspection. However, conventional optical lenses are heavy and bulky and difficult to integrate. An all-dielectric metasurface provides an attractive way to realize a planar lens of light weight that is ultrathin and offers ease of integration. Terahertz lenses based on various metasurfaces have been studied, especially for the application of wave focusing, while there are few experimental demonstrations of terahertz wave imaging lenses based on an all-dielectric metasurface. In the present work, we propose a metalens based on an all-dielectric metasurface with a sub-wavelength unit size of 0.39λ for terahertz wave imaging and experimentally demonstrate its performance in focusing and imaging. A large numerical aperture metalens was fabricated with a focal length of 300λ, radius of 300λ, and numerical aperture of 0.707. The experimental results show that the lens can focus THz waves with an incident angle up to 48°. More importantly, clear terahertz wave images of different objects were obtained for both different cases of forward- and inverse-incident directions, which demonstrate the reversibility of the metalens for imaging. Such a metalens provides a way for realization of all-planar-lens THz imaging system, and might find application in terahertz wave imaging, information processing, microscopy, and others.

All-dielectric metalens for terahertz wave imaging.

Planar lenses are attractive photonic devices due to its minimized size and easy to integrate. However, planar lenses designed in traditional ways are restricted by the diffraction limit. They have difficulties in further reducing the focal spot size beyond the diffraction limit. Super-oscillation provides a possible way to solve the problem. However, lenses based on super-oscillation have always been affected by huge sidelobes, which resulted in limited field of view and difficulties in real applications. To address the problem, in the paper, a far-field sub-diffraction lens based on binary amplitude-phase mask was demonstrated under illumination of linearly polarized plane wave at wavelength 632.8 nm. The lens realized a long focal length of 148λ (94 µm), and the full width at half maximum of the focal line was 0.406λ, which was super-oscillatory. More important is that such a flat lens has small sidelobes and wide field of view. Within the measured range of [-132λ, + 120λ], the maximum sidelobe observed on the focal plane was less than 22% of the central peak. Such binary amplitude-phase planar lens can also be extended to long focal length far-field sub-diffraction focusing lens for other spectrum ranges.

Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light.

In traditional optics, the focal spot size of a conventional lens is restricted to the diffraction limit 0.5λ/NA, where λ is the wavelength in vacuum and NA is the numerical aperture of the lens. Recently, various sub-diffraction focusing optical devices have been demonstrated, but they usually have short focal length and high numerical aperture. Moreover, they always suffer the problem of huge sidelobes near the focal spot and small field of view, especially when the focal spot size is less than the super-oscillation criteria 0.38λ/NA. To address the problem, here, we reported a far-field sub-diffraction point-focusing lens based on binary phase and amplitude modulation with ultra-long focal length 252.8 μm (399.5λ) and small numerical aperture 0.78 and experimentally demonstrated a super-oscillatory focusing of circularly polarized light with spot size 287 nm (0.454λ), smaller than the diffraction limit 0.64λ and the super-oscillation criterion 0.487λ. What’s more, on the focal plane, in the measured area within the radius of 142λ, the largest sidelobe intensity is less than 26% of the central lobe intensity. Such ultra-long distance super-oscillatory focusing with small sidelobes and large field of view has great potential applications in far-field super-resolution microscopy, ultra-high-density optical storage and nano-fabrication.

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Zhihai Zhang

Papers

Creation of Sub-diffraction Longitudinally Polarized Spot by Focusing Radially Polarized Light with Binary Phase Lens.

All-dielectric metalens for terahertz wave imaging.

Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light.

Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation.

Broadband Achromatic Sub-Diffraction Focusing by an Amplitude-Modulated Terahertz Metalens