We demonstrate a metamaterial superlens: a planar array of discrete subwavelength metamolecules with individual scattering characteristics tailored to vary spatially to create subdiffraction superoscillatory focus of, in principle, arbitrary shape and size. Metamaterial free-space lenses with previously unattainable effective numerical apertures -as high as 1.52 -and foci as small as 0.33λ in size are demonstrated. Superresolution imaging with such lenses is experimentally verified breaking the conventional diffraction limit of resolution and exhibiting resolution close to the size of the focus. Our approach will enable far-field label-free super-resolution nonalgorithmic microscopies at harmless levels of intensity, including imaging inside cells, nanostructures, and silicon chips, without impregnating them with fluorescent materials.

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing. Rev. E 67, 046611 (2003).

Unlabeled super-resolution is the next grand challenge in imaging. Stimulated emission depletion and single-molecule microscopies have revolutionized the life sciences but are still limited by the need for reporters (labels) embedded within the sample. While the Veselago–Pendry “super-lens,” using a negative-index metamaterial, is a promising idea for imaging beyond the diffraction limit, there are substantial technological challenges to its realization. Another route to far-field subwavelength focusing is using optical superoscillations: engineered interference of multiple coherent waves creating an, in principle, arbitrarily small hotspot. Here, we demonstrate microscopy with superoscillatory illumination of the object and describe its underlying principles. We show that far-field images taken with superoscillatory illumination are themselves superoscillatory and, hence, can reveal fine structural details of the object that are lost in conventional far-field imaging. We show that the resolution of a superoscillatory microscope is determined by the size of the hotspot, rather than the bandwidth of the optical instrument. We demonstrate high-frame-rate polarization-contrast imaging of unmodified living cells with a resolution significantly exceeding that achievable with conventional instruments. This non-algorithmic, low-phototoxicity imaging technology is a powerful tool both for biological research and for super-resolution imaging of samples that do not allow labeling, such as the interior of silicon chips.

Superoscillations are making a growing impact on an ever-increasing number of real-world applications, as early theoretical analysis has evolved into wide experimental realisation. This is particularly true in optics: the first application area to have extensively embraced superoscillations, with much recent growth. This review provides a tool for anyone planning to expand the boundaries in an application where superoscillations have already been used, or to apply superoscillations to a new application. By reviewing the mathematical methods for constructing superoscillations, including their considerations and capabilities, we lay out the options for anyone wanting to construct a device that uses superoscillations. Superoscillations have inherent trade-offs: as the size of spot reduces, its relative intensity decreases as high-energy sidebands appear. Different methods provide solutions for optimising different aspects of these trade-offs, to suit different purposes. Despite numerous technological ways of realising superoscillations, the mathematical methods can be categorised into three approaches: direct design of superoscillatory functions, design of pupil filters and design of superoscillatory lenses. This categorisation, based on mathematical methods, is used to highlight the transferability of methods between applications. It also highlights areas for future theoretical development to enable the scientific and technological boundaries to be pushed even further in real-world applications.

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