Optimising superoscillatory spots for far-field super-resolution imaging

2D Super-Resolution Metrology Based on Superoscillatory Light

Progress in the semiconductor industry relies on the development of increasingly compact devices consisting of complex geometries made from diverse materials. Precise, label-free, and real-time metrology is needed for the characterization and quality control of such structures in both scientific research and industry. However, optical metrology of 2D sub-wavelength structures with nanometer resolution remains a major challenge. Here, a single-shot and label-free optical metrology approach that determines 2D features of nanostructures, is introduced. Accurate experimental measurements with a random statistical error of 18 nm (λ/27) are demonstrated, while simulations suggest that 6 nm (λ/81) may be possible. This is far beyond the diffraction limit that affects conventional metrology. This metrology employs neural network processing of images of the 2D nano-objects interacting with a phase singularity of the incident topologically structured superoscillatory light. A comparison between conventional and topologically structured illuminations shows that the presence of a singularity with a giant phase gradient substantially improves the retrieval of object information in such an optical metrology. This non-invasive nano-metrology opens a range of application opportunities for smart manufacturing processes, quality control, and advanced materials characterization.

Polarization-insensitive high-numerical-aperture metalens for wide-field super-resolution imaging

The development of super-oscillatory lens (SOL) offers opportunities to realize far-field label-free super-resolution microscopy. Most microscopes based on a high numerical aperture (NA) SOL operate in the point-by-point scanning mode, resulting in a slow imaging speed. Here, we propose a high-NA metalens operating in the single-shot wide-field mode to achieve real-time super-resolution imaging. An optimization model based on the exhaustion algorithm and angular spectrum (AS) theory is developed for metalens design. We numerically demonstrate that the optimized metalens with an NA of 0.8 realizes the imaging resolution (imaging pixel size) about 0.85 times the Rayleigh criterion. The metalens can achieve super-resolution imaging of an object with over 200 pixels, which is one order of magnitude higher than the unoptimized metalens. Our method provides an avenue toward single-shot far-field label-free super-resolution imaging for applications such as real-time imaging of living cells and temporally moving particles.

Supergrowth and sub-wavelength object imaging

We further develop the concept of supergrowth [Quantum Stud.: Math. Found.7, 285 (2020)10.1007/s40509-019-00214-5], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function higher than its largest wavenumber. We identify a canonical oscillatory function's superoscillating and supergrowing regions and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation-based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging.

Super-resolution multicolor fluorescence microscopy enabled by an apochromatic super-oscillatory lens with extended depth-of-focus

Planar super-oscillatory lens (SOL), a far-field subwavelength-focusing diffractive device, holds great potential for achieving sub-diffraction-limit imaging at multiple wavelengths. However, conventional SOL devices suffer from a numerical-aperture-related intrinsic tradeoff among the depth of focus (DoF), chromatic dispersion and focusing spot size. Here, we apply a multi-objective genetic algorithm (GA) optimization approach to design an apochromatic binary-phase SOL having a prolonged DoF, customized working distance (WD), minimized main-lobe size, and suppressed side-lobe intensity. Experimental implementation demonstrates simultaneous focusing of blue, green and red light beams into an optical needle of ~0.5λ in diameter and DOF > 10λ at WD = 428 μm. By integrating this SOL device with a commercial fluorescence microscope, we perform, for the first time, three-dimensional super-resolution multicolor fluorescence imaging of the "unseen" fine structures of neurons. The present study provides not only a practical route to far-field multicolor super-resolution imaging but also a viable approach for constructing imaging systems avoiding complex sample positioning and unfavorable photobleaching.

Super-resolution imaging based on radially polarized beam induced superoscillation using an all-dielectric metasurface

Superoscillation is a kind of phenomenon which can generate oscillation faster than the fastest component of a band-limited function. For optics, superoscillation is generated by coherence of low spatial frequency waves. It can bring a localized region named "hot spot", which has a smaller size than the diffraction-limit, and this character has potential applicaions in super-resolution imaging. Using a high-order radially polarized Laguerre-Gaussian beam tightly focused by high-NA objective lens, we can easily obtain and control the superoscillation hot spot. Using a metasurface, which has compact volume and sub-wavelength pixel size, we can generate the high-order radially polarized Laguerre-Gaussian beam more simply than conventional methods like using a liquid crystal mode converter. We first analyze the properties of unit cells of the metasurface and simulate the performance of the metasurface. Then we analyze the property of the tightly focused high-order radially polarized Laguerre-Gaussian beam and design a super-resolution imaging system using our designed metasurface. Therefore, the 2-fold lateral resolution enhancement is realized in our approach. This method can be used to improve lateral resolution in conventional confocal imaging systems.

Generation and Manipulation of Superoscillatory Hotspots Using Virtual Fourier Filtering and CTF Shaping

Superoscillation is a technique that is used to produce a spot of light (known as ‘hotspot’) which is smaller than the conventional diffraction limit of a lens and even smaller than the optical wavelength. Over the past few years, several techniques have been realized for the generation of the superoscillatory hotspot. In this article, for the first time to the best of our knowledge, we propose a novel and a more efficient technique for producing superoscillation in microscopic imaging by shaping the Coherent Transfer Function (CTF) of a lens via virtual Fourier filtering followed by a phase retrieval algorithm. We design and realize a phase mask which when placed at the pupil plane of a diffraction-limited lens produces a superoscillatory hotspot with sidelobes properly matched to the field of view (FOV) required in microscopic imaging applications, i.e. hotspot always coexists with huge intense rings known as ‘sidebands’ close to it and hence limiting the FOV. Our technique is also capable of extending the FOV with minimal loss in resolution of the hotspot generated and considerable ratio between the intensity of the hotspot to that of the side lobes while optimizing the obtainable FOV to the requirement of microscopy.

Efficiency-enhanced and sidelobe-suppressed super-oscillatory lenses for sub-diffraction-limit fluorescence imaging with ultralong working distance

Super-oscillatory lens (SOL) optical microscopy, behaving as a non-invasive and universal imaging technique, as well as being a simple post-processing procedure, may provide a potential application for sub-diffraction-limit fluorescence imaging. However, the low energy concentration, high-intensity sidelobes and micrometer-scale working distance of the reported planar SOLs impose unavoidable restrictions on the ground-state applications. Here, we demonstrate step-shaped SOLs based on the multiple-phase-modulated (MPM) method to improve the focusing efficiency. Two pivotal advantages are thus generated: (i) the fabrication complexity can be effectively reduced based on several conventional optical lithography steps; (ii) the focusing efficiency is much higher than that of the random MPM ones due to the efficient manipulation of the wavefronts, bringing about a stronger light concentration to the focal spot. Additionally, the ratio of the sidelobe intensity is flexibly tuned to meet the customized requirements, and a 2 mm-working-distance MPM SOL with the sidelobe intensity highly suppressed is finally exploited. For the first time, as far as we know, a SOL-based fluorescence microscopy without the pinhole filter to map the horizontal morphology of the dispersive fluorescent particles is established. Compared with the results achieved by the conventional wide-field microscopy, the sample details beating the diffraction limit can be reconstructed by simple imaging fusion. This research demonstrates the promising applications of SOLs for low-cost, simplified and highly customized sub-diffraction-limit fluorescence imaging systems free from photobleaching and an extremely short working distance.

Superresolution quantitative imaging based on superoscillatory field

The superresolution imaging of high-contrast objects is of great interest to many researchers. We propose a new method to achieve superresolution in inverse-scattering imaging of high-contrast dielectric objects. In the scheme of nonlinear inverse scattering, spatial superoscillatory incident fields are designed and applied in this research in order to retain the high-spatial-frequency components of the objects. The reconstruction results show that the proposed method resolves two objects with spacing 0.13λ. Compared with the orbital angular momentum (OAM)-carrying fields that compose a typical superoscillatory wave, the designed waveform is capable of achieving superresolution over the entire region of interest (ROI), while OAM possesses a limited superresolution area near the center of the ROI, which verifies the effectiveness of the proposed method.

Sub-wavelength annular-slit-assisted superoscillatory lens for longitudinally-polarized super-resolution focusing

A binary metallic superoscillatory lens assisted with annular subwavelength slits is proposed, which generates a longitudinally-polarized super-resolution focal point. The annular slits are designed to selectively transmit radially-polarized light. Simulations using the finite element method show a 0.24 λ focal spot with 21.8 dB of polarization purity and only 0.342 dB reduction in efficiency compared to a standard superoscillatory lens.

Reflection confocal nanoscopy using a super-oscillatory lens

A superoscillatory lens (SOL) is known to produce a sub-diffraction hotspot that is useful for high-resolution imaging. SOLs have not yet been directly used in a confocal reflection setup, as the SOL suffers from poor imaging properties. Additionally, the illuminating intensity distribution of the SOL still has high-intensity rings called sidelobes coexisting with the central hotspot. By means of a reflection setup, which does not have the SOL in the detection chain, thereby mitigating the poor imaging properties, we assessed the resolution capabilities of a SOL. This was done for different objects, whose dimensions were both above and below the SOL field-of-view (FOV). We found that the sidelobe illumination degrades the imaging properties in the case of extended objects, limiting the applicability of a SOL system.

Fluorescence emission difference microscopy by superoscillation excitation

A superresolution fluorescence emission difference (FED) microscopy based on superoscillation excitation is investigated. The solid superoscillation excitation spot is produced by the radially polarised Laguerre-Gaussian beam (LG), and the donut superoscillation excitation spot is produced by the same LG beam with spiral phase modulation. We show that the superoscillation excitation can enhance the spatial resolution of FED microscopy. When the ratio of the pupil radius and the second moment radius of the LG_3,1 beam is 0.85 and the subtractive factor is 0.3, the resolution can be enhanced about 2 times than the general confocal microscopy. Compared with the general FED microscopy, the resolution can be enhanced about 1.1 times. Our simulations also demonstrate that two-view Richardson-Lucy (RL) deconvolution method can reduce the effect of side lobes, which is related to subtractive factor and pinhole. LAY DESCRIPTION: The fluorescence emission difference (FED) microscopy is a high-resolution light microscopy, which is based on the subtraction of images produced by two different confocal imaging modes. Here, the solid excitation spot is used in one imaging mode, and the donut excitation spot is in another imaging mode. There are various ways that the solid and donut excitation spots can be structured, but superoscillation excitation spots are still not used in the FED microscopy. Considering that the main lobe of superoscillation can be arbitrarily small in principle, we exploit the radially polarised Laguerre-Gaussian beam (LG) and spiral phase plate to produce superoscillation solid and donut spots. We present a detailed analysis about the performance of FED microscopy via superoscillation excitation. Our analysis is based on vector diffraction theory and supported by simulations of imaging. We find the proposed FED microscopy has better resolution than the confocal microscopy or the general FED microscopy excited by Gaussian beam. Especially, two-view Richardson-Lucy (RL) deconvolution method can reduce the negative impact of strong side lobes, which is related to the subtractive factor and the size of pinhole located at the detector.

Far-field super-focusing by a feedback-based wavefront shaping method

Abbe diffraction limit has always been an important subject in conventional far-field focusing and imaging systems, where the resolution of an image is usually limited to 0.5λ/NA. Recently, the studies of the optical super-oscillation lens (SOL) enable us to break the limitation in both theory and practice successfully. Here a genetic algorithm was introduced to design the SOL phase more controllably and precisely obtain much better focusing such as the focal spot with 0.105λ/NA (or 79.0% minification) in the simulation and 65.5% minification in the experimental demonstration. This technique is of great significance in advanced optical lithography or biology microscopy, because it promises non-invasive unlabelled imaging from the far field.

Hybrid phase-amplitude superoscillation element for nonscanning optical superresolution imaging

In this paper, we report a nonscanning optical superresolution imaging method based on a hybrid phase-amplitude superoscillation element. Using the Chebyshev polynomials as a basis set on the superoscillation waveform, the optimal combination of these, representing the optimal focal -spot in the local field of view, is found by genetic algorithm. Our numerical calculations demonstrate that a subwavelength focal spot with a full width at half-maximum as small as 253 nm is realized, which has more than 30 times improvement in sidelobe suppression ratio, and crucially, a greatly extended needle with continuously shrunken focal spot is yielded, which allows a large imaging tolerance in the axial displacement of the object. We then present our simulated results of the superresolution imaging on sparse point objects and continuous objects, where the practicality and effectiveness of this method are analyzed and discussed in detail.

Superoscillation: from physics to optical 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.

Flexible focusing pattern realization of centimeter-scale planar super-oscillatory lenses in parallel fabrication

Planar super-oscillatory lenses (SOLs) can exert far-field foci beyond the diffraction limit free from the contribution of evanescent waves. However, the reported design methods of SOLs are always complicated and divergent, leading to a poor control over the desired focusing patterns. Furthermore, the existing device sizes of SOLs are mainly within hundreds of micrometers accompanied by a subwavelength-scale feature size. Here, we propose a general optimization design model for realizing flexible focusing patterns, e.g. multifocal and achromatic contours. Additionally, a novel design called the chromatic-customized SOL fighting against the dispersion rule of traditional diffractive optical elements (DOEs) is also demonstrated based on the proposed flexible algorithm. The diameters for all the SOLs reach 12 mm with 30 μm minimum feature size, which can be easily fabricated by employing the conventional optical lithography technique. Such centimeter-scale, light weight and low-cost lenses reveal new capacities of arbitrarily customized optical patterns in various interdisciplinary fields including parallel particle trapping, full-color high-resolution imaging, and compact spectral imaging.

Super-Oscillatory Metalens at Terahertz for Enhanced Focusing with Reduced Side Lobes

In this paper, we design and numerically demonstrate an ultra-thin super-oscillatory metalens with a resolution below the diffraction limit. The zones of the lens are implemented using metasurface concepts with hexagonal unit cells. This way, the transparency and, hence, efficiency is optimized, compared to the conventional transparent–opaque zoning approach that introduces, inevitably, a high reflection in the opaque regions. Furthermore, a novel two-step optimization technique, based on evolutionary algorithms, is developed to reduce the side lobes and boost the intensity at the focus. After the design process, we demonstrate that the metalens is able to generate a focal spot of 0.46λ0 (1.4 times below the resolution limit) at the design focal length of 10λ0 with reduced side lobes (the side lobe level being approximately −11 dB). The metalens is optimized at 0.327 THz, and has been validated with numerical simulations.