Quantum super-oscillation of a single photon

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.

Investigation of the effect of chirped factors on the interference enhancement effect of an Airyprime beam propagating in free space

The first-order and the second-order chirped factors are imposed on the Airyprime beam, and the analytical expression of the chirped Airyprime beam propagating in free space is derived. The phenomenon that the peak light intensity on observation plane other than initial plane is greater than that on initial plane is defined as the interference enhancement effect, which is caused by the coherent superposition of the chirped Airyprime and the chirped Airy-related modes. The effects of the first-order and the second-order chirped factors on the interference enhancement effect are theoretically investigated, respectively. The first-order chirped factor only affects the transverse coordinates where the maximum light intensity appears. The strength of interference enhancement effect of the chirped Airyprime beam with any negative second-order chirped factor must be stronger than that of the conventional Airyprime beam. However, the improvement of the strength of interference enhancement effect caused by the negative second-order chirped factor is realized at the expense of shortening the position where the maximum light intensity appears and the range of interference enhancement effect. The chirped Airyprime beam is also experimentally generated, and the effects of the first-order and the second-order chirped factors on the interference enhancement effect are experimentally confirmed. This study provides a scheme to improve the strength of interference enhancement effect by controlling the second-order chirped factor. Compared with traditional intensity enhancement methods such as using lens focusing, our scheme is flexible and easy to implement. This research is beneficial to the practical applications such as spatial optical communication and laser processing.

Creation of pure longitudinal super-oscillatory spot

We present a method that creates a super-oscillatory focal spot of a tightly focused radially polarized beam using the concept of a phase mask. Using vector diffraction theory, we report a super-oscillatory focal spot that is much smaller than the diffraction limit and the super-oscillation criterion. The proposed mask works as a special polarization filter that enhances the longitudinal component and filters out the transverse component of radial polarization at focus, permitting the creation of a pure longitudinal super-oscillatory focal spot.

Elliptical Supercritical Lens for Shaping Sub-Diffractive Transverse Optical Needle

Supercritical lens can create a sub-diffraction-limited focal spot in the far field, providing a promising route for the realization of label-free super-resolution imaging through the point scanning mechanism. However, all of the reported supercritical lenses have circular shape configurations, and produce isotropic sub-diffraction-limited focal spots in the focal plane. Here, we propose and experientially demonstrate a sub-diffraction transverse optical needle by using an elliptical supercritical lens. Through breaking the circular symmetry and introducing ellipticity to the lens, a uniform sub-diffractive transverse optical needle with lateral length and width of 6λ/NA and 0.45λ/NA, respectively, was successfully created in the focal plane. Further, elliptical sector-shape cutting with an optimized apex angle of 60 degrees can lead to suppressed subsidiary focusing for improved uniformity and condensed field intensity of the transverse optical needle. The demonstration of sub-diffractive transverse optical needle with a high aspect ratio (length to width ratio) of 13:1 may find potential applications in line-scanning microscopy for video-rate label-free super-resolution imaging, and also enable advances in the fields from laser manufacturing to optical manipulation.

Superoscillation focusing with suppressed sidebands by destructive interference

Optical superoscillation, a phenomenon that the local optical field can oscillate much faster than that allowed by its highest harmonic, can significantly overcome the Abbe diffraction limit. However, as the spot size is compressed below the superoscillation criteria of 0.38λ/NA, huge sidebands will inevitably appear around the central lobe with intensity hundreds of times higher than that of the central lobe. Here, we propose an approach to realize superoscillation by using destructive interference. The central lobe size can be compressed beyond the superoscillation criteria without formation of strong sidebands by destructive interference between focused fields. Such a super-resolution metalens can find its application in label-free far-field super-resolution microscopy.

Theoretical study of freely propagating high-spatial-frequency optical waves

When it comes to the high-spatial-frequency electromagnetic waves, we usually think of them as the evanescent waves which are bounded at the near-field surface and decay along with propagation distance. A conventional wisdom tells us that the high-spatial-frequency waves cannot exist in the far field. In this work, we show, however, that these high-spatial-frequency waves having wavenumbers larger than the incident one can propagate freely to the far-field regions. We demonstrate theoretically a technique, based on an abrupt truncation of the incident plane wave, to generate these intriguing waves. The truncation functions describing the slit and the complementary slit are considered as typical examples. Our results show that both the slit structures are able to produce the high-spatial-frequency wave phenomena in the far field, manifested by their interference fringes of the diffracted waves. This work introduces the high-spatial-frequency propagating waves. Therefore, it may trigger potential investigations on such an interesting subject, e.g., one may design delicate experiment to confirm this prediction. Besides, it would stimulate potential applications such as in superresolution and precise measurement.

Sub-diffraction-limit light sheet enabled by a super-oscillatory lens with an enlarged field of view and depth of focus

Static light sheets are widely used in various super-resolution three-dimensional (3D) imaging applications. Here, a multifocal diffraction-free optimized design method is proposed for super-oscillatory lenses (SOLs) owning an enlarged field of view (FOV) to generate sub-diffraction-limit light sheets with reduced divergence. Various propagation lengths of sub-diffraction-limit thickness for light sheets can be obtained by adopting corresponding numbers of discrete foci and spacing between them. In particular, the propagation lengths of 150.4λ and 118.9λ are obtained by SOLs with an enlarged FOV of 150λ and 820λ, respectively, which show the longest depth of focus (DOF), as far as we know, and are the first to realize the combination of enlarged DOF and FOV for SOLs. We show a way of using binary-amplitude modulation to generate static light sheets with sub-diffraction-limit thickness and reduced divergence, which is simple, easy to integrate, and sidelobe-suppressed.

Longitudinal magnetization superoscillation enabled by high-order azimuthally polarized Laguerre-Gaussian vortex modes

We present an all-optical scheme for the generation of longitudinal magnetization superoscillation based on the vectorial diffraction theory and the inverse Faraday effect. To achieve this, an azimuthally polarized high-order Laguerre-Gaussian vortex mode is firstly focused by a high numerical aperture (NA) objective and then impinges on an isotropic magneto-optical material. It is found that, by judiciously controlling the intrinsic arguments (radial mode index (p) and truncation parameter (β)) of such a configurable vectorial vortex beam, the longitudinal magnetic domain induced in the focal plane can be switched from a peak sub-wavelength magnetization (> 0.36λ/NA), via the fastest Fourier magnetization component (∼0.36λ/NA), to a super-oscillation magnetization hotspot (< 0.36λ/NA). We further examine the dependence of the transverse size, the side lobe, and the energy conversion efficiency within the focal magnetization domain on both the p and β of the initial vortex modes, confirming that the higher-order structured vortex beams are preferable alternatives to trigger robust longitudinal magnetization superoscillation. In addition, the underlying mechanisms behind the well-defined magnetization phenomena are unveiled. The ultra-small-scale longitudinal magnetization demonstrated here may hold massive potential applications in high-density all-optical magnetic recording/storage, super-resolution magnetic resonance imaging, atom trapping and spintronics.

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.

Supercritical lens array in a centimeter scale patterned with maskless UV lithography

Microlens arrays (MLAs) are widely used in optical imaging, dense wavelength division multiplexing, optical switching, and microstructure patterning, etc. However, the light modulation capability for both the conventional refractive-type MLA and planar diffractive-type MLA is still staying at the diffraction-limited scale. Here we propose and experimentally demonstrate a high numerical aperture (NA) supercritical lens (SCL) array which could achieve a sub-diffraction-limited focal spot lattice in the far field. The intensity distribution for all the focal spots has good uniformity with the lateral size around ${0.45}\lambda {\rm /NA}$0.45λ/NA (0.75X Airy unit). The elementary unit in the SCL array composes a series of concentric belts with a feature size in micrometer scale. By utilizing an ultrafast ultraviolet lithography technique, a centimeter scale SCL array could be successfully patterned within 10 mins. Our results may provide possibilities for the applications in optical nanofabrication, super-resolution imaging, and ultrafine optical manipulation.

Ultrasonic super-oscillation wave-packets with an acoustic meta-lens

The Schrödinger equation is a fundamental equation to describe the wave function of a quantum-mechanical system. The similar forms between the Schrödinger equation and the paraxial wave equation allow a paradigm shift from the quantum mechanics to classical fields, opening up a plethora of interesting phenomena including the optical super-oscillatory behavior. Here, we propose an ultrasonic meta-lens for generating super-oscillation acoustic wave-packets with different spatial momenta and then superimposing them to a diffraction-limit-broken spot, visually represented by the ring-shaped trapping of tiny particles. Moreover, based on the focused super-oscillation packets, we experimentally verify proof-of-concept super-resolution ultrasound imaging, opening up the arena of super-oscillation ultrasonics for advanced acoustic imaging, biomedical applications, and versatile far-field ultrasound control.

Here, the authors propose an ultrasonic meta-lens for generating super-oscillation wave packets with different spatial momenta and then superimposing them to a diffraction-limit-broken spot. They experimentally verify super-resolution ultrasound imaging of subwavelength objects.

"Plasmonics" in free space: observation of giant wavevectors, vortices, and energy backflow in superoscillatory optical fields

Evanescent light can be localized at the nanoscale by resonant absorption in a plasmonic nanoparticle or taper or by transmission through a nanohole. However, a conventional lens cannot focus free-space light beyond half of the wavelength λ. Nevertheless, precisely tailored interference of multiple waves can form a hotspot in free space of an arbitrarily small size, which is known as superoscillation. Here, we report a new type of integrated metasurface interferometry that allows for the first time mapping of fields with a deep subwavelength resolution ~λ/100. The findings reveal that an electromagnetic field near the superoscillatory hotspot has many features similar to those found near resonant plasmonic nanoparticles or nanoholes: the hotspots are surrounded by nanoscale phase singularities and zones where the phase of the superoscillatory field changes more than tenfold faster than a free-propagating plane wave. Areas with high local wavevectors are pinned to phase vortices and zones of energy backflow (~λ/20 in size) that contribute to tightening of the main focal spot size beyond the Abbe-Rayleigh limit. Our observations reveal some analogy between plasmonic nanofocusing of evanescent waves and superoscillatory nanofocusing of free-space waves and prove the fundamental link between superoscillations and superfocusing, offering new opportunities for nanoscale metrology and imaging.

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.

An Investigation of Influencing Factors on Practical Sub-Diffraction-Limit Focusing of Planar Super-Oscillation Lenses

Planar super-oscillation lenses (SOLs) can fulfill super-resolution focusing and nanoscopic imaging in the far field without the contribution of evanescent waves. Nevertheless, the existing deviations between the design and experimental results have been seldomly investigated, leaving the practical applications of SOLs unpredictable and uncontrollable. In this paper, some application-oriented issues are taken into consideration, such as the inevitable fabrication errors and the size effect of the designed SOLs, with the aim of providing an engineering reference to elaborately customize the demanded focusing light field. It turned out that a thicker structural film makes the focal spots enlarged, while the sloped sidewalls just weaken the intensity of the focal hotspot. Furthermore, the focal lengths are diminished with the decrease of device size, while the focal spots are enlarged. This research will promote the wide-spread applications of SOLs for sub-diffraction-limit far-field focusing in the areas of nanoscopy and high-density optical storage.

Achromatic super-oscillatory lenses with sub-wavelength focusing

Lenses are crucial to light-enabled technologies. Conventional lenses have been perfected to achieve near-diffraction-limited resolution and minimal chromatic aberrations. However, such lenses are bulky and cannot focus light into a hotspot smaller than a half-wavelength of light. Pupil filters, initially suggested by Toraldo di Francia, can overcome the resolution constraints of conventional lenses but are not intrinsically chromatically corrected. Here we report single-element planar lenses that not only deliver sub-wavelength focusing, thus beating the diffraction limit of conventional refractive lenses, but also focus light of different colors into the same hotspot. Using the principle of super-oscillations, we designed and fabricated a range of binary dielectric and metallic lenses for visible and infrared parts of the spectrum that are manufactured on silicon wafers, silica substrates and optical fiber tips. Such low-cost, compact lenses could be useful in mobile devices, data storage, surveillance, robotics, space applications, imaging, manufacturing with light and spatially resolved nonlinear microscopies.