We report the experimental demonstration of deeply subwavelength far-field optical imaging of unlabelled samples with resolution better than $λ/20$. We beat the ~$λ$/2 diffraction limit of conventional optical microscopy several times over by recording the intensity pattern of coherent light scattered from the object into the far-field. We retrieve information about the object with a deep learning neural network trained on scattering events from a large set of known objects.
Recently it was reported that deeply subwavelength features of free space superoscillatory electromagnetic fields can be observed experimentally and used in optical metrology with nanoscale resolution [Science 364, 771 (2019)]. Here we introduce a new type of imaging, termed Deeply Subwavelength Superoscillatory Imaging (DSSI), that reveals the fine structure of a physical object through its far-field scattering pattern under superoscillatory illumination. The object is reconstructed from intensity profiles of scattered light recorded for different positions of the object in the superoscillato…
We experimentally demonstrate the effect of anomalous breakdown of the effective medium approximation in all-dielectric deeply subwavelength thickness ($d \simλ/160-λ/30$) multilayers, as recently predicted theoretically [H.H. Sheinfux et al., Phys. Rev. Lett. 113, 243901 (2014)]. Multilayer stacks are composed of alternating alumina and titania layers fabricated using atomic layer deposition. For light incident on such multilayers at angles near the total internal reflection we observe pronounced differences in the reflectance spectra for structures with 10-nm versus 20-nm thick layers, as we…
The technologies of heating, photovoltaics, water photocatalysis and artificial photosynthesis depend on the absorption of light and novel approaches such as coherent absorption from a standing wave promise total dissipation of energy. Extending the control of absorption down to very low light levels and eventually to the single photon regime is of great interest yet remains largely unexplored. Here we demonstrate the coherent absorption of single photons in a deeply sub-wavelength 50% absorber. We show that while absorption of photons from a travelling wave is probabilistic, standing wave abs…
It is common understanding that multilayered dielectric metamaterials, in the regime of deeply subwavelength layers, are accurately described by simple effective-medium models based on mixing formulas that do not depend on the spatial arrangement. In the wake of recent studies that have shown counterintuitive examples of periodic and aperiodic (orderly or random) scenarios in which this premise breaks down, we study here the effects of deterministic disorder. With specific reference to a model based on Golay-Rudin-Shapiro sequences, we illustrate certain peculiar boundary effects that can occu…
A theorem on subwavelength imaging with arrays of discrete sources is formulated. This theorem is analogous to the Kotelnikov (also named Nyquist-Shannon) sampling theorem as it represents the field at an arbitrary point of space in terms of the same field taken at discrete points and imposes similar limitations on the accuracy of the image. A physical realization of an imaging system operating exactly on the resolution limit enforced by the theorem is outlined.
In the framework of the hydrodynamic model describing the response of electrons in a metal, we show that arrays of very narrow and shallow metallic slits have an optical response that is influenced by the spatial dispersion in metals arising from the repulsive interaction between electrons. As a simple Fabry-Perot model is not accurate enough to describe the structure's behavior, we propose to consider the slits as generalized cavities with two modes, one being propagative and the other evanescent. This very general model allows to conclude that the impact of spatial dispersion on the propagat…
Metallic nano-structured lens has the potential applications of transporting subwavelength imaging information and it is achieved by manipulating the length of the nanorod and the periodicity of the rod array. In this paper, we demonstrate the impact of filling ratio on the subwavelength imaging capabilities of such a lens. Through full-wave electromagnetic simulation, we have demonstrated that the imaging performance of silver (Ag) nanorod array does not only depend on the length and periodicity but also on the filling ratios or the radius of the wire medium. We have investigated two differen…
In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea of sparse reconstruction. We show that the strongly disordered medium can serves as an efficient apparatus for compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines,…
A type of tunable plasmonic lens with nanoslits is proposed for subwavelength imaging in the far field at different wavelengths. The nanoslits array in the plasmonic lens, which have constant depths but varying widths, could generate desired optical phase retardations based on the particular propagation property of the Surface Plasmon Polaritons (SPPs) in the metal-dielectric-metal (MDM) slit waveguides. We theoretically and numerically demonstrate the tunability of a single plasmonic lens for subwavelength imaging (full width at half maximum, 0.37 ~0.47) by adjusting the surrounding dielectri…
Recently a hypothesis explaining the non-resonant mechanism of subwavelength imaging granted by a dielectric microsphere has been suggested. In accordance to the hypothesis, the far-field image of a subwavelength scatterer strongly coupled to a microsphere by near fields is offered by the scatterer polarization normal to the sphere surface. The radiation of a closely located normally oriented dipole is shaped by the microsphere so that the transmitted wave beam has a practically flat phase front. Then this beam turns out to be imaging -- keeping the subwavelength information about the dipole l…
We show that a metallic plate with fractal-shaped slits can be homogenitized as a plasmonic metamaterial with plasmon frequency dictated by the fractal geometry. Owing to the all-dimensional subwavelength nature of the fractal pattern, our system supports both transverse-electric and transverse-magnetic surface plasmons. As a result, this structure can be employed to focus light sources with all-dimensional subwavelength resolutions and enhanced field strengths. Microwave experiments reveal that the best achievable resolution is only, and simulations demonstrate that similar effects can be rea…
Role of the normal polarization in the far-field subwavelength imaging granted by a dielectric microsphere or microcylinder is discussed and the hypotheses explaining this experimental fact are suggested. One of these hypotheses is confirmed by exact numerical simulations. This mechanism of the magnifying superlens operation is based on the excitation of creeping waves at a curved dielectric interface by a normally polarized dipole. The set of creeping waves after their ejection from the surface creates an imaging beam which may mimic either a Bessel beam or a Mathieu beam depending on the mic…
For dielectric multilayered metamaterials, the effective-parameter representation is known to be insensitive to geometrical features occurring at deeply subwavelength scales. However, recent studies on periodic and aperiodically ordered geometries have shown the existence of certain critical parameter regimes where this conventional wisdom is upended, as the optical response of finite-size samples may depart considerably from the predictions of standard effective-medium theory. In these regimes, characterized by a mixed evanescent/propagating light transport, different classes of spatial (dis)…
Imaging with a layered superlens is a spatial filtering operation characterized by the point spread function (PSF). We show that in the same optical system the image of a narrow sub-wavelength Gaussian incident field may be surprisingly dissimilar to the PSF, and the width of PSF is not a straightforward measure of resolution. FWHM or std. dev. of PSF give ambiguous information about the actual resolution, and imaging of objects smaller than the FWHM of PSF is possible. A multiscale analysis of imaging gives good insight into the peculiar scale-dependent properties of sub-wavelength imaging.
The far-field subwavlength imaging is a challenging issue. In this letter we demonstrate numerically that the far-field subwavelength imaging of weakly scattering objects can be obtained by processing the data acquired by a single antenna, which benefits from the use of the strongly disordered medium. A mathematical model has been proposed for solving such problem based on the idea of sparse reconstruction. Moreover, this study leads to an important conclusion that the strongly disordered medium can serves as an efficient apparatus for the single-antenna compressive measurement, which shifts t…
Generation of a photonic nanojet by a linearly polarized wave beam or a plane wave impinging a dielectric microcylinder implies partial conversion of the propagating waves into the evanescent ones. This conversion is manifested in nanojet waist of subwavelength effective width. However, this known near-field effect is relatively weak. We theoretically show that the incidence of a wave beam formed by two plane waves enables much stronger near-field effects: a deeply subwavelength focusing of the incident beam and a strong enhancement of the electric field on the whole cylinder surface and near …
A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. It is shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Raylei…
Imaging below the diffraction limit is always a public interest because of the restricted resolution of conventional imaging systems. To beat the limit, evanescent harmonics decaying in space must participate in the imaging process. Here, we introduce the method of spatial spectrum sampling, a novel far-field superresolution imaging method for microwave and terahertz regime. Strong dispersion and momentum conservation allow the spoof surface plasmon polaritons (SSP) structure to become a sensitive probe for spatial harmonics. This enables that the spatial information of the targets including b…
Microsphere-based subwavelength imaging technique was first demonstrated in 2011. After nearly a decade of efforts, such technique has spawned numerous interests in fields such as laser nano-machining, imaging, sensing and biological detection. For wider industrial scale application of the technique, a robust, low-cost objective lens incorporating microsphere lens is highly desired and sought by many researchers. In this work, we demonstrate a unibody microscope objective lens formed by tipping a high-index microsphere onto a Plano-Convex lens and subsequently fitting them into a conventional …
Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens, which has been claimed recently to be able to achieve perfect imaging. We show that such a Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in the Maxwell's fish eye. If only zero order mode is excited, a subwavelength image can be achieved, however, its spot-size is larger than the spot size of the source field. The image resolution is determined b…
In this paper we study the characteristics of subwavelength imaging of a photonic crystal (PhC) superlens under the influence of source displacement. For square- and triangular-lattice photonic crystal lenses, we investigate the influence of changing the lateral position of a single point source on the imaging uniformity and stability. We also study the effect of changing the geometrical center of a pair of sources on the resolution of the double-image. Both properties are found to be sensitive to the displacement, which implies that a PhC slab cannot be treated seriously as a flat lens. We al…
We investigate the subwavelength imaging capacity of a two-dimensional fanned-out plasmonic waveguide array, formed by air channels surrounded by gold metal layers for operation at near-infrared wavelengths, via finite element simulations. High resolution is achieved on one side of the device by tapering down the channel width while simultaneously maintaining propagation losses of a few dB. On the other, low-resolution side, output couplers are designed to optimize coupling to free space and to minimize channel cross talk via surface plasmons. Point sources separated by λ/15 can still be clear…
Multilayered structures consisting of alternating negative-permittivity and dielectric layers are explored to obtain high-resolution imaging of subwavelength objects. The peaks with the smallest |ky| (ky is the transverse wave vector) on the transmission curves, which come from the guided modes of the multilayered structures, can not be completely damped by material loss. This makes the amplitudes of the evanescent waves around these peaks inappropriate after transmitted through the imaging structures, and the imaging quality is not good. To solve such a problem, the permittivity of the dielec…
Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens [bounded with a perfectly electrical conductor (PEC) boundary]. We show that such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in Maxwell's fish eye lens. If only zeroth order mode is excited, a subwavelength image of a sharp object may be achieved in some cases, however, its spot-size is larger than the spot size of the initial object field…
The limited resolution of a conventional optical microscope stems from the fact that the subwavelength information of an object is carried by evanescent waves, which exponentially decays in space and cannot reach the imaging plane. We introduce here a metamaterial solid immersion lens (mSIL), which utilizes closely-packed high-index nanoparticles as a composite media to effectively convert and transport evanescent waves from near-field to far-field. About 20% of evanescent wave energy of an ideal point source can be directed into far-field by mSIL. This has led to the exceptional imaging perfo…
We present a direct experimental investigation of the optical field distribution around a suspended tapered optical nanofiber by means of a fluorescent scanning probe. Using a 100 nm diameter fluorescent bead as a probe of the field intensity, we study interferences made by a nanofiber (400 nm diameter) scattering a plane wave (568 nm wavelength). Our scanning fluorescence near-field microscope maps the optical field over 36 $μ$m$^2$, with $λ/ 5$ resolution, from contact with the surface of the nanofiber to a few micrometers away. Comparison between experiments and Mie scattering theory allows…
This is the second article in a series of two dealing with the concept of "resonant metalens" we introduced recently [Phys. Rev. Lett. 104, 203901 (2010)]. It is a new type of lens capable of coding in time and radiating efficiently in the far field region sub-diffraction information of an object. A proof of concept of such a lens is performed in the microwave range, using a medium made out of a square lattice of parallel conducting wires with finite length. We investigate a sub-wavelength focusing scheme with time reversal and demonstrate experimentally spots with focal widths of λ/25. Throug…
Pixel size in cameras and other refractive imaging devices is typically limited by the free-space diffraction. However, a vast majority of semiconductor-based detectors are based on materials with substantially high refractive index. We demonstrate that diffractive optics can be used to take advantage of this high refractive index to reduce effective pixel size of the sensors below free-space diffraction limit. At the same time, diffractive systems encode both amplitude and phase information about the incoming beam into multiple pixels, offering the platform for noise-tolerant imaging with dyn…
We introduce the concept of subwavelength imaging with an opaque nonlinear left-handed lens by generating the second-harmonic field. We consider a slab of composite left-handed metamaterial with quadratic nonlinear response and show that such a flat lens can form, under certain conditions, an image of the second-harmonic field of the source being opaque at the fundamental frequency.
Spatial resolution of most imaging devices is fundamentally restricted by diffraction. This limitation is manifested in the loss of high spatial frequency information contained in evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here we propose a novel approach to recovering evanescent waves in the far field, thereby enabling subwavelength-resolved imaging and spatial spectroscopy. Our approach relies on shifting the frequency and the wave vector of near-field components via scattering on acoustic phonons. This process…
We demonstrate theoretically a large transverse magneto-optical Kerr effect (TMOKE) in subwavelength gratings consisting of alternating magneto-insulating and nonmagnetic dielectric nanostripes. The reflectivity of the grating reaches $96\%$ at the frequencies corresponding to the maximum of the TMOKE response. The combination of a large TMOKE response and high reflectivity is important for applications in $3$D imaging, magneto-optical data storage, and magnonics.
Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here we propose a novel approach to recovering evanescent waves in the far field, thereby enabling subwavelength-resolved imaging and spatial spectroscopy. Our approach relies on shifting the frequency and the wave vector of near-field components via scattering on acoustic phonons. This process effectively removes the spatial frequency cut-off for unambiguous far …
Subwavelength imaging by microsphere lenses is a promising label-free super-resolution imaging technique. There is a growing interest to use live cells to replace the widely used non-biological microsphere lenses. In this work, we demonstrate the use of yeast cells for such imaging purpose. Using fiber-based optical trapping technique, we successfully trapped a chain of yeast cells and bring them to the vicinity of imaging objects. These yeast cells work as near-field magnifying lenses and simultaneously pick up the sub-diffraction information of the nanoscale objects under each cell and proje…
We examine the possibility of using negative refraction stemming from the phonon response in an anisotropic crystal to create a simple slab lens with plane parallel sides, and show that imaging from such a lens should be possible at room temperature despite the effects of absorption that are inevitably present due to phonon damping. In particular, we consider the case of crystal quartz, a system for which experimental measurements consistent with all-angle negative refraction have already been demonstrated. Furthermore, we investigate the possibility of subwavelength imaging from such material…
This work presents a new super-resolution imaging approach by using subwavelength hole resonances. We employ a subwavelength structure in which an array of tiny holes are etched in a metallic slab with the neighboring distance $\ell$ that is smaller than half of the wavelength. By tuning the incident wave at resonant frequencies, the subwavelength structure generates strong illumination patterns that are able to probe both low and high spatial frequency components of the imaging sample sitting above the structure. The image of the sample is obtained by performing stable numerical reconstructio…
Simulation of detecting photoelectrons using multi-level multi-electron (MLME) finite-difference time-domain (FDTD) method with an application to near-field subwavelength imaging based on semiconductor nanophotodetector (NPD) array is reported. The photocurrents from the photodiode pixels are obtained to explore the resolution of this novel NPD device for subwavelength imaging. One limiting factor of the NPD device is the optical power coupling between adjacent detector pixels. We investigate such power coupling in the presence of absorbing media as well as the spatial distributions of the ele…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is essentially exact and leads to the random partial Fourier measurement matrix. In the case of square-integrable targets, the proposed sampling scheme in the Littlewood-Paley wavelet basis block-diagonalizes the scattering matrix with each block in the form of random partial Fourier matrix corresponding to each dyadic scale of the target. The resolution issue is anal…
End-to-end deep learning for superoscillatory subtraction imaging
College of Optical and Electronic Technology, China Jiliang University（中国计量大学光学与电子科技学院）；Centre for THz Research, China Jiliang University（中国计量大学太赫兹研究中心）
Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular diversity illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3 to 0.7 with a 4X0.1 NA objective due to the constraint of planar geometry with weak illumination brightness and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500 to 1000 nm, …
Using a spatially structured, optical pump pulse with a THz probe pulse, we are able to determine spatial variations of the ultrafast THz photoconductivity with sub-wavelength resolution (75 $μm \approx λ/5$ at 0.8 THz) in a planar graphene sample. We compare our results to Raman spectroscopy and correlate the existence of the spatial inhomogeneities between the two measurements. We find a strong correlation with inhomogeneity in electron density. This demonstrates the importance of eliminating inhomogeneities in doping density during CVD growth and fabrication for photoconductive devices.
Terahertz subwavelength imaging aims at developing THz microscopes able to resolve deeply subwavelength features. To improve the spatial resolution beyond the diffraction limit, a current trend is to use various subwavelength probes to convert the near-field to the far-field. These techniques, while offering significant gains in spatial resolution, inherently lack the ability to rapidly obtain THz images due to the necessity of slow pixel-by-pixel raster scan and often suffer from low light throughput. In parallel, in the visible spectral range, several super-resolution imaging techniques were…
Inspired by the capability of structured illumination microscopy in subwavelength imaging, many researchers devoted themselves to investigating this methodology. However, due to the free propagating feature of the traditional structured illumination fields, the resolution can be only improved up to double times compared with the diffractied limited microscopy. Besides, most of the previous studies, relying on incoherent illumination sources, are restricted to fluorescent samples. In this work, a subwavelength nonfluorescent imaging method is proposed based on the terahertz traveling wave and p…
We propose and numerically demonstrate a technique for subwavelength imaging based on a metal-dielectric multilayer hyperlens designed in such a way that only the large-wavevector waves are transmitted while all propagating waves from the image area are blocked by the hyperlens. As a result, the image plane only contains scattered light from subwavelength features of the objects and is free from background illumination. Similar in spirit to conventional dark-field microscopy, the proposed dark-field hyperlens is promising for optical imaging of weakly scattering subwavelength objects, such as …
We implemented the inverse design method to build a thin near-field lens that could produce a desired subwavelength focus by manipulating the near fields of a magnetic dipole source. The flat near-field lens represented by an artificial impedance surface was fabricated by lumped reactive elements (capacitor and inductor) with spatially varying values. In the experiment a desired annular focusing spot with a characteristic size nearly three times smaller than that allowed by the diffraction limit was obtained. Besides high-resolution imaging, the proposed near-field plate could be extended for …
Spatial frequency filtering is a fundamental enabler of information processing methods in biological and technical imaging. Most filtering methods, however, require either bulky and expensive optical equipment or some degree of computational processing. Here we experimentally demonstrate on-chip, all-optical spatial frequency filtering using a thin-film perfect absorber structure. We give examples of edge enhancement in an amplitude image as well as conversion of a phase gradient in a wave field into an intensity modulation.
In magnetic materials, skyrmions are nanoscale regions where the orientation of electron spin changes in a vortex-type manner. Here we show that spin-orbit coupling in a focused vector beam results in a skyrmion-like photonic spin distribution of the excited waveguided fields. While diffraction limits the spatial size of intensity distributions, the direction of the field, defining photonic spin, is not subject to this limitation. We demonstrate that the skyrmion spin structure varies on the deep-subwavelength scales down to 1/60 of light wavelength, which corresponds to about 10 nanometre len…
Near-field imaging with terahertz (THz) waves is emerging as a powerful technique for fundamental research in photonics and across physical and life sciences. Spatial resolution beyond the diffraction limit can be achieved by collecting THz waves from an object through a small aperture placed in the near-field. However, light transmission through a sub-wavelength size aperture is fundamentally limited by the wave nature of light. Here, we conceive a novel architecture that exploits inherently strong evanescent THz field arising within the aperture to mitigate the problem of vanishing transmiss…
A planar near-field magnetoinductive lens operating in the microwave range is presented. The proposed device consists of two parallel planar arrays of metallic broadside coupled (BC-) split ring resonators (SRRs), or BC-SRRs. Power coming from a point-like source located in front of the lens is focused into a receiver located in free space behind the device. This focus is clearly removed from the back side of the lens, and has a size which is an order of magnitude smaller than the free space wavelength of the incoming radiation. The imaging properties of the device mainly relies on the excitat…
By applying the optical nanocircuit concepts to metasurfaces, we propose an effective route to locally control light transmission over a deeply subwavelength scale. This concept realizes the optical equivalent of a transmitarray, whose use is demonstrated for light bending and focusing with unprecedented efficiency over a subwavelength distance, with crucial benefits for nano-optics applications. These findings may lead to large improvements in the manipulation of optical transmission and processing of nanoscale optical signals over conformal and Si-compatible substrates.
Subwavelength Imaging using a Solid-Immersion Diffractive Optical Processor
Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）；Peking University（北京大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；David Geffen School of Medicine, University of California, Los Angeles（加州大学洛杉矶分校大卫·格芬医学院）
We demonstrate perfect imaging in Maxwell's fish eye for microwaves. Our data show that the field of a line source is imaged with subwavelength resolution over superwavelength distances, provided the field is allowed to leave through passive outlets that play the role of a detector array in imaging.
Far-field characterization of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present a new imaging technique capable of fast and accurate characterization of two-dimensional structures with at least wavelength/25 resolution, based on a single far-field intensity measurement. Experimentally, we realized this technique resolving the smallest-available to us 180-nm-scale features with 532-nm laser light. A comprehensive analysis of machine lear…
The concepts of spoof surface plasmon polaritons and adiabatic field compression are employed to design metallic near-field probes that allow guiding and focusing of mid-infrared wavelength electromagnetic radiation and provides subwavelength field confinements and a lateral optical resolution of about 10 nm.
