We report that the classical phenomena of optical activity and circular dichroism, which are traditionally associated with chirality (helicity) of organic molecules, proteins and inorganic structures, can be observed in non-chiral artificial media. Intriguingly, our metamaterial structure yields exceptionally strong resonant optical activity, which also leads to the appearance of a backward wave, a characteristic sign of negative-index media.
Here, we report observations of photonic spin-momentum locking in the form of directional and chiral emission from achiral quantum dots (QDs) evanescently coupled to achiral hyperbolic metamaterials (HMM). Efficient coupling between QDs and the metamaterial leads to emergence of these photonic topological modes which can be detected in the far field. We provide theoretical explanation for the emergence of spin-momentum locking through rigorous modeling based on photon Green's function where pseudo spin of light arises from coupling of QDs to evanescent modes of HMM.
Using terahertz time domain spectroscopy we demonstrate tunable polarization rotation and circular dichroism in intrinsically nonchiral planar terahertz metamaterials without twofold rotational symmetry. The observed effect is due to extrinsic chirality arising from the mutual orientation of the metamaterial plane and the propagation direction of the incident terahertz wave.
Optical activity is a fundamental phenomenon originating from the chiral nature of crystals and molecules. While intrinsic chiroptical responses of ordinary chiral materials to circularly polarized light are relatively weak, they can be enhanced by specially tailored nanostructures. Here, nanorod metamaterials, comprising a dense array of vertically aligned gold nanorods, is shown to provide significant enhancement of the circular dichroism response of an embedded material. A nanorod composite, acting as an artificial uniaxial crystal, is filled with chiral mercury sulfide nanocrystals embedde…
We suggest that electromagnetic chirality, generally displayed by 3D or 2D complex chiral structures, can occur in 1D patterned composites whose components are achiral. This feature is highly unexpected in a 1D system which is geometrically achiral since its mirror image can always be superposed onto it by a 180 deg rotation. We analytically evaluate from first principles the bi-anisotropic response of multilayered metamaterials and we show that the chiral tensor is not vanishing if the system is geometrically one-dimensional chiral, i.e. its mirror image can not be superposed onto it by using…
We propose a model of tunable THz metamaterials. The main advantage is the blueshift of resonance and phase tunability due to toroidal excitation in planar metallic metamolecules with incorporated silicon inductive inclusions.
In a proof-of-principle experiment with metamaterials exhibiting electric dipolar and magnetic dipolar resonances, we demonstrated that the electric and magnetic resonances can be separately switches off and on by positioning the metamaterials along a standing wave, while both resonances are present in travelling-wave spectra.
We propose to achieve a strong bistable response of a thin layer of a saturable absorption medium by involving a planar metamaterial specially designed to bear a high-Q trapped-mode resonance in the infrared region.
Mechanism of the Fano resonances in planar metamaterials demonstrate based on the coupled two-oscillator model. We have described the optical spectrums like reflectance and transmittance near the resonances of bright mode (continuum mode) and dark mode (discrete mode) and explained their optical properties by the Fano formulism. the Fano formulism of the resonances in the planar metamaterials can predict the asymmetric shape line and radiative properties occurring in reflectance and transmittance from the coupling between bright and dark modes.
We report that resonant response with a very high quality factor can be achieved in a planar metamaterial by introducing symmetry breaking in the shape of its structural elements, which enables excitation of dark modes, i.e. modes that are weakly coupled to free space.
We report that normal incidence reflection and transmission of circularly polarized electromagnetic waves from and through planar split-ring metamaterials with chiral symmetry breaking depends on the incidence direction and handedness of circular polarization. The effect has a resonant nature and is linked to the lack of mirror-symmetry in the metamaterial pattern leading to a polarization-sensitive excitation of electric and magnetic dipolar responses in the meta-molecules.
The electronic Lorentz theory is employed to determine the electromagnetic response of planar split-ring metamaterials. Starting from the dynamics of individual free carriers, the effective permittivity tensor of the metamaterial is calculated. Whenever the split ring lacks in-plane mirror symmetry, the corresponding permittivity tensor has a crystallographic structure of an elliptically dichroic medium, and the metamaterial exhibits optical properties of planar chiral structures. Its transmission spectra are different for right-handed vs. left-handed circular polarization of the incident wave…
We report on a bistable light transmission through a planar metamaterial composed of a metal pattern of weakly asymmetric elements placed on a nonlinear substrate. Such structure bears the Fano-like sharp resonance response of a trapped-mode excitation. The feedback required for bistability is provided by the coupling between the strong antiphased trapped-mode-resonance currents excited on the metal elements and the intensity of inner field in the nonlinear substrate.
We demonstrate that use of the field effect to tune the effective optical parameters of a layered hyperbolic metamaterial leads to topological transitions in its dispersion characteristics in the optical regime. Field effect gating electrically modulates the permittivity in transparent conductive oxides via changes in the carrier density. These permittivity changes lead to active extreme modulation of ~200% of the effective electromagnetic parameters along with active control of the anisotropic dispersion surface of hyperbolic metamaterials and enable the opening and closing of photonic band g…
We present a theory which explains how to achieve an enhancement of nonlinear effects in a thin layer of nonlinear medium by involving a planar periodic structure specially designed to bear a trapped-mode resonant regime. In particular, the possibility of a nonlinear thin metamaterial to produce the bistable response at a relatively low input intensity due to a large quality factor of the trapped-mode resonance is shown. Also a simple design of an all-dielectric low-loss silicon-based planar metamaterial which can provide an extremely sharp resonant reflection and transmission is proposed. The…
We present a novel antireflection approach utilizing planar metamaterials on dielectric surfaces. It consists of a split-ring resonator array and a metal mesh separated by a thin dielectric spacer. The coating dramatically reduces the reflectance and greatly enhances the transmittance over a wide range of incidence angles and a narrow bandwidth. Antireflection is achieved by tailoring the magnitude and phase shifts of waves reflected and transmitted at metamaterial boundaries, resulting in a destructive interference in reflection and constructive interference in transmission. The coating can b…
We present a technique capable of producing subwavelength focal spots in the far-field of the source in planar non-resonant structures. The approach combines the diffraction gratings that generate the high-wavevector-number modes and planar slabs of homogeneous anisotropic metamaterials that propagate these waves and combine them at the subwavelength focal spots. In a sense, the technique combines the benefits of Fresnel lens, near-field zone plates, hyperlens, and superlens, and at the same time resolves their fundamental limitations. Several realizations of the proposed technique for visible…
Recently it was discovered that periodic lattices of metamaterial scatterers show optical activity, even if the scatterers or lattice show no 2D or 3D chirality, if the illumination breaks symmetry. In this Letter we demonstrate that such `pseudo-chirality' is intrinsic to any single planar metamaterial scatterer and in fact has a well-defined value at a universal bound. We argue that in any circuit model, a nonzero electric and magnetic polarizability derived from a single resonance automatically imply strong bianisotropy, i.e., magneto-electric cross polarizability at the universal bound set…
We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, co-rotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left/right-handed incident wave polarization.
Harnessing artificial optical magnetism requires rather complex two- and three-dimensional structures, examples include split-ring and fishnet metamaterials and nanoparticles with non-trivial magnetic properties. By contrast, dielectric properties can be tailored even in planar and pattern-free, one-dimensional (1D) arrangements, for example metal/dielectric multilayer metamaterials. These systems are extensively investigated due to their hyperbolic and plasmonic response, which, however, is considered to be limited to TM polarization, based on the general consensus that they do not possess in…
Chiroptical effects, characterized by different optical responses for left- (LCP) and right- handed circularly polarized light (RCP), are powerful and valuable tools in optics with wide applications in polarization resolved imaging and sensing. Previously observed strong chiroptical effects are limited to metamaterials with complex three-dimensional chiral structures at the sub-wavelength scale. Although asymmetrical transmission of LCP and RCP have been investigated in planar chiral metasurfaces, the observed weak chiroptical effects result from anisotropic Ohmic dissipation of the metal cons…
Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are approximated by at metamaterial layers that can be implemented by standard fabrication and stacking techniques. We illustrate the approximation approach for the specific example of a cylindrical invisibility cloak. First, we introduce a numerical method for the design of cloaks with arbitrary boundary shapes, and apply it to faceted shapes. Subsequently, we red…
We report the first experiential observation and theoretical analysis of the new phenomenon of planar chiral circular conversion dichroism, which in some aspects resembles the Faraday effect in magnetized media, but does not require the presence of a magnetic field for its observation. It results from the interaction of an electromagnetic wave with a planar chiral structure patterned on the sub-wavelength scale, and manifests itself in asymmetric transmission of circularly polarized waves in the opposite directions through the structure and elliptically polarized eigenstates. The new effect is…
Planar metamaterials have been recently proposed for thin dielectric film sensing in the terahertz frequency range. Although the thickness of the dielectric film can be very small compared with the wavelength, the required area of sensed material is still determined by the diffraction-limited spot size of the terahertz beam excitation. In this article, terahertz near-field sensing is utilized to reduce the spot size. By positioning the metamaterial sensing platform close to the sub-diffraction terahertz source, the number of excited resonators, and hence minimal film area, are significantly re…
We present an analytical model which permits the calculation of effective material parameters for planar metamaterials consisting of arbitrary unit cells (metaatoms) formed by a set of straight wire sections of potentially different shape. The model takes advantage of resonant electric dipole oscillations in the wires and their mutual coupling. The pertinent form of the metaatom determines the actual coupling features. This procedure represents a kind of building block model for quite different metaatoms. Based on the parameters describing the individual dipole oscillations and their mutual co…
Following our recent theoretical development of the concept of nano-inductors, nano-capacitors and nano-resistors at optical frequencies and the possibility of synthesizing more complex nano-scale circuits, here we theoretically investigate in detail the problem of optical nano-transmission-lines (NTL) that can be envisioned by properly joining together arrays of these basic nano-scale circuit elements. We show how, in the limit in which these basic circuit elements are closely packed together, the NTLs can be regarded as stacks of plasmonic and non-plasmonic planar slabs, which may be designe…
Electromagnetic response of metallic rod dimers is theoretically calculated for arbitrary planar arrangement of rods in the dimer. It is shown that dimers without an in-plane symmetry axis exhibit elliptical dichroism and act as "atoms" in planar chiral metamaterials. Due to a very simple geometry of the rod dimer, such planar metamaterials are much easier in fabrication than conventional split-ring or gammadion-type structures, and lend themselves to a simple analytical treatment based on coupled dipole model. Dependencies of metamaterial's directional asymmetry on the dimer's geometry are es…
We derive a set of design requirements that lead to structures suitable for molecular circular dichroism (CD) enhancement. Achirality of the structure and two suitably selected sequentially incident beams of opposite helicity ensures that the CD signal only depends on the chiral absorption properties of the molecules, and not on the achiral ones. Under this condition, a helicity preserving structure, which prevents the coupling of the two polarization handednesses, maximizes the enhancement of the CD signal for a given ability of the structure to enhance the field. When the achirality and heli…
We propose a simple design of all-dielectric silicon-based planar metamaterial manifested an extremely sharp resonant reflection and transmission in the wavelength of about 1550 nm due to both low dissipative losses and involving a trapped mode operating method. The quality factor of the resonance exceeds in tens times the quality factor of resonances in known plasmonic structures. The designed metamaterial is envisioned for aggregating with a pumped active medium to achieve an enhancement of luminescence and to produce an all-dielectric analog of a "lasing spaser". We report that an essential…
The total intensity of light transmitted at non-normal incidence thorough planar metamaterials can be different for forward and backward propagation. For metamaterial patterns of different symmetries we observe this effect for circularly or linearly polarized light.
The transmission of electromagnetic wave through the planar chiral structure, loaded with the gyrotropic medium on the longitudinal magnetic field is studied. The frequency dependence of the metamaterial resonance and the angle of rotation of the polarization plane are obtained. We define both theoretically and experimentally the range of frequencies and magnetic fields, where the angle of polarization plane rotation for the metamaterial is essentially higher than for a single ferrite slab.
Some novel quasi-planar chiral inclusions, feasible from standard photo-etching techniques, are proposed. It is shown that such inclusions can be designed in order to present balanced electric, magnetic and magneto-electric polarizabilities. Using these inclusions, random and periodic bi-isotropic artificial metamaterials exhibiting a balanced positive/negative refractive index can be build up. These metamaterials would exhibit reasonable bandwidths and excellent matching to free space.
We observe toroidal response from a planar metamaterial comprised of asymmetric split ring resonators (ASRRs). It is showed that a toroidal-molecule can be constructed through rational arrangement of planar ASRRs as meta-atoms via manipulating structural symmetry of the meta-atoms. Field maps clearly indicate that the toroidal resonance paves new electromagnetic confinement style in a subwavelength scale. Planar scheme of manipulating the coupling among the ASRRs may stimulate research in optical region involving toroidal multipoles. Toroidal geometry together with the Fano resonance made high…
We show for the first time that a planar metamaterial, an array of coupled metal split-ring resonators with a unit cell lacking mirror symmetry, exhibits asymmetric transmission of terahertz radiation (0.25-2.5 THz) propagating through it in opposite directions. This intriguing effect, that is compatible with Lorentz reciprocity and time-reversal, depends on a directional difference in conversion efficiency of the incident circularly polarized wave into one of opposite handedness, that is only possible in lossy low-symmetry planar chiral metamaterials. We show that asymmetric transmission is l…
In this work, we treat the rotation of the optical axis as a new degree of freedom and theoretically propose a tilted linear-crossing metamaterials (TLCMM). Specifically, the conical dispersions of the NLCMM and TLCMM have the same shapes as type-I and type-II Dirac cones, respectively, in condensed matter physics. Upon rotating the optical axis angle such that it is equal to the cone angle, we find that this special TLCMM has the shape of a type-III Dirac cone. This critical TLCMM can have many unique properties and is of a fundamentally different nature than neighboring phases. When EM waves…
We present a planar design of a metamaterial exhibiting electromagnetically induced transparency that is amenable to experimental verification in the microwave frequency band. The design is based on the coupling of a split-ring resonator with a cut-wire in the same plane. We investigate the sensitivity of the parameters of the transmission window on the coupling strength and on the circuit elements of the individual resonators, and we interpret the results in terms of two linearly coupled Lorentzian resonators. Our metamaterial designs combine low losses with the extremely small group velocity…
We present highly sub-wavelength magnetic metamaterials designed for operation at radio frequencies (RFs). A dual layer design consisting of independent planar spiral elements enables experimental demonstration of a unit cell size (a) that is ~ 700 times smaller than the resonant wavelength (λ0). Simulations indicate that utilization of a conductive via to connect spiral layers permits further optimization and we achieve a unit cell that is λ0/a ~ 2000. Magnetic metamaterials are characterized by a novel time domain method which permits determination of the complex magnetic response. Numerical…
We theoretically investigate the optical properties of parity-time (PT)-symmetric three dimensional metamaterials composed of strongly-coupled planar plasmonic waveguides. By tuning the loss-gain balance, we show how the initially isotropic material becomes both asymmetric and unidirectional. The highly tunable optical dispersion of PT -symmetric metamaterials provides a foundation for designing an entirely new class of three-dimensional bulk synthetic media, with applications ranging from sub-diffraction-limited optical lenses to non-reciprocal nanophotonic devices.
We present the first study of disorder in planar metamaterials consisting of strongly interacting metamolecules, where coupled electric dipole and magnetic dipole modes give rise to a Fano-type resonant response and show that positional disorder leads to light localization inherently linked to collective magnetic dipole excitations. We demonstrate that the magnetic excitation persists in disordered arrays and results in the formation of "magnetic hot-spots".
We present a new type of electromagnetic planar metamaterial that exhibit strong dispersion at a local minimum of losses and is believed to be the first metamaterial analog of electromagnetically induced transparency. We demonstrate that pulses propagating through such metamaterials experience considerable delay, whereas the thickness of the structure along the direction of wave propagation is much smaller than the wavelength, which allows successive stacking of multiple metamaterial slabs. This leads to a significant increase in the band of normal dispersion, as well as in transmission levels…
We present the new planar extrinsic chirality metamaterial (ECM) design that manifests giant circular dichroism (CD) in the visible spectrum range rather than usual near-infrared and terahertz range. Effects of incident beam angles and meta-molecules unit sizes on the CD spectrums were theoretically analyzed; Physical mechanism was illustrated in new figures of asymmetrical current excitation in neighboring unit cells.
Losses in metamaterials render the applications of such exotic materials less practical unless an efficient way of reducing them is found. We present two different techniques to reduce ohmic losses at both lower and higher frequencies, based on geometric tailoring of the individual magnetic constituents. We show that an increased radius of curvature, in general, leads to the least losses in metamaterials. Particularly at higher THz frequencies, bulky structures outperform the planar structures.
We report an experimental observation of three distinct resonances in split ring resonators (SRRs) for both vertical and horizontal electric field polarizations at normal incidence by use of terahertz time domain spectroscopy. Breaking the symmetry in SRRs by gradually displacing the capacitive gap from the center towards the corner of the ring allows for an 85% modulation of the fundamental inductive-capacitive resonance. Increasing asymmetry leads to the evolution of an otherwise inaccessible high quality factor electric quadrupole resonance that can be exploited for bio-sensing applications…
We demonstrate achieving the far-field super-resolution imaging can be realized by using a planar hyperbolic metamaterial lens (PHML), beyond the Fabry-Perot resonance condition. Although the thickness of the PHML is much larger than wavelength, the PHML not only can transmit radiative waves and evanescent waves with high transmission, but also can collect all the waves in the image region with the amplitudes of them being the same order of magnitude. We present a design for a PHML to realize the far-field super-resolution imaging, with the distance between the sources and the images 10 times …
We argue the possibility of realization of a polarization insensitive all-optical switching in a planar metamaterial composed of a 4-fold periodic array of two concentric metal rings placed on a substrate of nonlinear material. It is demonstrated that a switching may be achieved between essentially different values of transmission near the resonant frequency of the high-quality-factor Fano-shape trapped-mode excitation.
Investigating planar Proca metamaterials in nonlinear (2+1)-Electrodynamics
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；Universidade Estadual do Sudoeste da Bahia（巴伊亚西南州立大学）
We theoretically analyze the experimental observations of a spectral line collapse in a metamaterial array of asymmetric split ring resonators [Fedotov et al., Phys. Rev. Lett. 104, 223901 (2010)]. We show that the ensemble of closely-spaced resonators exhibits cooperative response, explaining the observed system-size dependent narrowing of the transmission resonance linewidth. We further show that this cooperative narrowing depends sensitively on the lattice spacing and that significantly stronger narrowing could be achieved in media with suppressed ohmic losses.
Large imaging arrays of detectors at millimeter and submillimeter wavelengths have applications that include measurements of the faint polarization signal in the Cosmic Microwave Background (CMB), and submillimeter astrophysics. We are developing planar lenslet arrays for millimeter-wavelength imaging using metamaterials microlithically fabricated using silicon wafers. This metamaterial technology has many potential advantages compared to conventional hemispherical lenslet arrays, including high precision and homogeneity, planar integrated anti-reflection layers, and a coefficient of thermal e…
We study numerically and experimentally magnetic metamaterials based on cut-wire pairs instead of split-ring resonators. The cut-wire pair planar structure is extended in order to create a truly two-dimensional metamaterial suitable for scaling to optical frequencies. We fabricate the cut-wire metamaterial operating at microwave frequencies with lattice spacing around 10% of the free-space wavelength, and find good agreement with direct numerical simulations. Unlike the structures based on split-ring resonators, the nearest-neighbor coupling in cut-wire pairs can result in a magnetic stop-band…
We introduce a simple theoretical model that describes the interaction of light with optical metamaterials in terms of interfering optical plane waves. In this model, a metamaterial is considered to consist of planar arrays of densely packed nanoparticles. In the analysis, each such array reduces to an infinitely thin homogeneous sheet. The transmission and reflection coefficients of this sheet are found to be equal to those of an isolated nanoparticle array and, therefore, they are easy to evaluate numerically for arbitrary shapes and arrangements of the particles. The presented theory enable…
We will report on the electromagnetic response due to induced dipolar currents in metamaterials of 2-dimensional array of metallic elements. Used as frequency selectors, the metamaterial transmittance presents a single resonance in the region from 1 to 8 THz that can be easily selected and scaled maintaining unaltered the quality factor by choosing the size and shape of the planar metallic element and exploiting the scalability properties of the Maxwell equations. Basing on these studies, we have designed and tested a series of simple and inexpensive frequency selective metamaterials fabricate…
Planar metamaterials with tailorable electromagnetic properties in the terahertz domain offer customized optics solutions that are needed for the development of imaging and spectroscopy systems. In particular, metamaterials carry the potential to substitute conventional bulky optics or can be basic building blocks for completely novel devices. In this respect it is advantageous that metamaterials can be devised to be impedance-matched to another material regarding their electromagnetic properties. Here, we design, fabricate and investigate a metamaterial with tailorable refractive index and im…
It is shown theoretically that a nonchiral, two-dimensional array of metallic spheres exhibits optical activity as manifested in calculations of circular dichroism. The metallic spheres occupy the sites of a rectangular lattice and for off-normal incidence they show a strong circular-dichroism effect around the surface plasmon frequencies. The optical activity is a result of the rectangular symmetry of the lattice which gives rise to different polarizations modes of the crystal along the two orthogonal primitive lattice vectors. These two polarization modes result in a net polar vector, which …
We investigate the light transmission through a nanoaperture in a metal film deposited on a planar metamaterial. An effect of an anomalously high light transmission through the nanoaperture is revealed, which we associate with the enhancement of the field at the interface of the planar structure "metamaterial-metal" due to the appearance of an optical Tamm state. In this structure, we also observe an "optical diode" effect: the light transmission radically changes as the direction of irradiation of the structure is reversed. Our numerical results agree well with experimental data.
In planar metamaterial lenses, the focal point moves with the frequency. Here it is shown numerically that this movement can be controlled by properly engineering the dimensions of the metamaterial-based phase shifters that constitute the lens. In particular, such lenses can be designed to exhibit unusual chromatic aberration with the focal length increasing, rather than decreasing, with the frequency. It is proposed that such an artificial "reverse" chromatic aberration may optimize the transverse resolution of millimeter wave diagnostics of plasmas and be useful in compensating for the natur…
Asymmetric transmission of circularly polarized waves is a well-established property of lossy, anisotropic, two-dimensionally chiral patterns. Here we show that asymmetric transmission can be observed for oblique incidence onto any lossy periodically structured plane. Our results greatly expand the range of natural and artificial materials in which directionally asymmetric transmission can be expected making it a cornerstone electromagnetic effect rather than a curiosity of planar chiral metamaterials. Prime candidates for asymmetric transmission at oblique incidence are rectangular arrays of …
Based on operations prescribed under the paradigm of Complex Transformation Optics (CTO) [1-5], it was recently shown in [5] that a complex source point (CSP) can be mimicked by a parity-time ($\mathcal{PT}$) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to non-symmetric complex coordinate…
Metamaterials and meta-surfaces represent a remarkably versatile platform for light manipulation, biological and chemical sensing, nonlinear optics, and even spaser lasing. Many of these applications rely on the resonant nature of metamaterials, which is the basis for extreme spectrally selective concentration of optical energy in the near field. The simplicity of free-space light coupling into sharply-resonant meta-surfaces with high resonance quality factors Q>>1 is a significant practical advantage over the extremely angle-sensitive diffractive structures or inherently inhomogeneous high-Q …
Designing broadband enhanced chirality is of strong interest to the emerging fields of chiral chemistry and sensing, or to control the spin orbital momentum of photons in recently introduced nanophotonic chiral quantum and classical optical applications. However, chiral light-matter interactions have an extremely weak nature, are difficult to be controlled and enhanced, and cannot be made tunable or broadband. In addition, planar ultrathin nanophotonic structures to achieve strong, broadband, and tunable chirality at the technologically important visible to ultraviolet spectrum still remain el…
We show that planar a plasmonic metamaterial with spatially variable meta-atom parameters can focus transmitted light into sub-wavelength hot-spots located beyond the near-field of the metamaterial. By nano-structuring a gold film we created an array of meta-lenses generating foci of 160 nm (0.2λ) in diameter when illuminated by a wavelength of 800 nm. We attribute the occurrence of sub-wavelength hotspots beyond the near field to the phenomenon of superoscillation.
