Theoretical study of arrays of graphene ribbons is currently of high interest due to its potential application in beam splitters, absorbers, and polarizers. In this paper, an analytical method is presented for diffraction analysis of graphene ribbon arrays. Previous analytical studies were carried out in the regime where the lateral separation between the ribbons is much smaller than the wavelength of the incident wave. As such, they could not be used to calculate the reflection coefficients of higher diffracted orders. By contrast, the method proposed here can predict electromagnetic response of graphene ribbon arrays even when the array constant is larger than the wavelength. To reach our results, we first derive an analytical expression for the surface density of electric current induced on the ribbons by an incident, transverse-magnetic (TM), plane wave. Next, closed-form and analytical expressions are obtained for the reflection coefficients of the zeroth and higher diffracted orders. The results are in excellent agreement with those obtained from full-wave simulations. The method presented facilitates the design of tunable gratings with many potential applications in THz and optics.
We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction can be tailored both in magnitude and in sign by varying the geometric features of the waveguides. Diffraction management on a subwavelength scale is demonstrated by numerical solution of Maxwell equations in frequency domain.
In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with $100\%$ diffraction efficiency. Here, we present modified diffraction equations that provide mechanisms to control light diffraction beyond the subwavelength limit. We show that resonant diffraction phenomena are governed by the superposition of scattering processes, owing to higher Fourier harmonic components. By appropriately engineering the Fourier harmonic co…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam at a given distance from the aperture. We show that a subwavelength-sized beam propagating without diffractive broadening can be produced in free space by the constructive interference of multiple beams of a Fresnel source of the respective high-refraction-index waveguide. Moreover, it is shown that such a source can be constructed not only for continuous wav…
A multi-reflection model of grating diffraction based on the simplified modal method is proposed. Simulation results for a guided mode resonance Brewster grating using our method and rigorous coupled wave analysis are presented to verify our model. The solution of our method is in good agreement with that of rigorous coupled wave analysis. Benefiting from its clear physical view, this model helps us to better understand the diffraction process inside subwavelength gratings. On the basis of the multi-reflection model, we developed a matrix Fabry-Perot (FP) resonance condition and a single-mode …
We consider Wood anomalies in diffraction spectrum from two-dimensional dielectric periodic grid embedded in a surrounding media. The grid is of subwavelength thickness, and diffraction of wave having S-polarization is investigated in the vicinity of the emergence of first diffraction maximum. We reduce Maxwell equations to coupled-mode theory with three parameters, which are integral characteristics of material arrangement in the grid. In particular, we show that such grids are capable to have full reflectance in parametrically narrow frequency bandwidth. The effect is accompanied by a parame…
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 …
Diffraction-free natural optical skyrmions and their subwavelength confinement around vortices
Nanyang Technological University（南洋理工大学）；Universidad Politécnica de Madrid（马德里理工大学）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）；Consejo Superior de Investigaciones Científicas (CSIC)（西班牙国家科研委员会）
We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wavefields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far-field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far-field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.
Subwavelength plasmonic waveguides show the unique ability of strongly localizing (down to the nanoscale) and guiding light. These structures are intrinsically two-way optical communication channels, providing two opposite light propagation directions. As a consequence, when light is coupled to these planar integrated devices directly from the top (or bottom) surface using strongly focused beams, it is equally shared into the two opposite propagation directions. Here, we show that symmetry can be broken by using incident circularly polarized light, on the basis of a spin-orbital angular moment…
A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to normally incident plane waves, the current distribution is derived leading to analytical expressions for the reflection/transmi…
We present an intuitive analytical model for extraordinary optical transmission (EOT) through corrugated metallic films. In the framework of this model, EOT emerges from standing wave resonances of the different diffraction orders, and is an inherent property of periodic structures, which does not require specific polarization dependent properties such as surface plasmons. The model correctly predicts the conditions for the EOT resonances in various geometrical configurations, in both TE and TM polarizations,and in the subwavelength and non-subwavelength spectral regimes, using the same underl…
Existing methods for the localization of light at the nanoscale use either a structure with negative permittivity, by exploiting subwavelength plasmonic resonances, or a dielectric structure with a high refractive index, which reduces the wavelength. In this paper, we provide an alternative to these two methods based on a modification of the modes of dielectric resonators by means of an active medium. We show that an active medium can promote subwavelength light localization in the dielectric structure. We consider a dielectric layer of size substantially smaller than a half-wavelength of ligh…
We obtain in TM polarization an analytical expression of the scattering matrix of one infinitely conducting metallic lamellar grating with subwavelength slits. The theory is based on the Monomode Modal Method which consists in considering only one propagative mode in grating slits. Two expressions are exposed. The first one comes directly from the theory equations and the second one clearly reveals the Airy-like form of the scattering matrix terms. The theory is validated on a multi-grating object and the stability of the numerical results are shown at the same time. This work provides a basic…
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)] leads to the basic question: Can a light pulse be enhanced and simultaneously localized in space and time by a subwavelength slit? To address this question, the spatial distribution of the energy flux of an ultrashort (femtosecond) wave-packet diffracted by a subwavelength (nanometer-size) slit was analyzed by using the conventional approach based on the Neerho…
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)] leads to the basic question: Can a light be enhanced and simultaneously localized in space and time by a subwavelength slit? To address this question, the spatial distribution of the energy flux of an ultrashort (femtosecond) wave-packet diffracted by a subwavelength (nanometer-size) slit was analyzed by using the conventional approach based on the Neerhoff and…
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…
The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous reports have described focusing or imaging with light and sound "below the diffraction limit". We argue that the diffraction limit defined in a reasonable way, for example in terms of the upper bound on the wave numbers corresponding to the spatial Fourier components of the intensity profile, or in terms of the spot size into which at least 50% of the inciden…
We present an analytical model of the resonantly enhanced transmission of light through a subwavelength nm-size slit in a thick metal film. The simple formulae for the transmitted electromagnetic fields and the transmission coefficient are derived by using the narrow-slit approximation and the Green's function formalism for the solution of Maxwell's equations. The resonance wavelengths are in agreement with the semi-analytical model [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)], which solves the wave equations by using the Rayleigh field expansion. Our formulae, however, show great resonant …
Laser science has tackled physical limitations to achieve higher power, faster and smaller light sources. The quest for ultra-compact laser that can directly generate coherent optical fields at the nano-scale, far beyond the diffraction limit of light, remains a key fundamental challenge. Microscopic lasers based on photonic crystals, micro-disks, metal clad cavities and nanowires can now reach the diffraction limit, which restricts both the optical mode size and physical device dimension to be larger than half a wavelength. While surface plasmons are capable of tightly localizing light, ohmic…
The backward scattering of TM-polarized light by a two-side-open subwavelength slit in a metal film is analyzed. We show that the reflection coefficient versus wavelength possesses a Fabry-Perot-like dependence that is similar to the anomalous behavior of transmission reported in the study [Y. Takakura, Phys. Rev. Lett. \textbf{86}, 5601 (2001)]. The open slit totally reflects the light at the near-to-resonance wavelengths. In addition, we show that the interference of incident and resonantly backward-scattered light produces in the near-field diffraction zone a spatially localized wave whose …
We present an analytical description and an experimental realization of interscale mixing microscopy, a diffraction-based imaging technique that is capable of detecting wavelength/10 objects in far-field measurements with both coherent and incoherent broadband light. This method aims at recovering the spatial spectrum of light diffracted by a subwavelength object based on far-field measurements of the interference created by the object and a finite diffraction grating. A single measurement, analyzing the multiple diffraction orders, is often sufficient to determine the parameters of the object…
Flat lens concept based on negative refraction proposed by Veselago in 1968 has been mostly investigated in monochromatic regime. It was recently recognized that time development of the super-lensing effect discovered in 2000 by Pendry is yet to be assessed and may spring surprises: Time-dependent illumination could improve the spatial resolution of the focusing. We investigate dynamics of flexural wave focusing by a 45\degre-tilted square lattice of circular holes drilled in a Duraluminium plate. Time-resolved experiments reveal that the focused image shrinks with time below diffraction limit…
Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus the nonpropagating near-fields, thereby achieving a subdiffraction image. In this work we discuss the sensitivity of the subwavelength focus to various slab parameters, pointing out the connection to slab plasmon modes. We also note and resolve a paradox associated with the perfect imaging of a point source. We conclude that subwavelength resolution is achieva…
We present a theorical investigation of the optical transmission of a dielectric grating carved in a tungsten layer. For appropriate wavelengths tungsten shows indeed a dielectric behaviour. Our numerical simulations leads to theoretical results similar to those found with metallic systems studied in earlier works. The interpretation of our results rests on the idea that the transmission is correlated with the resonant response of eigenmodes coupled to evanescent diffraction orders.
We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength…
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…
A single-order transmission diffraction grating based on dispersion engineered all-dielectric metasurfaces is proposed and its wavelength discriminating properties have been theoretically described and confirmed using numerical simulations. The metasurface is designed using a 2D array of all-dielectric resonators, which emulates a Huygens source configuration to achieve a perfect match to free-space in broad bandwidth. Using a holey dielectric nanodisk structure as the unit cell, the resonant wavelength is tapered across the metasurface to engineer the wavelength dependent spatial phase gradie…
The canalization of terahertz surface plasmon polaritons using a modulated graphene monolayer is investigated for subwavelength imaging. An anisotropic surface conductivity formed by a set of parallel nanoribbons with alternating positive and negative imaginary conductivities is used to realize the canalization regime required for hyperlensing. The ribbons are narrow compared to the wavelength, and are created electronically by gating a graphene layer over a corrugated ground plane. Good quality canalization of surface plasmon polaritons is shown in the terahertz even in the presence of realis…
Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provide extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This paper provides a relation between the achievable focus spot size, the amplification available and the focal length. This may be considered as a revised version of Abbe's diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations, as well as determining whe…
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…
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 …
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…
A method is presented for generation of a subwavelength (0.43 lambda) longitudinally polarized beam, which propagates without divergence over lengths of about 4 lambda in free space. This is achieved by controlling the amplitude, phase and polarization property of the Bessel-Gaussian field on the aperture of a high numerical aperture focusing lens.
Recents works deal with the optical transmission on arrays of subwavelength holes in a metallic layer deposited on a dielectric substrate. Making the system as realistic as possible, we perform simulations to enlighten the experimental data. This paper proposes an investigation of the optical properties related to the transmission of such devices. Numerical simulations give theoretical results in good agreement with experiment and we observe that the transmission and reflection behaviour correspond to Fano's profile correlated with resonant response of the eigen modes coupled with nonhomogeneo…
We propose the Subwavelength Localization via Adiabatic Passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementa…
Far-field imaging beyond the diffraction limit is a long sought-after goal in various imaging applications, which requires usually an array of antennas or mechanical scanning. Here, we present an alternative and novel concept for this challenging problem: a single radar system consisting of a spatial-temporal resonant aperture antenna (referred to as the slavery antenna) and a broadband horn antenna (termed the master antenna). We theoretically demonstrate that such resonant aperture antenna is responsible for converting parts of the evanescent waves into propagating waves, and delivering them…
We study electromagnetic scattering and subsequent plasmonic excitations in periodic grids of graphene ribbons. To address this problem, we develop an analytical method to describe the plasmon-assisted absorption of electromagnetic radiation by a periodic structure of graphene ribbons forming a diffraction grating for THz and mid-IR light. The major advantage of this method lies in its ability to accurately describe the excitation of graphene surface plasmons (GSPs) in one-dimensional (1D) graphene gratings without the use of both time-consuming, and computationally-demanding full-wave numeric…
Microscopes and various forms of interferometers have been used for decades in optical metrology of objects that are typically larger than the wavelength of light λ. However, metrology of subwavelength objects was deemed impossible due to the diffraction limit. We report that measurement of the physical size of sub-wavelength objects with accuracy exceeding λ/800 by analyzing the diffraction pattern of coherent light scattered by the objects with deep learning enabled analysis. With a 633nm laser, we show that the width of sub-wavelength slits in opaque screen can be measured with accuracy of …
Investigations of the optical response of subwavelength structure arrays milled into thin metal films has revealed surprising phenomena including reports of unexpectedly high transmission of light. Many studies have interpreted the optical coupling to the surface in terms of the resonant excitation of surface plasmon polaritons (SPPs), but other approaches involving composite diffraction of surface evanescent waves (CDEW) have also been proposed. We present here a series of measurements on very simple one-dimensional (1-D) subwavelength structures with the aim of testing key properties of the …
Metasurfaces composed of subwavelength unit cells usually require a large number of unit cells which leads to complicated design and optimization. Aggressive discretization in a metasurface can significantly reduce the number of unit cells within a period, resulting in lower requirement for phase and/or surface impedance coverage. Additionally, the enlarged unit cells will encounter negligible mutual couplings when combined together, hence making straightforward the process of metasurface design. These advantages combine to allow the design of a novel class of metasurfaces which support the hi…
In order to confine waves beyond the diffraction limit, advances in fabrication techniques have enabled subwavelength structuring of matter, achieving near-field control of light and other types of waves. The price is often expensive fabrication needs and the irreversibility of device functionality, as well as the introduction of impurities, a major contributor to losses. In this Letter, we propose temporal inhomogeneities, such as a periodic drive in the electromagnetic properties of a surface which supports guided modes, to circumvent the need for subwavelength fabrication in the coupling of…
We show both theoretically and experimentally that an electromagnetic wave can be totally absorbed by an overdense plasma when a subwavelength diffraction grating is placed in front of the plasma surface. The absorption is due to dissipation of surface plasma waves (plasmons-polaritons) that have been resonantly excited by the evanescent component of the diffracted electromagnetic wave. The developed theoretical model allows one to determine the conditions for the total absorption.
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize surfaces that can be thousands of wavelengths in diameter, with thousands (or millions) of parameters, the key is a fast approximate solver for the scattered field. We employ a "locally periodic" approximation in which the scattering problem is approximated by a composition of periodic scattering problems from each unit cell of the surface, a…
The ability to effectively guide electromagnetic radiation below the diffraction limit is of the utmost importance in the prospect of all-optical plasmonic circuitry. Here, we propose an alternative solution to conventional metal-based plasmonics by exploiting the deep subwavelength confinement and tunability of graphene plasmons guided along the apex of a graphene-covered dielectric wedge or groove. In particular, we present a quasi-analytic model to describe the plasmonic eigenmodes in such a system, including the complete determination of their spectrum and corresponding induced potential a…
It is shown that a smooth metal film (or a plasma layer) can be made transparent for an electromagnetic wave when two identical subwavelength diffraction gratings are placed on both sides of the film. The electromagnetic wave transmission through the metal film is caused by excitation of evanescent surface waves (plasmons) and their transformation into propagating waves at the gratings. A model which is developed analytically shows that the problem of the wave transmission is physically equivalent to the problem of excitation of two coupled resonators of evanescent waves which are formed at th…
