In this talk we present and discuss a new general approach to the synthesis of metasurfaces for full control of transmitted and reflected fields. The method is based on the use of an equivalent impedance matrix which connects the tangential field components at the two sides on the metasurface. Finding the impedance matrix components, we are able to synthesize metasurfaces which perfectly realize the desired response. We will explain possible alternative physical realizations and reveal the crucial role of bianisotropic coupling to achieve full control of transmission through perfectly matched metasurfaces. This abstract summarizes our results on metasurfaces for perfect refraction into an arbitrary direction.
We optimize optical performance of metasurfaces based on periodically corrugated silicon layers by adjusting the Fourier coefficients of their surface profile. For smooth corrugations, we demonstrate an excellent quantitative accuracy of semi-analytical approach based on the Rayleigh hypothesis. We employ the approach to design metasurfaces with anomalous refraction due to dominant first order diffraction. Unlike conventional Huygens' dielectric metasurfaces, corrugated silicon layers are capable of efficient anomalous refraction in grazing directions: we obtain corrugation shapes allowing to …
Non-uniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent i…
We report the design, fabrication, and characterization of bianisotropic Huygens' metasurfaces (BHMSs) for refraction of normally incident beams towards 71.8 degrees. As previously shown, all three BHMS degrees of freedom, namely, electric polarizability, magnetic polarizability and omega-type magnetoelectric coupling, are required to ensure no reflections occur for such wide-angle impedance mismatch. The unit cells are composed of three metallic layers, yielding a printed-circuit-board (PCB) structure. The fabricated BHMS is characterized in a quasi-optical setup, used to accurately assess sp…
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisfy, they are Monge-Ampère partial differential equations, and we prove existence of solutions.
The optical Kerr effect of material with negative refraction is estimated for the first time. This is done via three-dimensional finite-difference time-domain (FDTD) simulations of disordered bidisperse metasurfaces consisting of high index (GaP) spheres at the wavelength of 532~nm. The metasurfaces comprise spherical particles randomly arranged on plane having two sizes close to the magnetic and electric dipole Mie resonances. The real part of the effective nonlinear refractive index of the metasurfaces is computed in the vicinity of the Mie resonances where the metasurface possesses the nega…
The general reflection and refraction laws at the metasurface with the abrupt phase shift were derived by two different methods of Fermat's principle and the boundary conditions respectively. It is found that one or two critical angles for total internal reflection exist when a light hits on the optical sparse material from the optical denser material, and one such a critical angle exists when light spreads from the optical sparse material to the optical denser material. Anomalous reflection and refraction, such as, negative reflection and negative refraction may occur when a light passes thro…
This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell-Descartes laws. Our main finding is that the generalized laws of refrac-tion and reflection as previously stated have to be modified in order to describe the propagation of light through metasurfaces made of diffractive elements. We provide the appropriate laws that take a different form depending on the properties of the metasurface. Ou…
Effective refractive index of disordered all-dielectric metasurfaces consisting of gallium phosphide (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532~nm. It is shown that a mixture of the high index nanoparticles with sizes close to the first magnetic and electric resonances randomly dispersed on metasurface may possess negative refraction. The dependence of the metasurface effective refractive index on the nanoparticle concentration and size is constructed. The feasibility of negative refraction at large concentra…
Metasurfaces are an enabling technology for complex wave manipulation functions, including in the terahertz frequency range, where they are expected to advance security, imaging, sensing, and communications technology. For operation in transmission, Huygens' metasurfaces are commonly used, since their good impedance match to the surrounding media minimizes reflections and maximizes transmission. Recent theoretical work has shown that Huygens' metasurfaces are non-optimal, particularly for large angles of refraction, and that to eliminate reflections and spurious diffracted beams it is necessar…
Negative refraction plays an important role in acoustic wave manipulation and imaging. However, conventional systems based on acoustic metamaterials suffer from the limits induced by loss-related and resolution issues. In this work, a parity-time (PT)-symmetric system is introduced to realize loss-free bidirectional acoustic negative refraction. The system is composed of a pair of locally PT-symmetric multi-layer metasurfaces sandwiching a region of free space, which also forms a global PT-symmetry. The property of bidirectional negative refraction, which is rare for regular PT-symmetric struc…
Optical spin Hall (OSH) shift has been observed by weak measurement amplification in a refraction beam passing through air-glass interface, the refractive index gradient $\vec{\nabla} n$ being normal to the interface. Phase-discontinuity metasurface (PMS) possesses $\vec{\nabla} n$ tangential to the metasurface, and depending on the incidence angle either positive or negative refraction takes place satisfying the generalized Snell's law. Rapid phase-change over subwavelength distance at PMS leads to a large $\vec{\nabla} n$, enabling a direct observation of OSH shift. Here, we identify that th…
Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.
Maxwell's fish eye has been known to be a perfect lens within the validity range of ray optics since 1854. Solving Maxwell's equations we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.
Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we argue that the unlimited resolution is an artifact of having introduced an unphysical drain at the position of the geometrical image. The correct solution gives focusing consistent with the standard diffraction limit.
Perfect imaging has been believed to rely on negative refraction, but here we show that an ordinary positively-refracting optical medium may form perfect images as well. In particular, we establish a mathematical proof that Maxwell's fish eye in two-dimensional integrated optics makes a perfect instrument with a resolution not limited by the wavelength of light. We also show how to modify the fish eye such that perfect imaging devices can be made in practice. Our method of perfect focusing may also find applications outside of optics, in acoustics, fluid mechanics or quantum physics, wherever …
Kinsler and Favaro point out correctly that Blaikie's numerical solution of Maxwell's equations in Maxwell's fish eye is causal and hence valid, a solution where no perfect image is formed. It is wrong to conclude from the existence of a causal solution with perfect imaging that one without perfect resolution is not causal; both are allowed by causality. However, Maxwell's fish eye can still perfectly image, as the Reply shows.
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.
Refraction represents one of the most fundamental operations that may be performed by a metasurface. However, simple phasegradient metasurface designs suffer from restricted angular deflection due to spurious diffraction orders. It has been recently shown, using a circuit-based approach, that refraction without spurious diffraction, or diffraction-free, can fortunately be achieved by a transverse metasurface exhibiting either loss-gain or bianisotropy. Here, we rederive these conditions using a medium-based - and hence more insightfull - approach based on Generalized Sheet Transition Condition…
Whether or not perfect imaging is obtained in the mirrored version of Maxwell's fisheye lens is debated in the comment/reply sequence [Blaikie-2010njp, Leonhardt-2010njp] discussing Leonhardt's original paper [Leonhardt-2009njp]. Here we show that causal solutions can be obtained without the need for an "active localized drain", contrary to the claims in [Leonhardt-2010njp].
We demonstrate bending of light on the same side of the normal in a free standing corrugated metal film under bi-directional illumination. Coherent perfect absorption (CPA) is exploited to suppress the specular zeroth order leading to effective back-bending of light into the `-1' order, while the `+1' order is resonant with the surface mode. The effect is shown to be phase sensitive yielding CPA and superscattering in the same geometry.
We propose a tunable coherent perfect absorber based on ultrathin nonlinear metasurfaces. The nonlinear metasurface is made of plasmonic nanoantennas coupled to an epsilon-near-zero material with a large optical nonlinearity. The coherent perfect absorption is achieved by controlling the relative phases of the input beams. We show that the optical response of the nonlinear metasurface can be tuned from a complete to a partial absorption by changing the intensity of the pump beam. The proposed nonlinear metasurface can be used to design optically tunable thermal emitters, modulators, and sensor…
In this paper we show that a negative index of refraction is not a direct implication of transformation optics with orientation-reversing diffeomorphisms. Rather a negative index appears due to a specific choice of sign freedom. Furthermore, we point out that the transformation designed lens, which relies on the concept of spacetime folding, does not amplify evanescent modes, in contrast to the Pendry-Veselago lens. Instead, evanescent modes at the image point are produced by a duplicated source and thus no imaging of the near field (perfect lensing) takes place.
The in-plane negative refraction of high-momentum (i.e., high-k) photonic modes could enable many applications such as imaging and hyperlensing in a planar platform at deep-subwavelength scales. However, its practical implementation in experiments remains elusive so far. Here we propose a class of hyperbolic metasurfaces, which is characterized by an anisotropic magnetic sheet conductivity and can support the in-plane ultrahigh-k magnetic designer polaritons. Based on such metasurfaces, we report the first experimental observation of the all-angle negative refraction of designer polaritons at …
Negative index of refraction has become an accepted part of transformation optics, which is encountered in transformations that change the orientation of the manifold. Based on this concept, various designs of perfect lenses have been proposed, which all rely on a folding of space or spacetime, where the maps from electromagnetic space to laboratory space are multi-valued. Recently, a new concept for perfect imaging has been proposed by Leonhardt and Philbin, which also uses multi-valued maps, but does neither include negative index of refraction nor an amplification of evanescent modes. In th…
Time-varying metasurfaces are emerging as a powerful instrument for the dynamical control of the electromagnetic properties of a propagating wave. Here we demonstrate an efficient time-varying metasurface based on plasmonic nano-antennas strongly coupled to an epsilon-near-zero (ENZ) deeply sub-wavelength film. The plasmonic resonance of the metal resonators strongly interacts with the optical ENZ modes, providing a Rabi level spitting of ~30%. Optical pumping at frequency ω induces a nonlinear polarisation oscillating at 2ω responsible for an efficient generation of a phase conjugate and a ne…
Based on an analytic approach, we present a theoretical review on the absorption, scattering, and extinction of both dipole scatterers and regular arrays composed of such scatterers i.e., metasurfaces. Besides offering a tutorial by outlining the maximum absorption limit for electrically/magnetically resonant dipole particles/metasurfaces, we give an educative analytical approach to their analysis. Moreover, we put forward the analysis of two known alternatives in providing perfect absorbers out of electrically and or magnetically resonant metasurfaces; one is based on the simultaneous presenc…
We propose a device with a positive isotropic refractive index that creates an approximate magnified perfect real image of an optically homogeneous three-dimensional region of space within geometrical optics. Its key ingredient is a new refractive index profile that can work as an approximate perfect lens on its own, having a very moderate index range.
We introduce a paradigm for accurate design of metasurfaces for intricate beam manipulation, implementing functionalities previously considered impossible to achieve with passive lossless elements. The key concept involves self-generation of auxiliary evanescent fields which facilitate the required local power conservation, without interfering with the device performance in the far field. We demonstrate our scheme by presenting exact reactive solutions to the challenging problems of reflectionless beam splitting and perfect reflection, verified via full wave simulations.
Absorption of terahertz waves by a metasurface comprising a biperiodic array of pixellated meta-atoms on top of a dielectric substrate backed by a perfect electric conductor was simulated using a commercial software, with either all or a few of the pixels in every meta-atom patched with graphene. Absorptances as high as 0.99 over a 1.16-THz-wide spectral regime for normal incidence were found for a metasurface comprising meta-atoms with only a few pixels patched with graphene, regardless of the polarization state. In comparison to metasurface absorbers comprising two graphene layers separated …
We demonstrate that the metamaterial perfect absorber behaves as a meta-cavity bounded between a resonant metasurface and a metallic thin-film reflector. The perfect absorption is achieved by the Fabry-Perot cavity resonance via multiple reflections between the "quasi-open" boundary of resonator and the "closed" boundary of reflector. The characteristic features including angle independence, ultra-thin thickness and strong field localization can be well explained by this model. With this model, metamaterial perfect absorber can be redefined as a meta-cavity exhibiting high Q-factor, strong fie…
The widely-accepted theoretical treatment of the electromagnetic boundary problem of evanescent wave transfer at an interface between a normal medium of n=1 and an ideal negative index medium of n=-1 neglects the non-zero induced surface current and charge densities at the interface and is self-inconsistent. We re-solve the electromagnetic boundary problem by taking into account the non-zero induced surface current and charge densities that have been neglected so far by others. We give the exact induced surface current and charge distributions for this special case and solve the refracted and …
Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction o…
Enhancing absorption in optically thin semiconductors is the key in the development of high-performance optical and optoelectronic devices. In this paper, we resort to the concept of degenerate critical coupling and design an ultra-thin semiconductor absorber composed of free-standing GaAs nanocylinder metasurfaces in the near infrared. The numerical results show that perfect absorption can be achieved through overlapping two Mie modes with opposite symmetry, with each mode contributing a theoretical maximum of 50% in their respective critical coupling state. The absorption also shows the pola…
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…
Dielectric metasurfaces perform unique photonics effects and serve as the engine of nowadays light-matter technologies. Here, we suggest theoretically and demonstrate experimentally the realization of a high transparency effect in a novel type of all-dielectric metasurface, where each constituting meta-atom of the lattice presents the so-called transverse Kerker effect. In contrast to Huygens' metasurfaces, both phase and amplitude of the incoming wave remain unperturbed at the resonant frequency and, consequently, our metasurface totally operates in the invisibility regime. We prove experimen…
In this paper, theoretical and numerical studies of perfect/nearly-perfect conversion of a plane wave into a surface wave are presented. The problem of determining the electromagnetic properties of an inhomogeneous lossless boundary which would fully transform an incident plane wave into a surface wave propagating along the boundary is considered. An approximate field solution which produces a slowly growing surface wave and satisfies the energy conservation law is discussed and numerically demonstrated. The results of the study are of great importance for the future development of such device…
A discussion of a question, studied earlier by V.Veselago in 1967 and by J. Pendry in 2000, is given. The question is: can a slab of the material with negative refraction make a perfect lens? Pendry's conclusion was: yes, it can. Our conclusion is: no, in practice it cannot, because of the fluctuations of the refraction coefficient of the slab. Resolution ability of linear isoplanatic optical instruments is discussed.
Metasurfaces in metal/insulator/metal configuration have recently been widely used in photonics research, with applications ranging from perfect absorption to phase modulation, but why and when such structures can realize what kind of functionalities are not yet fully understood. Here, based on a coupled-mode theory analysis, we establish a complete phase diagram in which the optical properties of such systems are fully controlled by two simple parameters (i.e., the intrinsic and radiation losses), which are in turn dictated by the geometrical/material parameters of the underlying structures. …
An explicit time-domain finite-difference technique for modelling zero-thickness Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modelled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens' metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time-domain…
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase discontinuities. The approach contains both the near and far field cases. A starting point is the formulation of a vector Snell law in presence of abrupt discontinuities on the interfaces.
A perfect lens with unlimited resolution has always posed a challenge to both theoretical and experimental physicists. Recent developments in optical meta-materials promise an attractive approach towards perfect lenses using negative refraction to overcome the diffraction limit, improving resolution. However, those artificially engineered meta-materials usually company by high losses from metals and are extremely difficult to fabricate. An alternative proposal using negative refraction by four-wave mixing has attracted much interests recently, though most of existing experiments still require …
We extend designs of perfect lenses to the focussing of surface plasmon polaritons (SPPs) propagating at the interface between two anisotropic media of opposite permittivity sign. We identify the role played by the components of anisotropic and heterogeneous tensors of permittivity and permeability, deduced from a coordinate transformation, in the dispersion relation governing propagation of SPPs. We illustrate our theory with three-dimensional finite element computations for focussing of SPPs by perfect flat and cylindrical lenses.
Based on both analytical dipole model analyses and numerical simulations, we propose a concept of coherent perfect nanoabsorbers (CPNAs) for divergent beams. This concept makes use of the properties of a slab with negative refraction and small losses. The proposed CPNA device would allow focusing radiation in nanoscale regions, and hence could be applied in optical nanodevices for such diverse purposes as reading the results of quantum computation which is based on single photon qubits.
Orbital angular momentum (OAM) is a promising degree of freedom for fundamental studies in electromagnetics and quantum mechanics. The unlimited state space of OAM shows a great potential to enhance channel capacities of classical and quantum communications. By exploring the Pancharatnam-Berry phase concept and engineering anisotropic scatterers in a metasurface with spatially varying orientations, a plane wave with zero OAM can be converted to a vortex beam carrying nonzero OAM. In this paper, we proposed two types of novel PEC (perfect electric conductor)-PMC (perfect magnetic conductor) ani…
Fully reconfigurable metasurfaces would enable new classes of optical devices that provide unprecedented control of electromagnetic beamforms. The principal challenge for achieving reconfigurability is the need to generate large tunability of subwavelength, low-Q metasurface resonators. Here, we demonstrate large refractive index tuning can be efficiently facilitated at mid-infrared wavelengths using novel temperature-dependent control over free-carrier refraction. In doped InSb we demonstrate nearly two-fold increase in the electron effective mass leading to a positive refractive index shift …
We uncover and identify the regime for a magnetically and ferroelectrically controllable negative refraction of light traversing multiferroic, oxide-based metastructure consisting of alternating nanoscopic ferroelectric (SrTiO$_2$) and ferromagnetic (Y$_3$Fe$_2$(FeO$_4$)$_3$, YIG) layers. We perform analytical and numerical simulations based on discretized, coupled equations for the self-consistent Maxwell/ferroelectric/ferromagnetic dynamics and obtain a biquadratic relation for the refractive index. Various scenarios of ordinary and negative refraction in different frequency ranges are analy…
Ultrahigh-Q All-Metallic Metasurfaces with Robust Near-Perfect Absorption
College of Electronics and Information Engineering, Sichuan University（四川大学电子信息学院）；School of Physics and Optoelectronic Engineering, Guangdong University of Technology（广东工业大学物理与光电工程学院）
Black phosphorus (BP), a relative new plasmonic two-dimensional (2D) material, offers unique photonic and electronic properties. In this work, we propose a new tunable and broadband ultrathin coherent perfect absorber (CPA) device operating in the terahertz (THz) frequency range. It is based on a bifacial metasurface made of BP patch periodic arrays separated by a thin dielectric layer. Broadband CPA bandwidth is realized due to the ultrathin thickness of the proposed device and the extraordinary properties of BP. In addition, a substantial modulation between CPA and complete transparency is a…
Here we make use of vanadium dioxide (VO2) to design a bifunctional metasurface working at the same targeted frequency. With the increase of temperature, the functionality of the designed metasurface can switch from a multi-channel retroreflector to a perfect absorber, caused by the phase transition of VO2 from insulator to conductor. Different from traditional bifunctional metasurfaces designed by simple composition of two functionalities, our proposed bifunctional metasurface is based on the interaction between two functionalities. The device shows good potential for the combination of wavef…
A perfect metal film with a periodic arrangement of cut-through slits, an anisotropic metallic metamaterial film, mimics a dielectric slab and supports guided electromagnetic waves in the direction perpendicular to the slits. Here, we introduce metallic metasurface superlattices that include multiple slits in a period, and demonstrate that the superlattices support the Fano resonances and bound states in the continuum. The number of Fano resonances and bound states depend on the number of slits in a period of superlattices. The metallic metasurface superlattices provide new mechanisms to manip…
We introduce topological theory of perfect isolation: perfect transmission from one side and total reflection from another side simultaneously. The theory provides an efficient approach for determining whether such a perfect isolation point exists within a finite parameter space. Herein, we demonstrate the theory using an example of a Lorentz non-reciprocal metasurface composed of dimer unit cells. Our theory also suggests that perfect isolation points can annihilate each other through the coalescence of opposite topological charges. Our findings could lead to novel designs for high-performanc…
Control of the phase and polarization states of light is an important goal for nearly all optical research. The development of an efficient optical component that allows the simultaneous manipulation of the polarization and phase distribution is needed. Traditional methods require the combination of multiple optical devices, and a single optical device cannot easily realize full control of light. We theoretically predict and experimentally verify that our proposed dual-metasurfaces provide an excellent means to simultaneously manipulate the phase and polarization of transmission light at the n…
