The full-wave simulations corresponding to these transformations are plotted in Figure 11A and B , respectively. The simulated power transmission of these two structures is These efficiencies are mostly limited to the inherent dielectric and metallic losses of the scattering particles and, to a lesser extent, to the undesired diffraction orders due to the imperfection of these particles.

A corresponding metasurface was demonstrated in Ref. Full-wave simulations showing the performance of two refractive metasurfaces [ ]. Metasurface remote spatial processing, introduced in Ref. Figure 12 presents an example of such remote spatial processing. Initially, the signal beam in blue in Figure 2A is refracted by the metasurface according to some initial specification.

When the control beam in red is next added to the signal beam on the metasurface, as in Figure 12B , it changes the overall radiation pattern of the metasurface. Example of a remote spatial processing operation: A signal beam being refracted by the metasurface and B superposition of signal and control beams interacting with each other, which leads to a different transmitted wave.

The operation principle of such a modulator is presented in Figure To avoid the collocation of the control and signal beam sources, the control beam impinges on the metasurface at an angle while the signal beam is normally incident. To independently control the transmission of both beams, they must be orthogonally polarized on the incident side of the metasurface. However, they must exhibit the same polarization on the transmit side to interfere. On the transmit side, the two beams interfere and the corresponding amplitude thus depends of the phase difference between them.

The signal and control beams are impinging on the metasurface at different angles to avoid collocation of their source. The amplitude of the transmitted wave depends on the phase difference between the two beams by interference. The fabricated metasurface performing the operation depicted in Figure 13 has been experimentally measured, and the corresponding results are plotted in Figure 14 for an operating frequency of 16 GHz.

Measured transmission coefficients for the metasurface in Figure The blue curve is the transmission of the signal beam only, whereas the black and green curves are the destructive and constructive interferences of the signal and control beams, respectively. In the perspective of enhancing the efficiency of light-emitting diodes LEDs , we have reported in Ref.

Such refraction suppresses the wave trapping loss, as represented in Figure 15A. The requirement of total normal refraction, as represented in Figure 15B , is excessively stringent, leading to susceptibilities with prohibitive spatial variations, and is not required in this application. A better strategy consists, as illustrated in Figure 15C , in allowing partial local reflection and ultimately collecting the reflected part of the energy by Fabry-Perot resonance in the PRMC formed with a mirror plane at the bottom of the slab.

The double-metasurface cavity, as depicted in Figure 15D , is an even more sophisticated design, leading to dramatic LEE enhancement. Radiation of a light source quantum well embedded in a semiconductor e. GaN substrate: A bare structure; B reflectionless metasurface, placed on top of the slab, which collimates the dipole fields; C introduction of PRMC; and D double-metasurface cavity, with partially reflective top metasurface and fully reflective bottom metasurface.

The SER is enhanced by maximizing the confinement of coherent electromagnetic energy in the vicinity of the source and leveraging the Purcell effect, which is particularly well achieved in the double-metasurface PRMC Figure 15D. Finally, the far-field directivity is maximized as an optimization tradeoff for maximal overall power conversion ratio. Original images from Ref. The case of a real LED is more complex due to the incoherence and distribution emission of the quantum well emitters.

Different metasurface strategies are currently being investigated to maximize the power conversion efficiency of a complete LED. Thus far, we have only discussed linear metasurfaces, i. Given the wealth of potential applications of nonlinear metasurfaces, it is highly desirable to develop tools for the design of such metasurfaces. Therefore, we extended our susceptibility-GSTC technique to the case of a second-order nonlinear metasurface in Ref.

For the sake of simplicity, we assume that these susceptibility tensors are scalar. The relevant GSTCs are then, in the case of x -polarized waves, given by From these relations, we can either perform a synthesis, i. Here, for the sake of briefness, we will not elaborate on the synthesis and analysis operations but shall rather present one of the main results obtained in Ref. The metasurface with susceptibility 67 and 68 exhibit different reflectionless conditions for the two propagation directions as, due to the presence of the square of both the electric and magnetic fields, relation 67 and 68 is asymmetric with respect to the z -direction.

An important consequences of the fact that the metasurface cannot be matched from both sides is that its SHG is inherently nonreciprocal. We have presented an overview of electromagnetic metasurface designs, concepts, and applications based on a bianisotropic surface susceptibility tensor model. This overview probably represents only a small fraction of this approach, which nevertheless already represents a solid foundation for future metasurface technology.

Metamaterials ;— An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials. Functional and nonlinear optical metasurfaces. Laser Photon Rev ;— Metasurfaces: from microwaves to visible. Phys Rep ;— Planar photonics with metasurfaces. Science ; Lamb H.

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On the reflection and transmission of electric waves by a metallic grating. Proc Lond Math Soc ;— Marconi G, Franklin C. Reflector for use in wireless telegraphy and telephony. April 22 , US Patent 1,, Buskirk LV, Hendrix C. The zone plate as a radio-frequency focusing element. Munk BA. Frequency Selective surfaces: theory and design. An overview of three-dimensional frequency-selective structures. Huang J, Encinar JA. Reflectarray antenna. The reflectarray antenna. Malagisi C.

Microstrip disc element reflect array. Montgomery JP. A microstrip reflectarray antenna element. Antenna Applications Symposium, University of Illinois, Stangel J. The thinned lens approach to phased array design. Kahrilas PJ. Hapdar an operational phased array radar. Proc IEEE ;— McGrath D. Planar three-dimensional constrained lenses. Pozar DM. Flat lens antenna concept using aperture coupled microstrip patches. Electron Lett ;— Implementation of transmitarray antenna concept by using aperture-coupled microstrip patches.

Layered lens antennas. Thin microwave quasi-transparent phase-shifting surface PSS. Imani MF, Grbic A. An analytical investigation of near-field plates. Near-field plates: subdiffraction focusing with patterned surfaces. Science ;—3. Imani M, Grbic A. Planar near-field plates.

Scalar and tensor holographic artificial impedance surfaces. Metasurfing: addressing waves on impenetrable metasurfaces. Appl Phys Lett ; A multilayer circular polarizer based on bisected split-ring frequency selective surfaces. A novel four-face polarization twister based on three-dimensional magnetic toroidal dipoles. Circular polarization converters based on bi-layered asymmetrical split ring metamaterials.

Appl Phys A ;—8. Controlling the polarization state of light with a dispersion-free metastructure. Phys Rev X ; Opt Commun ;—8. Multiple-band reflective polarization converter based on complementary L-shaped metamaterial. Microw Opt Technol Lett ;— Plasmonic planar antenna for wideband and efficient linear polarization conversion. Flexible chiral metamaterials in the terahertz regime: a comparative study of various designs. Opt Mater Express ;— J Phys D ; Novel triple-band polarization-insensitive wide-angle ultra-thin microwave metamaterial absorber. J Appl Phys ; Perfect magnetic mirror and simple perfect absorber in the visible spectrum.

Phys Rev B ; Planar broadband and high absorption metamaterial using single nested resonator at terahertz frequencies. Opt Lett ;— Polarization angle independent perfect metamaterial absorbers for solar cell applications in the microwave, infrared, and visible regime. Prog Electromagn Res ;— Yoo M, Lim S. Polarization-independent and ultrawideband metamaterial absorber using a hexagonal artificial impedance surface and a resistor-capacitor layer. Total absorption of electromagnetic waves in ultimately thin layers.

Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science ;—7. Yu N, Capasso F. Flat optics with designer metasurfaces. Nat Mater ;— Genevet P, Capasso F. Opt Express ;— Efficient flat metasurface lens for terahertz imaging. Opt Express ;—9. Functional metamirrors using bianisotropic elements. Phys Rev Lett ; Metamaterial apertures for coherent computational imaging on the physical layer.

J Opt Soc Am A ;— Metamaterial apertures for computational imaging. Perfect co-circular polarization reflector: a class of reciprocal perfect conductors with total co-circular polarization reflection. Phase-compensated metasurface for a conformal microwave antenna. Tailoring reflections from thin composite metamirrors. Transmitarray antenna design using cross-slot elements with no dielectric substrate. Gradient metasurface with both polarization-controlled directional surface wave coupling and anomalous reflection. Nye J, Berry M. Dislocations in wave trains. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface.

Light Sci Appl ;3:e Pfeiffer C, Grbic A. Controlling vector Bessel beams with metasurfaces. Phys Rev Appl ; Generation of cylindrical vector vortex beams by two cascaded metasurfaces. Vortex beams with strong longitudinally polarized magnetic field and their generation by using metasurfaces. J Opt Soc Am B ;— Spinning light on the nanoscale. Nano Lett ;—9. Nanostructured holograms for broadband manipulation of vector beams.

Nano Lett ;— Metamaterial microwave holographic imaging system. Nat Nanotechnol ;— Generating stable tractor beams with dielectric metasurfaces. Monolayer graphene photonic metastructures: giant Faraday rotation and nearly perfect transmission.

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Degiron A, Smith DR. One-way glass for microwaves using nonreciprocal metamaterials. Phys Rev E ; One-way transparent sheets. Artificial Faraday rotation using a ring metamaterial structure without static magnetic field. Electromagnetic modeling of a magnetless nonreciprocal gyrotropic metasurface.

Active control of chirality in nonlinear metamaterials. Nonlinear superchiral meta-surfaces: tuning chirality and disentangling non-reciprocity at the nanoscale. Adv Mater ;— Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature ;—9. Analog computing using reflective plasmonic metasurfaces. Nano Lett ;—7.

Performing mathematical operations with metamaterials. Metamaterial broadband angular selectivity. Optical broadband angular selectivity. Science ;— General metasurface synthesis based on susceptibility tensors. Metasurface synthesis for time-harmonic waves: exact spectral and spatial methods. Salem MA, Caloz C.

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Manipulating light at distance by a metasurface using momentum transformation. Millimeter-wave transmitarrays for wavefront and polarization control. Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis. Design of unit cells and demonstration of methods for synthesizing Huygens metasurfaces. Selvanayagam M, Eleftheriades G.

Polarization control using tensor Huygens surfaces. Epstein A, Eleftheriades G. Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation. Synthesis of polarization transformers. Idemen MM. Discontinuities in the electromagnetic field. Electromagnetic characterization of bianisotropic metasurfaces on refractive substrates: general theoretical framework. Ann Phys ;— Kong J. Electromagnetic wave theory. A Wiley-Interscience publication. Electromagnetic waves in chiral and bi-isotropic media.

The Artech House Antenna Library. Artech House, Electromagnetics of Bi-anisotropic Materials — Theory and Application. Amsterdam, Gordon and Breach Science Publishers, Mathematical synthesis and analysis of a second-order magneto-electrically nonlinear metasurface.

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Averaged transition conditions for electromagnetic fields at a metafilm. Synthesis of electromagnetic metasurfaces: principles and illustrations. EPJ Appl Metamater ; Electromagnetic metasurface performing up to four independent wave transformations. Computational analysis of metasurfaces. Saleh B, Teich M.

Fundamentals of photonics, wiley series in pure and applied optics. New York, Wiley, Sounas DL, Caloz C. Electromagnetic non-reciprocity and gyrotropy of graphene. Appl Phys Lett ;—3. Normal vs tangential polarizations in metasurfaces. Optical metasurfaces with robust angular response on flexible substrates. IEEE — Bianisotropic effective parameters of optical metamagnetics and negative-index materials.

Simulation of the electromagnetic properties of helices with optimal shape, which provides radiation of a circularly polarized wave. J Adv Res Phys ;2. Determining polarizability tensors for an arbitrary small electromagnetic scatterer. Photon Nanostruct Fundam Appl ;— Berreman DW. Optics in stratified and anisotropic media: matrix formulation. J Opt Soc Am ;— Dmitriev V. Group theoretical approach to complex and bianisotropic media description. Eur Phys J AP ;— Group-theory approach to tailored electromagnetic properties of metamaterials: an inverse-problem solution.

Polarization properties of optical metasurfaces of different symmetries. High performance bianisotropic metasurfaces: asymmetric transmission of light. Epstein A, Eleftheriades GV. Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces. Reflectionless wide-angle refracting metasurfaces. Dielectric gradient metasurface optical elements. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission.

Towards all-dielectric metamaterials and nanophotonics. Proc SPIE ;— Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science ;—5. Comparison of two synthesis methods for birefringent metasurfaces. Refracting metasurfaces without spurious diffraction. Simultaneous enhancement of light extraction and spontaneous emission using a partially reflecting metasurface cavity. Phys Rev A ; Metasurface spatial processor for electromagnetic remote control.

Nonreciprocal nongyrotropic magnetless metasurface. Dielectric resonator metasurface for dispersion engineering. Achouri K, Caloz C. Metasurface solar sail for flexible radiation pressure control, arXiv preprint arXiv Thus far, and throughout this paper, we essentially consider metasurfaces illuminated by waves incident on the them under a nonzero angle with respect to their plane, i.

However, metasurface may also be excited within their plane, i. This approximation is justified by the fact that a physical metasurface is electromagnetically very thin, so that it cannot support significant phase shifts and related effects, such as Fabry-Perot resonances. Note that these relations can also be obtained following the more traditional technique of box integration, as demonstrated in Ref. These conditions are identical to those for a bianisotropic medium [ 93 ], [ 94 ], except that the metasurfaces in Eq.

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The overall design procedure thus consists of the combination of the synthesis and analysis operations. This paper focuses on the direct synthesis of the susceptibility functions, as this is the most important aspect for the understanding of the physical properties of metasurfaces, the elaboration of related concepts, and the development of resulting applications. Moreover, in the particular case where all the specified waves are normal to the metasurface, the excitation of normal polarization densities does not induce any discontinuity in the fields.

This is because the corresponding fields, and hence the related susceptibilities, are not functions of the x and y coordinates, so that the spatial derivatives of P z and M z in Eqs. Thus, susceptibilities producing normal polarizations can be ignored, and only tangential susceptibility components must be considered, when the metasurface is synthesized for normal waves.

Even if it would be solved, this would probably result in an inefficient metasurface, as it would use more susceptibility terms than required to accomplish the specified task. Mathematically, the number of combinations would be 16! For instance, the specification of a reciprocal transformation, corresponding to the metasurface properties in Eq.

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Incidentally, the equality between the electric and magnetic susceptibilities results from the specification of zero reflection in addition to normal incidence. The reader may easily verify that, in the presence of reflection, the equalities do not hold. If, for instance, the incident was polarized along x only, then only the susceptibilities in Eq.

It is also possible to solve a system of equations that contains less than these 16 susceptibility components. In that case, less than four wave transformations should be specified so that the system remains fully determined. For instance, two independent wave transformations possessing both x - and y -polarizations could be solved with eight susceptibilities.

Similarly, three wave transformations could be solved with 12 susceptibilities. For instance, if the fields of the first transformation are only x -polarized, the fields of the second transformation are only y -polarized. The synthesis technique yields the susceptibilities for an ideal zero-thickness metasurface. This means that Huygens theorem cannot be used to find purely tangential equivalent surface currents corresponding to these fields. Note that is possible to obtain all 36 susceptibility components of a scattering particle provided that the four GSTC relations are solved for nine independent sets of incident, reflected, and transmitted waves.

In practice, such an operation is particularity tedious and is thus generally avoided. The quasi-totality of the refracting metasurfaces discussed in the literature thus far has been reciprocal. The following argument does not hold for the nonreciprocal case, where perfect refraction could in principle be achieved by a symmetric metasurface structure. In these expressions, the susceptibilities are dispersion less. Export Citation. Here you can find all Crossref-listed publications in which this article is cited.

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Abstract The scalar Huygens—Fresnel principle is reformulated to take into account the vector nature of light and its associated directed electric and magnetic fields. Focal shifts in diffracted converging electromagnetic waves. Kirchhoff theory Yajun Li J. Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials. Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture using Borgnis potentials.

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