1 General Introduction to optical metasurfaces
Unexpected and unusual effects have been recently reported in various fields of research, such as but not limited to acoustics, seismology, thermal physics, and electromagnetism. At the heart of these developments is a progressive understanding of the wave-matter interaction and our ability to artificially manipulate it, particularly at small length scales. This has in turn been largely driven by the discovery and engineering of materials at extreme limit. These “metamaterials” possess exotic properties that go beyond conventional or naturally occurring materials. Encompassing many new research directions, the field of metamaterials is rapidly expanding, and therefore, writing a complete review on this subject is a formidable task; here instead, we present a comprehensive review in which we discuss the progress and the emerging materials for metasurfaces, i.e. artificially designed ultrathin two dimensional optical metamaterials with customizable functionalities to produce designer outputs.
Metasurfaces are often considered as the two dimensional versions of 3D metamaterials. The former, also known as frequency selective surfaces, or reflect- and transmit-arrays in the microwave community [1–6], which has been recently shown to produce a variety of spectacular optical effects ranging from negative refraction , super/hyper-lensing [8–10], optical mirages to cloaking [11–19], are comprised of artificial materials engineered at the subwavelength scale to guide light along any arbitrary direction. The functionalities of individual optical components, which were previously essentially determined by the optical properties of materials, can now be specified at will. Effective material optical parameters can be rigorously derived via homogenization techniques by averaging the electromagnetic fields over a subwavelength volume encompassing each individual element of the periodic ensemble of resonant inclusions, with arbitrary geometry [12, 15–19]. Thus although metamaterials can be tailored for exotic optical functions, the basic mechanism responsible for shaping the optical wavefronts remains the same as that in conventional refractive optics: it is based on the propagation of light in the composite materials. Nevertheless the idea of manipulating light deep into the subwavelength regime can be further exploited to the extreme case where metamaterials become infinitely – or at least sufficiently-thin with respect to the wavelength of light to create metasurfaces (Fig. 1a).
Breaking away from our reliance on gradual phase accumulation, one can instead consider functional interfaces covered with a collection of subwavelength nanostructures/slits or structured optical thin-films (i.e. almost 2D) to introduce abrupt modifications on the wavefront of light over the scale of the wavelength. For example by imposing gradients of optical phase discontinuities at interfaces [20–29], it became possible to bend light propagation in any desired directions in perfect agreement with the generalized laws of reflection and refraction (Fig. 1b) : (1)
where θj and θt denote respectively the incident and the transmitted angles, ni, nt are the refractive indices of the incident and the transmitted medium and λo is the vacuum wavelength. Equation 1 assumes that the phase gradient is a continuous function of position; however in reality, the interface is comprised of discrete resonators. Similarly, although the basic mechanism for controlling light with an array of subwavelength scatterers can be intuited by considering a subwavelength distribution of discrete phase delayed light sources, its theoretical description is rather more complex. The effective medium theory, which is well suited to derive the bulk-parameters of 3D metamaterials, may not always apply for media with reduced dimensionality such as interfaces. This point has been discussed in detail by C.L. Holloway et al. [3–6]. In these papers, it is shown that the scattering of light by nanostructures of sub-wavelength thickness is best characterized by a generalized version of the boundary conditions, known as generalized sheet transition conditions (GSTCs) :
where Δ represents the difference between the fields in the two side of the interface, and P and M are the surface electric and magnetic polarization densities derived from the local electric and magnetic induced dipole moments in the plane z=0. Considerable efforts have been made to express the GSTCs using macroscopic quantities and we can now rewrite the GSTCs using the equivalent six-by-six surface susceptibility tensor1 to relate the fields and the induced currents on the metasurfaces by using the relation :
where the average fields are defined by:
Unlike 3D metamaterials where both permittivity and/or permeability are engineered for the bulk, metasurfaces act directly upon the boundary conditions of Maxwell’s equations, and for this reason the surface susceptibility (or equivalently the admittance) becomes the most appropriate quantity characterizing the optical response [4–6]. The large number of degrees of freedom in choosing the components of the tensor in Eq. (3) is such that solving the system in Eq. (2) poses a complex theoretical challenge, particularly in terms of design. The characterization of a metasurface at the microscopic level given arbitrary electromagnetic fields at either side represents a tremendous task, and we believe that this may provide potentials for even greater theoretical progress in this direction.
From the above discussion, it is clear that the manipulation of light with metasurfaces goes beyond the phase; it is possible to achieve simultaneous control of the amplitude, phase (full 2π coverage), as well as polarization and the dispersion of light at interfaces. These techniques have already been exploited to create numerous new and intrinsically flat devices such as phase plates , collimators , waveplates  and flat lenses [34, 35] for diverse applications ranging from holography [36–38], subdiffraction imaging [39–41] and nano-circuitry [42–44] to cloaking [13, 45–48].
In addition, from the manufacturing point of view metasurfaces possess a number of advantages compared to traditional metamaterials. Since light is not propagating in the bulk, metasurfaces are less absorbing and are particularly easier to fabricate than their 3D counterparts. While metasurfaces are created using planar micro/nanofabrication technologies, 3D metamaterials are fabricated using mature but still expensive processes that involve carving, polishing and surface coating of different sort of bulk materials. Traditional manufacturing optics technology requires a large amount of raw materials and qualified engineers that have to deal with difficult and precise tasks. Fabrication of refractive devices consumes a lot of materials, coating the surfaces is performed by depositing multilayers of various dielectrics, and, the characterization of the end products is generally performed manually one-by-one, device after device. Instead, 2D planar metasurfaces can be created using advanced manufacturing processes that are now already well-established in the semiconductor integrated circuit industry. Thus one could in principle arbitrarily engineer the phase, polarization and amplitude profile with a single device fabricated using in a single lithographic step, subject to the complexities introduced by near-field coupling between individual elements. In the following, we highlight various materials and design techniques developed in the recent years and comment on the progress in utilizing them for novel metasurface applications, with particular emphasis on non-traditional and emerging materials.
One key concern in almost any device application is loss. Despite significantly mitigating propagation losses due to their reduced spatial footprint compared to bulk metamaterials, metasurfaces can have considerable intrinsic absorption. To fully understand the origin of the problem, one should bear in mind that the individual building blocks of metasurfaces may in principle be optically resonant elements. Traditional optical resonators have consisted of Fabry-Perot cavities, whispering gallery structures, or photonic crystals and various forms of dielectric waveguides [49, 50]. While these generally low loss structures have proved to be incredibly useful for applications ranging from lasers to sensitive biochemical sensors and even frequency generation devices [51–56], they present an overly large physical footprint. Rigorously the electromagnetic mode volume either exceeds or is on the order of (λ/n)3, where n is the refractive index of the material. It was only with the development of plasmonics [57, 58] that deeply subwavelength confinement, or manipulation of light beyond the Rayleigh diffraction limit, became a real and enticing possibility. Plasmonics involves the study of electromagnetic surface waves (plasmons) which exist at the interface between media whose dielectric permittivities have opposite signs; in turn, electromagnetic energy is confined to mode volumes significantly smaller than λ3 at resonance . This combination of possessing a strong resonance at a deeply subwavelength size scale lends itself readily to metasurface applications, and for enhanced light-matter interactions in general [59, 60]. As a result, the discussion of traditional metasurface materials has been until recently the discussion of plasmonic materials.
Figure 2 illustrates various plasmonic materials, both traditional and emerging, consolidated on a common plot of quality factor (Q) of their localized surface plasmon resonance (within scaling constants) against wavelength. The Q factor is rigorously defined as the ratio of stored electromagnetic energy to the energy dissipated (or absorbed) per cycle in a resonator; it is an indication of photon lifetime in a cavity and thus loosely corresponds to how “good” a resonance is. This is a meaningful metric to assess the relative strengths of plasmonic materials beyond simply ensuring that they satisfy the plasmon dispersion condition (negative real permittivity or that they have minimal imaginary permittivity), although numerous other figures-of-merit exist and might be more useful depending on the area of application, such as normalized surface plasmon propagation lengths . Here we consider only the contributions arising from material properties, i.e. neglecting the influence of shape, size and structure in influencing resonance behaviour. Although important for the practical implementations of efficient metasurfaces, we do not include scattering losses of the resonators in order to make a fair comparison based on intrinsic material properties alone. This intrinsic Q factor can be shown [62, 63] to scale as the ratio of the real and imaginary permittivities −ε′/ε″ (its propagating surface plasmon counterpart scales as ε′2/ε″) in the quasistatic limit, and with low losses (e.g. finite ε″). In terms of the standard Drude model the former expression becomes (correspondingly : intuitively we seek materials with a large ratio of plasma frequency to damping, as well as intrinsically small damping. It would be inadequate to base the discussion on either one of these quantities alone.
From Fig. 2, it is clear that while there are an abundance of plasmonic materials in general, ranging from noble metals like gold and silver which perform well at optical to near-infrared wavelengths [64, 65], to transparent conducting oxides (ITO) , as well as silicides , graphene [68, 69] and refractory plasmonic materials like titanium nitride [70, 71] whose resonances span the near to mid-infrared region, their material quality factors are generally in the same order of magnitude (between 10 to 100). This value is low, particularly in comparison to, for example, values approaching 108 that can now be routinely achieved in whispering gallery mode dielectric resonators [72, 73]. This implies that traditional plasmonic materials discovered so far are unavoidably lossy at optical and infrared wavelengths, due to the finite skin depth of the mode in a lossy medium. In turn, metasurface efficiencies have been significantly affected by these losses alone . This strongly motivates the search for better materials (not necessarily plasmonic) that still satisfy the criteria of supporting optical resonances with subwavelength confinement [75–77], as well as alternative design schemes and strategies that can mitigate all sources of loss (e.g. both absorption and reflection) and achieve high efficiencies via interplay between multiple resonant channels.
One such method to fully and efficiently engineer the phase of a light beam consists of utilizing an anisotropic nanostructure designed to have two orthogonal polarization states with a π phase difference . This element can be intuitively visualized as a tiny half wave plate whose principal axis is determined by its orientation with respect to the incident polarization. By employing a series of the same anisotropic scatterers that are geometrically rotated with respect one to another, resulting in the acquisition of a geometric Pancharatnam-Berry phase [79–82], one can achieve holographic projection of an image with a record reflection efficiencies close to unity [78, 83]. A recent example is illustrated in Fig. 3a. Instead of using two distinct modes of resonance whose transmission is largely fixed by the desired phase profile, these metasurfaces have an additional degree of freedom: the final imparted phase originates only from the geometric phase acquired as a circularly polarized light beam is taken along a closed cycle in the polarization space due to interacting with geometrically rotated scatterers. This leaves room to separately design the transmission amplitude of the metasurface by varying geometrical parameters (besides orientation, which is fixed). This is in contrast to regular dynamic phase acquired via propagation or from resonator response. In this way, the basic structure of each individual scatterer can be optimized to provide results with better efficiency, for example, by suppressing transmission channel and improving reflection via constructive interference with cavity resonances (Fig. 3a), although it does not overcome intrinsic losses and operates with the caveat of being in cross polarization.
We also note here an added subtlety that while this technique applies to incident light beams, the same is generally not true for bound electromagnetic waves such as surface plasmons, particularly in planar geometries such as interfaces. The reason is the lack of helicity (σ) in the latter which limits overall phase acquired to π, instead of the whole range of 2π. This situation is illustrated in the panels on the right in Fig. 3a and 3b . For the same rotation angle of 90° in the rectangular resonator element, it is seen that the accompanying phase changes for the cross polarized and surface plasmon beams are π and π/ 2 respectively (Fig. 3b), in contrast to circularly polarized free space light beams that possess helicities ±1 (Fig. 3a). It is only in certain geometries (e.g. cylindrical) where multiple surface plasmon modes can be superposed with a defined phase relationship, that surface plasmons can possess helicity and chirality .
An alternative approach to achieving high performance efficiencies is via engineered interfaces (without the use of geometric phase), particularly in a cavity configuration utilizing regular reflectors or multiple metasurface layers. This has been employed in the design of highly efficient reflectors and absorbers by overlaying patterned metallic structures over opaque metal ground plates separated by a dielectric spacer [86–88]. By considering the interplay between the radiated fields of the induced image dipole in the ground plane upon resonant excitation of the top metasurface , or equivalently the formation of “gap surface plasmon” (GSP) modes in the entire composite structure [88, 89], any incident power in a spectrally broad range can be almost entirely absorbed or reflected. Importantly such designs utilize an optically thin spacer, such that the overall device is compact and subwavelength in all dimensions. For transmission mode devices, a similar principle applies, although neither reflection nor absorption can be trivially suppressed. Intuitively a single interface can only support tangential electric currents that radiate equally on both sides, thereby giving rise to unavoidable reflection loss. By utilizing the notion of optical metatronics [42, 90] and employing a series of cascaded metasurfaces with prescribed transverse inhomogeneity, one can realize sufficient degrees of freedom to achieve full control of the transmission phase, while at the same time to minimize reflection via impedance matching . A proposed design from  is illustrated in Figure 4a. It utilizes a basic building block of fixed geometry with varying fractions of a plasmonic material and dielectric. By varying the fill factor, both inductive reactances are obtained which span a broad range of values .
A variant of this technique utilizes magnetic responses in addition to electrical ones in traditional metasurfaces, also via a cascaded metasurface geometry [92–94]. A representative example of such schemes is shown in Fig. 4b. The overlay of multiple interfaces generates a magnetic response due to longitudinal circulating electrical currents, so that ideally (absent material losses) each unit cell radiates unidirectionally due to interference. By optimizing the net anisotropic sheet admittance of the layers, it is shown that a minimum of three surfaces is sufficient to achieve maximum transmission. It is worth noting that despite requiring proper design of interlayer spacing in order to tailor the magnetic response, these cascaded sheets are still subwavelength in thickness and can be modelled as a single, bianisotropic metasurface capable of exhibiting electric, magnetic and chiral responses .
The aforementioned techniques demonstrate how overall losses in a metasurface can be minimized by exploiting device architecture; however net efficiencies are still constrained by intrinsic material parameters (which in the language of the previous examples, manifest as shunt resistances and complex sheet admittances with non-zero real components). From a materials perspective, the recent investigation of strong resonances in subwavelength high index dielectric particles thus opens up tremendous opportunities for the further development of nanoscale optics in general. In particular, the observation that the strong electrical displacement currents in such particles support an orthogonal magnetic dipole, in addition to the electric dipole caused by the driving field of incident light, makes these structures especially relevant for metasurfaces [95–98]: the aforementioned criteria of strong resonances at subwavelength scales while maintaining full phase control has been satisfied.
3 Metasurfaces based on resonant dielectric elements
Due to their low intrinsic absorption at visible wavelengths, transparent dielectrics have always been considered as major materials of choice for constructing optical components. Apart from conventional bulk optics various quasi-flat devices, such as binary optics, have been extensively developed . Flat elements have obvious advantage of compactness, which now becomes more and more important in the context of wearable and mobile photonic devices. Some of the earlier approaches, such as binary blazed gratings , directly relied on subwavelength patterning of the dielectric surface to achieve variations of effective refractive index profile in 2D, which allows for transmitted or reflected phase engineering. This approach typically requires densely-packed micrometertall nanostructures, which are challenging to fabricate and implement into a robust device. High refractive index materials such as silicon allows reduction of the thickness while still keeping it on the order of half micron or above and maintaining a high aspect ratio (typically >1) [101, 102]. Another approach for phase control with structured dielectric surfaces relies on rotating grating elements and Pancharatnam-Berry (PB) phase, as previously introduced. Initially proposed for metallic gratings  it was quickly adapted to dielectric materials , resulting in e.g. demonstration of metasurface-based holography . In recent studies a similar approach was applied to realize silicon gratings, lenses and axicons with only 100 nm thickness on quartz substrate . Figure 5a shows an example of an axicon constructed from sub-diffractive arrays of silicon nanorods .
The studies mentioned above considered dielectric structures, which rely on additional mechanisms to achieve the full phase control (e.g. PB phase). Recently the field of resonant dielectric nanophotonics has witnessed a rapid development, providing completely new solutions for both isolated dielectric nanoantennas as well as metasurfaces. Although resonances in small dielectric spherical particles with high refractive index have attracted the attention of numerous theorists over the last century – a case completely solved by the Mie theory  – it is only very recently these resonances were experimentally realized in the visible and near-IR spectrum. We also invite the reader to consider several major examples treated in references [105–107]. Coming back to recent work, the first example of controlled first-order resonance at visible frequencies was performed with germanium  and silicon  nanorods and later with silicon [97, 98] and gallium arsenide  nanoparticles. It was shown [97, 98, 111] that such nanoparticles may have strong electric and magnetic dipole resonances at visible and IR frequencies. Both types of dipoles can be excited simultaneously within simple nanoparticle geometries (such as spheres or disks) which provide numerous possibilities for directivity control of scattering. In particular, as was first predicted by Kerker  and recently demonstrated at microwaves  and in the visible spectrum [110, 113], the two dipoles may interfere and strongly suppress the particle radiation pattern in backward direction, making it analogous to Huygens’ source with only forward scattering. Tuning the particle shape (e.g. by changing aspect ratio of disks [114, 115] or spheroids ) enables one to control spectral position of the electric and magnetic dipole resonances maxima and have them coincide in amplitude and in phase at a single wavelength, which makes the effect of directional forward scattering broadband.
Combining these directional dielectric scatterers with only forward scattering into an array allows constructing a Huygens’ metasurface with enhanced transmission at resonant wavelengths [92–94, 115]. This allows for the possibility of full 2π control of transmission phase (π phase shift for each of the electric and magnetic dipole resonances) . The operation principle of such a metasurface is similar to multi-layer plasmonic Huygens’ metasurfaces described above . The obvious advantages compared to metals are lower intrinsic losses, and compatibility with CMOS processes, which makes them more likely to have an impact in real-world applications. Very recently high efficiency resonant transmission (>85%) and transmitted beam deflection (efficiency >45%) with these dielectric metasurfaces with only 130 nm thickness has been experimentally demonstrated  (Fig. 5b). A similar principle has also been applied to vortex beam generation [119, 120]. Additionally, efficiencies exceeding 80% for beam focusing and forming has been achieved with high-aspect ratio pillars (see example of vortex beam generation in Fig. 5c) [121, 122]. In this case however, due to the high-aspect ratio of the nanostructures fabrication and handling of such a device can become more challenging.
Apart from transmitted phase engineering, resonant dielectric metasurfaces may provide multiple other functionalities related to the interplay between electric and magnetic resonances of their constituent elements. Some examples are extra-high reflectivity at a single metasurface layer , which can also be combined with wavefront engineering , or ultra-narrow electromagnetically induced transparency window obtained with dielectric nanoantenna array . Recently analogy to magnetic mirror behavior  and demonstration of generalized electro-magnetic Brewster effect  with dielectric metasurfaces have been reported. The latter case is depicted in Fig. 5d and shows that a single-layer dielectric metasurface can produces an equivalent effect of a conventional bulk material with both electric and magnetic properties at visible wavelengths (ε ≠ 1, μ ≠ 1).
These effects which have been demonstrated in the visible and near infrared spectral region are not restricted to a particular material or a specific spectral range. Similar exciting optical properties can be observed at any frequency by scaling the size of the nanostructures (e.g. for mid-IR frequencies [111, 127]), providing that the dielectric material possesses a relatively high refractive index (>2) and low losses in the required frequency range. In general, strong electric and magnetic resonant behavior, low losses, advanced scattering directivity control, high melting temperature and CMOS compatibility make resonant dielectric nanoantennas and metasurfaces very promising for real-world applications.
4 Active/2D materials
A cornerstone of device operation is active behaviour where output changes in response to a control signal. For example, spatial light modulators comprising of liquid crystal displays are capable of modulating amplitude, phase and polarization of light in both space and time, and are integral components of many systems such as imaging and projection devices in consumer electronics as well as advanced microscopy (optical tweezing, stimulated emission depletion (STED) microscopy) setups. It is thus apparent that in order for the concept of photonics, and by extension metasurfaces, to truly realize the vision of superseding traditional optical components and even optoelectronics, a robust system that enables active behaviour and preserves key advantages of these structures must be established. To this end, significant work has been done in the research and synthesis of new functional materials, and their integration with traditional metamaterial building blocks . Examples include the use of microelectromechanical (MEMs) systems [129–131], charge carrier injection [132–136], phase change materials [137–145] and liquid crystals [146–148] for dynamic reconfigurability.
Here we highlight in particular the emerging and rapidly developing field of two dimensional (2D) materials, as exemplified by the earliest isolated carbon monolayer graphene. While it is now well-known that graphene for example has significant potential in various electronic applications due to its 2D nature that results in effectively massless electrons capable of ballistic transport at room temperature [149–151], significantly less attention has been paid to its use in various photonic applications. The latter is capable of leveraging upon most of graphene’s advantages for electronic devices, but without the corresponding drawbacks (most notably, the lack of a bandgap which severely hinders electrical switching devices). Intuitively and as a starting point, we consider its use as a functional, passivation layer whose dielectric permittivity can be dynamically altered by a wide range. The low intrinsic carrier concentration of graphene and its unique band structure implies that the former can be tuned by a much larger percentage than traditional bulk materials via external doping, and is typically only limited by gate breakdown voltages. This is the basic principle behind graphene’s use as an electrical transducer, due to its gate-tunable Fermi energy level and hence conductivity [152–154]. Optically, this directly translates to a highly tunable dielectric permittivity [155–162]. Examples of planar photonic devices that make use of this principle abound (Fig. 6), ranging from standard plasmonic nanoantenna [163, 164], to exotic Fano resonant asymmetric structures  and even various biosensors . The key principle underlying the performance is the mode overlap and the interaction volume of the graphene monolayer with the resonantly enhanced electromagnetic fields: for waveguide-like structures where the fields are concentrated in very small gaps for extended distances (30 nm and approximately 500 nm respectively), a tuning range of 20% of the central resonant frequency can be achieved  (Fig. 6).
Thus far the physical mechanisms involved in the active control of metasurfaces are similar to the charge injection or phase change materials. Graphene truly comes into its own when we consider it to be the active photonic element, since it is capable of supporting plasmonic resonances at mid-infrared frequencies and beyond with relatively high quality factors comparable to noble metals [157, 167, 168] (with variations dependent on doping, see curves denoted by Gr on Fig. 2). Graphene plasmons possess an extremely small mode volume, and consequently exhibit very high field confinement and light matter interaction strengths [168–173]. Intuitively the mode volume of localized plasmonic resonances scales proportionally to the particle size; as a result, graphene represents the ultimate limit in scaling, and patterned graphene structures are in many ways the ideal planar metasurface; e.g. in terms of transverse spatial localization, overall device footprint and field enhancement strengths. These structures, ranging from nanorods, to disks and inverse hole arrays [157, 170, 174] (Fig. 6) have been shown to exhibit resonances that are in some cases tunable by several times of their FWHM, enabling broadband functional behavior, which is in turn made possible because of the linear band-structure around their Dirac point.
Moreover, it ought to be emphasized these aforementioned properties are general features of two-dimensional electron gas (2DEG) systems, of which graphene is the most well-known example due to the relative ease of isolation and room temperature operation. Detailed studies into alternative plasmonic 2DEG systems, such as GaAs/AlGaAs at cryogenic temperatures indicate that their properties are robust to standard industrial fabrication processes . As a result the entire spectrum of optoelectronic components, ranging from gated plasmonic circuits operating at GHz frequencies to optical band filters, interferometers, and negative-index screens in the optical regime can be realized [175, 176]. Similar to their graphene counterparts, the intrinsic low dimensionality of such devices enables them to possess unprecedented miniaturization. Examples of such components are illustrated in Figure 7. As such the complete manipulation of amplitude, phase and polarization of electromagnetic waves and their associated charge carriers is shown to be possible at a truly planar level at a wide range of operating frequencies.
5 Broadband and achromatic operation
Beyond active tunability of devices, the bandwidth of operation is also a key figure of merit in many applications. Numerous examples of broadband anomalous behavior  based on metasurfaces have already been reported. For example, a tunable metasurface comprised of graphene nanostructures is termed broadband because the resonances can be dynamically varied over a range equivalent to several FWHM [170, 178]. Similar examples abound, e.g. 80% efficiency reflect-metasurface which has high transmission over an approximate 300–500 nm range in the visible – near infrared regime . Alternatively, one can make use of deeply subwavelength nanostructures which interact with broadband white light to achieve high fidelity colors at various design wavelengths for applications ranging from imaging to printing [179–181].
We highlight here an additional subtlety: broadband does not equate to achromaticity. A standard example is that of a metasurface lens: it cannot be truly broadband if its functionality (e.g. 2π phase accumulation) is inherently monochromatic. In other words, the spatial phase profile, which is key to focusing light, is still dispersive, even though the lens might possess high efficiency values across a wide range of wavelengths (i.e. suffer from chromatic aberration). An ideal “broadband” metasurface lens should retain an achromatic phase response for different wavelengths within its operating bandwidth. Clearly this is a significant challenge that fundamentally departs from the design philosophy and methodology of the vast majority of current devices.
It was recently demonstrated [182, 183] (Fig. 8) that such achromatic devices, where the spatial phase profiles are constant at various wavelengths, are indeed possible with only a single interface by designing the overall phase response to take into account both the dispersive phase accumulation in free space for several different wavelengths and the intrinsic metasurface phase response. In other words, the general design principle takes the form φp + φm = φtot = constant, where φp,m refer to phase accumulation from free space propagation and metasurface respectively. This in turn implies that where l (r) is the physical distance between the interface at some position r, and contains information corresponding to the device function. By introducing multiple coupled resonators , one can in principle obtain sufficient degrees of freedom to design the desired phase mask for an arbitrary number of discrete wavelengths. This approach is completely generalizable to almost arbitrary wavelengths, and is limited only by intrinsic material properties such as absorption losses; most importantly this design strategy retains the single-step fabrication of metasurfaces even for complex, multiple wavelength operation.
6 Emerging Materials
The previous discussions share the underlying theme of how metasurface functionality can be improved, by a combination of appropriate device level design together with judicious choice of materials. At this juncture it is appropriate to highlight some emerging materials which push the limits of the traditional optics paradigm and promise to extend functionalities of metasurfaces into areas previously thought impossible.
One intriguing example is that of electronic topological insulators, a new class of materials which exhibit strong spin-orbit coupling in charge carriers, resulting in an insulating bulk state and conducting surface states that are protected under time-reversal symmetry [185, 186]. In particular, the charge carriers in these surface states exhibit spin-momentum locking (the spin being always directed in the surface plane, but orthogonal to the momentum) which makes it possible to support a new class of collective charge carrier oscillations with welldefined spin states (i.e. spin polarization), known as “spinplasmons” [173, 187–189]. It is instructive to note that by definition of the spin-orbit interaction, these spin excitations are separate from and always transverse to the usual charge oscillations that comprise the plasmon response in the form s⊥ ∝ k × n, which refer to the directions of the spin, plasmon propagation and surface normal vectors respectively. This does not equate to the surface plasmons or charge excitations picking up non-zero angular momentum (optical spin): their excitation and polarization conditions remain the same as with traditional systems, and they therefore retain a helicity of zero. However, due to different screening effects in the host material these charge and spin excitations generally possess different amplitudes and occur at slightly different frequencies. This gives rise to the possibility of observing and manipulating their response via helicity-dependent optical sources, opening up an additional degree of freedom in the study of nanoscale light-matter interactions [190–192]. This is not unlike the rapidly evolving field of spintronics [193, 194], and could serve to further increase the information/bit density for optics-based communication purposes. In addition, due to topologically protected states, plasmon excitations in such systems are immune to non-magnetic scatterers/ defects, and hence possess even greater propagation lengths than their 2DEG counterparts .
Of more immediate interest, the family of bismuth based topological insulator compounds have been studied and shown to possess strong plasmonic responses in the ultra-violet spectrum [195, 196], far beyond the generally expected terahertz regime for such materials . This could potentially bridge a critical gap in the general functionality of nanophotonic devices: most plasmonic materials, ranging from noble metals to transition metal oxides and graphene, have their responses centered in the visible to IR spectral regime (Fig. 2). Interband transitions prevent any plasmonic response in the noble metals at short wavelengths, while plasmonic frequencies in the NIR represent the limit of realistically achievable doping levels in graphene and conducting oxides. Similarly, the requirement of a high refractive index in dielectrics at ultra-violet wavelengths in order to sustain strong electric and magnetic resonances, as well as low losses, imposes strict constraints on the range of available materials. Currently the only semi-viable choice is aluminium, which suffers from persistent native oxidation.
Ref.  (Fig. 9) shows evidence in favour of plasmonic resonances observed in nano-slit patterned Bi1.5Sb0.5Te1.8Se1.2, which is known to be a stable topological insulator at room temperature. The data is found to agree well with a theoretical model of the material as a thin-film Drude metal overlaid on a bulk insulating substrate, analogous to the distribution of charge carrier states in a topological insulator. Similarly, Ref.  presents evidence in favour of plasmonic enhancement of photoluminescence in ZnO structures using a topological insulator flake from the same family (Bi2Te3). These are intriguing results and warrant significantly more research into these materials. Of particular interest is how the native screening of the surface state excitations that usually result in plasmonic resonances occurring in the far-infrared to terahertz regime could lead to responses for the demonstrated structures in the ultraviolet.
Finally, we highlight the concept of artificial engineered materials , which invites a re-think of the entire paradigm of material choice to fit application requirements. Analogous to the concept of modern computing, which can formulate and solve tasks to almost arbitrary complexity despite working with only binary valued bits, it is interesting to consider if one can make redundant the entire previous portion of this article on material properties by considering some fundamental building blocks of materials that, when appropriately combined, could yield any desired, arbitrary permittivity at a specific wavelength. This is frequently introduced as the concept of “digital metamaterials”. We also briefly highlight works that extend the idea of “digital building blocks” to metasurface design, by using only a few different unit cell elements in various sequences to achieve tailored near and far-field radiation patterns.
7 ‘Digital’ Materials Building Blocks
One of the interesting features of the concept of metamaterials and metasurfaces is the possibility to engineer composite materials with desired values for material parameters, such as permittivity and permeability for bulk three-dimensional (3D) volumetric metamaterials, or surface impedance for two-dimensional (2D) cases of metasurfaces. Depending on different scenarios, sometimes one is required to have access to a relatively wide range of values for one or more of these material parameters. For example, if one wants to design a converging lens that is geometrically flat (and thin), the permittivity along the transverse dimensions of the lens needs to be inhomogeneous with higher value in the middle and lower values at points away from the center. It would be hard, if not impossible, to make structures with varying values of permittivity along such structures using different materials (or different doping concentrations in semiconductors). However, another way to achieve such a goal is to exploit the notion of “digital metamaterials” , which is briefly outlined here: First, for the case of binary structures one needs to select two elemental materials, which we can call metamaterial ‘bits’ (Fig. 10a). From the electromagnetic point of view, for such bits one needs to choose two materials whose permittivity functions have oppositely-signed real parts at the operating frequency of interest. Other considerations, e.g., thermal properties, mechanical properties, etc., may be taken into accounts in selecting these two building blocks. Then one needs to combine these two bits, each of which is deeply subwavelength, in order to construct another cell, bigger but still subwavelength, which we can call metamaterial ‘byte’ (Fig. 10b). With a suitable combination, the effective permittivity of the byte as viewed by an outside observer may exhibit values vastly different from the permittivity values of the bits. This is consistent with the notion of ‘internal homogenization’. Intuitively speaking, since the two bits have permittivity values whose real parts have opposite signs, their combination into the form of a ‘byte’ may lead to plasmonic resonance whose polarizability may be higher than that of each bit, and therefore, the effective permittivity of such a byte can be outside the range between the two permittivity values of the original constituents. The reader is referred to Ref.  for more detail. It is interesting to note that analogous to the notion of binary numbers, where the positions of “1’s” and “0’s” may affect the final value of the multibit binary numbers, here also the location of bits within a byte influences the value of the effective permittivity of the byte. This is symbolically shown in Fig. 10b. Consider the subwavelength sized spherical ‘byte’ comprised of 3 layers made of the two bits ∈1 and ∈2 (where Re∈1 and Re∈2have opposite signs). Two examples are shown in the Figure, differing in the locations (i.e., the arrangement order) of the bits in the spherical structure. One is symbolically shown as ‘1 0 1” representing three layers of bits ∈2, ∈1 and ∈2. The other is formed by three layers of ∈1, ∈2 and ∈1 effectively “0 1 0”. The effective polarizability values of such spherical blocks are different when they are illuminated with electromagnetic waves, thus highlighting the analogy with the binary systems and the importance of spatial orders of the elemental material blocks in constructing structures with a range of values of effective permittivity. These bytes themselves can be used as new building blocks to construct larger structures with the desired functionalities such as the one shown in Fig. 10c, showing how alternate layers of collections of such elements can lead to macroscopic layers with alternating effective permittivity values. This method can be exploited to construct a variety of 3D metameterials and 2D metasurfaces using the combinations of only two elemental materials judiciously chosen in the wavelength of interest. It is also worth noting that while here we discuss the case of binary digital metamaterials, in which two materials can be used as the “bits”, the concept can be generalized to ternary or N-ary composites in which 3 or N different materials can be used as the digital building blocks.
A related but conceptually distinct demonstration of tailoring electromagnetic device functionality by the use of binary valued building blocks is shown in Fig. 11 . By using periodic sequences comprised of alternating bytes in arbitrarily sized lattices, e.g. “010101. . . /101010. . . /. . . ”, large scale metasurfaces that alter the directivity of reflection and strongly modify scattering properties can be realized . In the example illustrated in Fig. 11, the constituent bytes are comprised of metallic structures with two different dimensions overlaid on dielectric substrates, to realize a null or π phase response (the “0” and “1” bytes respectively) at the targeted wavelength. Note the subtle distinction between the “digital metamaterial” concept introduced earlier, which centers on the realization of any arbitrary (effective) permittivity through the use of two fixed permittivities (of opposite sign) and these current examples, where different combinations and sequences of two basic metasurface elements are used to generate the farfield response. In this case the phase and amplitude response of each unit cell arises from geometric scales and structural design. This latter concept can be extended to comprise of multi-resonance elements in order to achieve multi-bit coding and to broaden the bandwidth of coding metasurfaces . In addition, the concept of digital metamaterials can be naturally extended to encompass active behaviour, i.e. flipping between individual bytes in response to external stimuli, which paves the way for more complicated operations that are in line with the general, overarching concept of computational metasurfaces.
A key reason for nanotechnology’s prominence in recent research efforts lies in its twin promise of unprecedented device miniaturization, which in turn leads to performance enhancements by virtue of improved spatial resolution, as well as the development of completely new functionalities. The field of optics is a prime example: driven by the ability to create artificial materials with nearly arbitrary optical responses, it has undergone paradigm shifts from traditional ray optics to metadevices, and more recently to planar metasurfaces.With each step, novel functionalities for a wide range of applications have emerged, accounting for phenomena as diverse as cloaking, holographic imaging and even computing. In this article, we have highlighted multiple areas of interest for further research from a materials perspective. Nevertheless it can be argued that in this era of rapid technological advancement and rise of consumer-driven demand, merely being “faster” or “smaller” is not enough. One needs to open up to the possibility of “multi-physics” devices, which integrate multiple diverse functionalities (such as electrical, thermal, and acoustic) on a single platform synergistically. Such devices could redefine the limits of what is possible, and result in the creation of disruptive technologies. On the one hand, the efficient integration of (planar) photonics and electronics could deliver on the long-held vision of vastly improved telecommunications, and even handheld consumer products, beyond the bulk nano-scale optical components and Si interconnects available today. On the other hand, it could also offer a number of new solutions that represent the first step towards conformal and/orwearable photonic gadgets for diverse applications ranging from beam shaping, smart materials, all the way to the implementation of virtual and augmented reality applications.
A.Y.Z., A.I.K. and B.L. have been supported by DSI core funds and A*STAR Science and Engineering Research Council (SERC) Pharos grant #1527300025. A.Y.Z. also acknowledges support under the A*STAR National Science Scholarship (BS-PhD) scheme. N. E. acknowledges partial supports from the US office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) grant number N00014-10-1-0942 and the US Air Force Office of Scientific Research (AFOSR) MURI grant number FA9550-14-1-0389. P. G. gratefully acknowledges financial supports from the European Research Council under grant no. 639109.
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About the article
Published Online: 2016-05-29
Published in Print: 2017-03-01
Citation Information: Nanophotonics, Volume 6, Issue 2, Pages 452–471, ISSN (Online) 2192-8614, ISSN (Print) 2192-8606, DOI: https://doi.org/10.1515/nanoph-2016-0032.
© 2017 Alexander Y. Zhu et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0