Chapter 1: Metasurfaces: Theoretical Basis and Application Overview

Since the disruptive and celebrated work by Veselago (1968) showing the possibility to radically modify the way physics and, in particular, optics were conceived until that time, research has gradually moved toward flatter metamaterial systems commonly identified as metasurfaces. Several drawbacks of so-called bulk metamaterials bring about the attention of scientists to metasurfaces. Indeed, due to the presence of strong subwavelength inclusions, bulk metamaterials are capable of profound control of electromagnetic waves with significant opportunities for novel generation of devices working from the microwave to visible spectrum. However, their use is de facto limited when considered for real applications: bulk metamaterials are difficult to fabricate because they typically include periodic (or aperiodic) 3D arrays made of subwavelength elements, especially hard to realize for visible light applications. Their characteristic thickness is quite large so that their operation inevitably involves wave propagation through long distances with intrinsic and substantial losses. Finally, they are inherently bulky, thus preventing their implementation in applications, such as metalenses, that are typically integrated in ultracompact optical systems. Metasurfaces, instead, have largely demonstrated their ability to reproduce most bulk metamaterials functionalities and many more. As schematically illustrated in Fig. 1.1, the range of operation of metasurfaces is quite vast, enabling a wide scenario of possible uses (Glybovski et al., 2016). In the following, the peculiar physical aspects of these systems will be described which require a novel theoretical approach for a correct interpretation and prediction of their functionalities.

When light interacts with matter, the resulting optical behavior is strongly influenced by the structuring of the boundary between two homogeneous media. When the boundary is flat and smooth, a typical Snell's behavior takes place where part of the impinging radiation is reflected and part of it is refracted in the matter. The angle of reflection is equal to the angle of incidence (θ_i), whereas the angle of refraction (θ_t) is exactly determined by Snell's law:

with n_i and n_t representing the refractive indices of incoming and outcoming media [Fig. 1.2(a)]. The situation immediately changes when a periodic corrugation of the surface is present. In this case, the optical behavior depends on the periodicity (Λ) of the corrugation. If Λ is comparable with the wavelength of the incoming light (Λ ≈ λ), the corrugation behaves like a diffraction grating with the appearance of several orders corresponding to as many directions of light transmitted through the interface into matter (transmitted diffracted orders) or reflected at the interface (reflected diffracted orders). The angles of various diffracted orders are predicted by the so-called grating equation:

where m is an integer number indicating the specific order of diffraction and θ_t identifies the angle that this order makes with the normal to the interface [Fig. 1.2(b)].

When the periodicity of the interface corrugation is much smaller than the incoming wavelength (Λ ≪ λ), i.e. subwavelength, the incoming light does not go through it unaffected as in the case of the flat interface, but it is also not diffracted as in the presence of a grating. The optical behavior requires more attention because it depends on the nature of the elements that compose the corrugation. By considering an array of subwavelength resonators of negligible thickness on the interface, the reflection and transmission coefficients will be dramatically changed because the boundary conditions depend on the resonant excitation of an effective current within the resonators. In particular, reflected and transmitted waves carry a phase change that can vary from −π to π, depending on the wavelength of the incident wave relative to the collective resonance of the resonators. For instance, when the resonators are plasmonic elements, such as gold (Au) nanocylinders, the position of the collective resonance depends on the geometrical parameters, such as the periodicity, height, and radius of the nanocylinders on the surface. Furthermore, it has been demonstrated that this resonance is very sensitive to the angle of light incident on the structured interface and undergoes a sensitive red shift (about 60 nm) with an angle increase of about 60° (Marae-Djouda et al., 2017).

A uniform phase change along the interface leaves the directions of reflection and refraction unaltered. Instead, when the resonators are anisotropic, the polarization state of light may be also affected. When a resonant excitation introduces a discontinuous phase change along the interface, it is possible to design a specific spatial phase variation with subwavelength resolution that effectively controls the direction of wave propagation and the shape of the wavefront. It is at this point that the structuring of the interface defines its peculiar behavior as a metasurface. Indeed, inherited by the meaning of metamaterial, a metasurface is considered as a physical system, with negligible height, whose properties and functionalities do not depend intrinsically on the materials it is constituted of but on the arrangement of its subelements. The quantitative control of the wave propagation direction in the presence of phase discontinuities is obtained by using Fermat's principle. This principle states that, of the infinite paths between two points A and B, light travels on the path that takes the least amount of time (Feynman et al., 1965).

By considering, also in this case, a wave incident on the interface at an angle θ_i and assuming that the two paths between the points A and B are infinitesimally close to the actual light path (Fig. 1.3), then their phase difference is zero:

Φ and Φ + dΦ, respectively, represent the phase discontinuities at the points where the two paths cross the interface, dx is the distance between the crossing points, and k₀ = 2π/λ. If the phase gradient (dΦ) along the interface is designed to be constant, the previous equation leads to a generalized Snell's law of refraction that can be written as follows for light reflected and transmitted, respectively:

These generalized laws reduce to the standard Snell's law when there is no abrupt change of phase along the interface (dΦ/dx = 0). It is noteworthy that these laws imply that transmitted and reflected light beams can be arbitrarily bent in their respective half space, depending on the direction and magnitude of the interfacial phase gradient as well as the refractive indices of the surrounding media (Yu et al., 2011).

A possible way to design a phase gradient to achieve a specific optical behavior is by exploiting the resonator dispersions. In other words, given a fixed electromagnetic wavelength and a variation of resonator geometries or fixing the resonator geometries and varying the excitation wavelengths, a phase variation is obtained of the waves scattered by the resonators. In the case of metallic resonators, impinging light can couple with the resonators through the excitation of surface electromagnetic (EM) waves propagating back and forth along the resonator surface. These surface waves are typically accompanied by charge oscillations and are thus known as surface plasmons. Depending on the size of the resonator, the incident EM wave can be in phase or out of phase with the current excited in the resonator. The condition for the length (L) of the resonator to be resonant with the incident wave is L ≈ λ/2. When L is smaller or larger than λ/2, the current leads or lags the driving field. As such, by properly choosing the length of the given resonator, it is possible to control the phase of the resonator current and thus the phase change of the EM waves created by the oscillating current (i.e., scattered waves from the resonator). The tuning range of this phase is up to π if a single resonator is involved. By coupling several resonators in an array, it is possible to extend this range up to 2π, thus achieving complete control of the wavefront shape.

The excitation of plasmons in metals determines the presence of electric currents accompanied by significant ohmic losses, especially in the optical frequency range. This poses a severe issue to the realization of efficient devices for the large amount of incoming radiation that is simply absorbed by the system.

Besides metallic resonators, wavefront control can also be the result of standing wave patterns in dielectric resonators due to the excitation of Mie resonances. In fact, Mie demonstrated that the scattering behavior of small particles illuminated by light can be modeled by taking into account an infinite series of spherical vector wave functions characterized by electric (a_n) and magnetic (b_n) coefficients. When the incoming wavelength is of the order of the particle diameter, the first resonance arising is a magnetic dipole resonance (Mie, 1908). In high index dielectric resonators, dipolar magnetic resonances are essentially excited by the electric field and not by the magnetic contribution. For dielectric nanoparticles with diameters of 100–200 nm, these resonances occur in the visible spectral range. As pointed out by Evlyukhin et al. (2012) and Kuznetsov et al. (2012), the magnetic activity of dielectric nanoparticles is due to the curl of the displacement current and, unlike in plasmonic materials, is not associated with large nonradiative losses. Moreover, dielectric resonators offer invaluable opportunities for the realization of metasurfaces, allowing full control (2π range) of the phase delay retardation (Yu et al., 2015). As demonstrated by Kerker et al. (1983), a dielectric sphere with equal relative dielectric permittivity and magnetic permeability, ε = µ, exhibits zero backscattering and no depolarization, thus behaving as an ideal “Huygens” secondary source. Indeed, particles with ε = µ show equal a_n and b_n Mie coefficients and, if the particle size is comparable with the light wavelength, the Mie expansion is essentially dominated by dipolar (electric and magnetic) terms. This effect is known as the first Kerker condition. In this case, the first two coefficients (a₁ and b₁) are sufficient to describe the electric and magnetic dipole polarizabilities:

If the oscillation between the electric and magnetic dipoles is in phase (Δϕ = 0), the simultaneous excitation of these dipolar terms can lead to a minimum of the backscattering cross section:

The arrangement of an array of such Huygens sources results in a low-loss metasurface where the single dielectric element, with its specific Δϕ value, can locally control the phase of an incident wave and the amount of front scattered or backscattered light.

In dielectric cylinders, tuning parameters of the scattering could be the height, diameter, or periodicity of the cylinders. By exploiting the Kerker condition, it is then possible to realize a dielectric Huygens metasurface that can achieve the same wavefront control discussed for the plasmonic system but with (a) low absorption losses and (b) a much larger dimension of individual resonators. Indeed, unlike plasmonic arrays that require strongly sub-λ elements to correctly work, Huygens sources require near-λ sizes to be resonant with the incident light. This aspect obviously represents an invaluable advantage for scaling metasurface functionalities in the visible range.

A general approach valid for both plasmonic or dielectric resonant systems to control the direction of wave propagation and shaping the wavefront is theoretically possible by locally varying the state of polarization of incident light. In general, the state of polarization of an EM wave is modified by the presence on its path of a birefringent slab that introduces a phase retardation between the orthogonal electric field components of the incident wave. When the slab is made by an array of anisotropic scatterers that selectively introduce a space-dependent phase retardation, the various portions of the wavefront transmitted by the scatterers will be modified accordingly. A phase element with specific optical functionalities can be thus realized by the appropriate design of an array of subwavelength scatterers with identical geometric parameters but spatially varying orientations (Bomzon et al., 2002). In order to relate the phase retardation to the state of polarization of light while passing through a birefringent scatterer, the most suitable way is using the Jones matrix formalism (Jones, 1941). The Jones matrix of a birefringent scatterer can be written as

where

As in a typical birefringent material (waveplate), ϕ represents the relative phase difference acquired by the electric field components of the EM wave while propagating through the material along the slow and fast axes of the scatterer, whereas its optical axis (fast axis) is oriented at a generic angle θ with the y axis of a Cartesian reference system. The phase retardation ϕ = ϕ(x,y) is spatially variant and depends on the geometry or orientation of the single scatterer. As in Desiatov et al. (2015), the scatterer can be considered as the individual pixel of an array constituting the metasurface. In such a design, the fundamental condition for avoiding diffraction effects that could affect the wavefront shape in an undesired way (e.g., intensity decrease) is that the scatterer size is strongly subwavelength. If the phase retardation ϕ is assumed as a constant for all the scatterers, the only free parameter in the system remains the rotation angle α. Indeed, when considering a right- or left-handed incident polarization with the corresponding Jones vector E_in,R = (1, i)^T and E_in,L = (1, −i)^T, the application of the scatterer matrix (1.7) to E_in,R/L results in the following:

To calculate the previous equations, the expression used,

is obtained by combining (1.8) with (1.7) and using some algebra. Equation (1.9) significantly simplifies their expression when the phase retardation introduced by the scatterer is exactly equal to π:

In this condition, the first term in Eq. (1.11) represents a circularly polarized scattered wave with the same handedness as the incident light that passes through the scatterer without any (amplitude or phase) modification. The second term contains instead a circularly polarized scattered wave with opposite handedness as the incident wave and an additional ±2θ phase term with the sign depending on the incident handedness. This phase modulation is defined as the Pancharatnam–Berry (P–B) phase and can cover the entire 2π range when the angle θ of the birefringent scatterer is rotated from 0° to 180°. The Pancharatnam–Berry phase is also valid for light with linear polarization. The wavefront of a circularly polarized wave passing through the scatterer is then influenced by the P–B phase. In particular, a space-variant polarization state manipulator can be realized by designing an array of scatterers with unit cells consisting of identical scatterers rotated on an incremental angle between adjacent elements up to 180°. Depending on the specific design of the array of scatterers, such a metasurface can reshape the original wavefront, thus realizing specific optical functionalities, e.g., diffractive elements for head-up displays (Zhan et al., 2019), broadband waveplates (Zhao and Alù, 2011; and Yu et al., 2012), aberration-free flat lenses (Aieta et al., 2012a; and Ni et al., 2013), or optical holograms (Chen et al., 2014; and Zheng et al., 2015).

In the last 15 years, remarkable research efforts have been devoted to the experimental development of metasurfaces with diverse functionalities. Recent innovative applications range from efficient solar energy harvesting (Chang et al., 2018), hydrophobicity amplification (Mitridis et al., 2020), water purification (Dongare et al., 2019), acoustic insulation (Zhang et al., 2016), and THz medical imaging (Sun et al., 2017). In several of these applications, the validity of the theoretical background described in the previous paragraphs has been demonstrated and efficiently exploited for the design of the considered metasurface. The experimental demonstration of theoretical predictions becomes more difficult when the considered system operates in the near-infrared and visible electromagnetic range. As detailed in Sec. 1.2.2, plasmonic metasurfaces require compliance with the subwavelength regime, thus implying the realization of sub-λ geometrical details, even two orders of magnitude smaller than the involved free-space wavelength. In this circumstance, the realization of an array of scatterers is only enabled by sophisticated nanoscale fabrication, especially when large area samples are needed. One of the first experimental demonstrations of the generalized laws of refraction was by Yu et al. (2011) in the mid-infrared (MIR) spectral range, later confirmed by Ni et al. (2012) in the near-infrared (NIR). In both cases, V-shaped gold scatterers (Fig. 1.4) were employed. These anisotropic elements support two plasmonic eigenmodes with different resonant properties. The geometry and orientation of the scatterers in the array are chosen in such a way that an x-polarized incident wave [8 µm wavelength; Fig. 1.4(a)], with a wide range of incident angles, creates a y-polarized scattered component that accumulates an incremental phase of π/4 between adjacent V-elements in the unit cell of the metasurface. In particular, the first four V-shaped plasmonic elements produce a controllable phase retardation in cross polarization over the π-phase range. The following four elements in the unit cell are identical to the previous ones, but rotated by π/2 so that they provide an additional π retardation. The array of 4 + 4 elements can therefore cover the entire 2π range. This system then exploits a hybrid P–B and plasmonic resonant tuning over the incoming light to achieve the phase control. The amplitude of the y-polarized component is also tuned to be uniform across the array of scatterers. The metasurface creates anomalously refracted and reflected beams satisfying the generalized laws over a wide wavelength range with negligible spurious beams and optical background, as shown in Fig. 1.4(b). This broadband behavior is related to the broad effective resonance offered by the scatterers, whose scattering efficiency is nearly constant and the phase response approximately linear (Aieta et al., 2012b; and Kats et al., 2012). In Fig. 1.4(c), the case is considered of a metasurface with the same morphology but scaled to work in the NIR. Here also, the angle made by the anomalously reflected beam follows the prediction of the generalized law of refraction (Ni et al., 2012).

In order to bring the wavefront control closer to the visible range, a Pancharatnam–Berry metasurface comprising an array of tiny Au nanorods has been recently realized [Fig. 1.5(a)]. The metasurface is optimized to work in reflection, indicated as a reflectarray, and achieves a high polarization conversion efficiency by exploiting a multilayer design including a ground metal plane (Au), a dielectric (MgF₂) spacer layer, and the Au nanorods top layer (Hao et al., 2007; and Zheng et al., 2015). In particular, a generic half-wave plate fully converts a circularly polarized beam into the oppositely polarized one in transmission when a π phase delay exists between its fast and slow axes. In the case of the metasurface reflectarray, the aim was to achieve high conversion between the incident and the reflected circular polarization states. For realizing this condition, numerical simulations provided the optimal size of the single Au nanorod to obtain a phase difference of π between the reflection with polarization along the long and the short axis of the nanorod antenna. As shown in Fig. 1.5(b), this half-wave plate performs pretty well as a hologram with diffraction efficiencies of 80% at 825 nm and a broad bandwidth between 630 and 1050 nm [Fig. 1.5(c)].

However, the significant efficiency of polarization conversion achieved in this work is a peculiar case, mainly due to the use of a multilayer design. Typically, plasmonic systems suffer from low-coupling efficiency and ohmic losses. For this reason, the recent research trend in metasurfaces is rapidly drifting to the choice of the dielectric counterpart. Indeed, as reported in Sec. 1.2.2, several advantages motivate this choice. In particular, the wavefront control achievable with dielectric matasurfaces is better than for plasmonic ones, and the subelements of the array only require near-λ geometrical details to be resonant with visible light. A brilliant demonstration of the possibilities offered by dielectric systems is provided in the work of Yang et al. (2014). In this paper, a broadband (200 nm bandwidth) dielectric reflectarray was able to convert a linear polarization with more than 98% conversion efficiency operating in the short-wave infrared band (SWIR). As shown in Fig. 1.6(a), the device essentially works as a half-wave plate in reflection with near-unity reflectance. The array is made by structured silicon (Si) cut-wire resonators that exploit Mie resonances to convert the polarization state (linear) of normally incident light [Figs. 1.6(b) and 1.6(c)]. The resonators are placed on a silver layer (150 nm thick) serving as the ground plane mirror and embedded in PMMA (200 nm thick), whereas a quartz wafer caps them from above. The array is tilted 45° with respect to the x-axis of the reference system [see inset in Fig. 1.6(a)] and the electric field of a linearly x- or y-polarized wave incident on it is decomposed into two perpendicular components, u and v, which correspond to the short and long axis of the resonator, respectively. The reflection amplitudes of both of these components are close to unity [Fig. 1.6(d)], whereas their relative phase after reflection is exactly π [Fig. 1.6(e)], so that the incident polarization (linear x or y) undergoes a π/2 rotation upon interacting with the reflectarray. This effect is strongly related to the orientation of the array, chosen aspect ratio, and geometric parameters of the cut-wires resonators that result in constructive and destructive interference of cross- and co-polarized light, respectively (Yang et al., 2014).

In the previous example, the cut-wire resonators were designed to exactly introduce a π relative phase retardation between orthogonal electric field components of the incident light, thus resulting in a cross-polarized reflection with near-unity efficiency. However, in the presence of dielectric elements, there are no particular constraints in the achievable phase retardation. Indeed, a suitable choice of the cut-wire geometry can provide a desired phase shift value in the 0–2π range so that a properly engineered spatially varying phase retardation profile can realize a specific wavefront deformation. The same authors fabricated a second sample with a spiral phase profile ranging from 0 to 2π, with a phase increment of π/4 along the azimuthal direction [Figs. 1.7(a) and 1.7(b)]. The two-dimensional colormaps [Figs. 1.7(d) and 1.7(e)] of the numerically simulated reflectance (|r_cross|²) and phase (φ_cross) of the reflectarray evidence how a variation of the Si cut-wire dimensions can strongly modify its optical response. In particular, it can be observed that there is a region of high reflectance in which four antenna dimensions were chosen [circles in Figs. 1.7(d) and 1.7(e)] to provide an incremental phase shift of π/4 up to π for cross-polarized reflected light. By simply rotating these structures by 90°, the additional π-phase shift can be attained for realizing full 2π coverage while maintaining near-unity efficiency. The cut-wire resonators design is reproduced in the sketch shown in Fig. 1.7(f). This particular phase profile leads to the generation of a Laguerre–Gaussian beam with a theoretical cross-polarized reflectance that is above 94.5% for each section of the reflectarray when probed at the center wavelength of 1550 nm [Fig. 1.7(c)]. The wavefront of the Laguerre–Gaussian beam is helical, showing a phase singularity in the center characterized by an azimuthally dependent phase term, exp(ilφ), where l represents the topological charge, chosen in this case as l = 1, and φ is the azimuthal angle (Yang et al., 2014).

In the quest for realizing dielectric metasurfaces with functionalities in the visible spectral range, noteworthy results have been reported by Capasso et al. Especially interesting are the works involving the design, fabrication, and characterization of metalenses based on transmitarrays of titanium dioxide (TiO₂) nanopillars deposited on glass substrate (Khorasaninejad et al., 2016). To accomplish the focusing functionality, each nanopillar of the array, located at a given (x, y) position, must locally modify a portion of the incident light wavefront by introducing a phase retardation given by

where λ_d is the design wavelength and f is the desired focal length. In this way, the wavefront scattered by the planar lens, based on a metasurface, is given by the envelope of the secondary spherical waves originating from the near-λ scattering elements (Huygens sources) with subwavelength separation. When these scatterers are very dense, the phase profile φ(x, y) can be considered as continuous and, by assuming a hyperboloid shape as in Eq. (1.12), it determines a perfect spherical wavefront molding of the normally incident light. The desired spatially dependent phase profile, and thus the focusing functionality of the metalens, is obtained by mainly varying the diameter of the nanopillar as a function of its position in the array. The height of the nanopillar and pitch of the unit cell are slightly varied to optimize the metalens efficiency at the given λ_d. In Figs. 1.8(a)–1.8(c), SEM micrographs of the fabricated metalens highlight its sophisticated nanoscale morphology. The cross section of the measured focal spot produced by a metalens operating at λ_d = 532 nm is reported in Fig. 1.8(d) together with the corresponding horizontal cut in Fig. 1.8(e). This metalens has a diameter of 300 µm and a focal length of 200 µm, thus giving a numerical aperture NA = 0.6.

An improvement of this concept has been recently implemented by the same group for achieving an achromatic behavior of metalenses (Chen et al., 2018). Also in this case, the utilized metasurface comprises TiO₂ near-λ subelements with a slightly different geometry. As shown in Fig. 1.9(a), the unit cell is now made by two counterposed nanofins of different sizes. These coupled nanofins vary their relative size and orientation throughout the array [Fig. 1.9(b)], thus enabling the engineered transmitarray to focus a broad range of wavelengths at the same distance (63 µm). The realized metalens has a diameter of 220 µm and a NA = 0.02, whereas the focal spot profiles for different wavelengths are shown in Fig. 1.9(c). The imaging ability of the realized metalens has been tested by using a standard United States Air Force resolution target [Fig. 1.9(d)]. By moving toward red wavelengths, a slight decrease of the contrast in the images is observed. This is mainly due to the feature size of the target (∼15 µm) that is close to the diffraction limit of the achromatic metalens; a decrease in efficiency of the metalens at red wavelengths also contributes to the worsening of the image contrast.

A general definition of physics in English identifies a metastructure as a system based upon the combination of several metamaterials. However, without losing ourselves in semantics, we can enrich the meaning of this term by regarding a metastructure as a system that unlocks a wider framework of possibilities through the combination of different metamaterials or metamaterial functions. As shown in the previously reported examples, metasurfaces are revealing more and more novel and exotic properties that intrigue scientists and boost research efforts. However, the aimed-for functionality is very often “one way,” as once designed and successfully realized, the system exclusively performs a specific task in a fixed mode. In the case of achromatic metalenses, for instance, outstanding optical properties are fully renowned, but, how better would a metalens perform if the achromatic focal distance could also be tunable? This unpretentious example unveils the urge to push the field toward the realization of disruptive systems characterized by reprogrammable functionalities and reconfigurable designs. One of the most promising approaches to achieve such active behavior is possibly based on the combination of stimuli-responsive metasurfaces with synergic functionalities resulting in intelligent metastructures.

Throughout the following chapters, various examples of hybrid metastructures will highlight and clarify this novel perspective with case studies very different from one another. Trying to exhaustively categorize all possible metastructure cases in a single sketch is probably unrealistic. However, some of the most representative typologies are suggested in Fig. 1.10. In this context, a metasurface is considered as the most elementary metastructure whose level of “activity” can be upgraded by introducing abilities to respond to external stimuli. In Figs. 1.10(b)–1.10(f), some of the possible stimuli are schematically represented. In these cases, the active functionality is mainly related to a physical property of the involved subelements. A mechanically responsive metastructure has been successfully realized by immobilizing plasmonic nanoparticles on a flexible substrate (Cataldi et al., 2014). On that occasion, the underlying physical property was the plasmonic coupling between metallic nanoparticles that, induced by an external mechanical stress applied to the sample, results in an active shift of the plasmonic response of the system and the tuning of the reflected color. Recently, a metastructure of a pair of metal–insulator–metal (MIM) nano-cut-wires and a pair of insulator–metal–insulator (IMI) nano-cut-wires was presented (Xiong et al., 2021). Plasmon-induced transparency (PIT) is achieved because of the near-field coupling between the dipole supported by the IMI nano-cut-wire and two quadrupoles supported by the MIM structures. Being the metastructure realized on a flexible substrate, the PIT windows can be blue-shifted or even flipped over by stretching the substrate along one direction or be switched off by stretching along the other direction. A remarkable example of optically responsive metastructure has been proposed by Estakhri et al. (2019) with a platform capable of solving integral equations by using monochromatic electromagnetic fields as an input. Electrically responsive intelligent metastructures have been demonstrated by Liu et al. (2019). The system in this case was controlled by a computer that influences the individual electromagnetic properties of each metasurface inclusion. Different concepts for expanding the functionalities of the bare metastructure are shown in Figs. 1.10(g)–1.10(i). A typical way used to enhance metamaterial properties is by exploiting the reconfigurable character of certain materials used as an overlayer for a given metasurface [Fig. 1.10(g)]. Liquid crystals (LCs) are outstanding birefringent materials, easy to process, and intrinsically tunable via application of electric, magnetic, optical, and temperature fields.

Remarkable photonic results have been achieved by using them as surrounding medium for plasmonic subentities (Franklin et al., 2015). Due to their tunability, LCs can be adopted for realizing particularly sophisticated metastructures where the overlayer is also stimuli-responsive. Another interesting metastructure design comprises a functional substrate supporting a meta-array of plasmonic nanoparticles. In this case, an interesting combination of metamaterial effects can be enabled [Fig. 1.10(h)]. In particular, metal–dielectric multilayer structures are renowned for trapping electromagnetic radiation as surface plasmon excitations. Leveraging on the coupling between delocalized and localized surface plasmon modes gives rise to novel metamaterial functionalities that are strongly dependent on the nanoparticle–interface gap (Nicolas et al., 2015). Finally, several micro- and nanostructured overlayers can be considered to realize metastructures with a high degree of complexity [Fig. 1.10(i)]. Such systems are typically fabricated in an additive manufacturing scheme, and the achieved metamaterial functionalities find large application in engineering (Yang et al., 2019), biomedical (Palermo et al., 2020), and counterfeiting technology (Emanuele Lio et al., 2020). The overview of hybrid metastructure configurations highlighted in Fig. 1.10 represents only a premise of the next fundamental and applied research in many fields. Indeed, it is easy to realize that the simple combination of these configurations to realize novel metastructure solutions would result in a number of possibilities whose limit is only the imagination.

In a book dealing with a definite topic like hybrid flatland metastructures, it is fundamental to put each eventual reader with a general knowledge in physics and material science in a position to fully comprehend the content of the following chapters. This is the aim of this first chapter. A gradual description is utilized to bring the reader from the wide framework of metamaterials to the more actual definition of hybrid metastructures. A general introduction briefly explains the need to reduce the typical size of bulk metamaterials to more efficient, virtually 2D systems, indicated as metasurfaces. Besides their negligible thickness, metasurfaces efficiently reproduce most of the metamaterials functions, though introducing much smaller losses and fewer hindrances for eventual applications requiring ultracompact dimensions. Metasurfaces typically comprise subwavelength scatterers for which the classical laws of refraction are not applicable due to discontinuities in the phase introduced in an incoming electromagnetic wave. For this reason, the theoretical approach utilized to predict the behavior of metasurfaces exploits generalized laws of refraction. This approach is valid for both metallic and dielectric metasurfaces. Another convenient and largely utilized theoretical approach useful to model the effect of metasurfaces on the wavefront of an impinging wave is based on the Pancharatnam–Berry phase. This phase value is usually calculated in the presence of systems where the phase is spatially variant and allows designing of beam-shaping meta-arrays that can be operated in transmission (transmitarrays) or reflection (reflectarrays). After having dealt with the physical grounds of metasurfaces, it is appropriate to consider those systems where this theoretical background has been effectively applied. Hence, a series of examples begins detailing several representative applications of metasurfaces. The order of appearance of these examples is mainly chronological and shows how research slowly drifted from plasmonic and strongly sub-λ systems to dielectric and near-λ ones toward implementation in the visible spectral range. The transition to dielectric metasurfaces has invaluable advantages because of low absorption losses and much larger individual resonators, which are easier to fabricate when scaling to visible frequencies. Once some of the outstanding and exotic possibilities offered by metasurfaces have been illustrated, the concept of hybrid metastructure is introduced. Being ideally a system based on the combination of different metamaterials, a metastructure is expected to access a richer scenario of functionalities, including reprogrammable features and reconfigurable geometry. With this motivation in mind, it is not difficult to imagine several basic configurations that open a wide scenario of possibilities for fundamental and applied research in different fields, including engineering, photonic, biomedical, and security applications.