1. Introduction
Art is a creative human activity that encompasses visual arts such as drawing, sculpting, and architecture and other forms such as literature, music, dance, and more. Art has been integral to the emergence and development of human civilization, serving as an essential component of human society. From prehistoric times to the present, people have utilized art to document real life, imagine future possibilities, and express reverence for the unknown forces of nature. Art is a powerful form of expression, embodying human thoughts, creativity, and ideals.
In the material world, the most basic element is the materials that have accompanied the emergence and development of human civilization. From the simple tools used by prehistoric humans to today’s highly developed modern civilization, various historical stages such as the Stone Age, Bronze Age, and Iron Age fully expressed the progress of material technology, while occurring within the confines of the materials existing in nature. At the turn of the century, the emergence of the concept of metamaterials revolutionized human understanding of materials
[1]. Just as art comes from life but goes beyond it, metamaterials are composed of natural materials but can exhibit properties beyond those found in nature. Metamaterials, which are analogous to the art of materials science, are a form of human creativity that breaks through the existing materials ideology and turns fantasies that have only existed in art for tens of thousands of years into reality.
2. Origin
The concept of metamaterials first originated from a thought experiment by the Soviet scientist Victor Veselago, who hypothesized the existence of materials with a negative refractive index
[2]. The refractive index is a basic optical property of materials that is always positive in conventional materials and never negative in naturally occurring materials. Therefore, it was originally impossible to observe and experimentally verify a material of negative refractive index and its related novel physical effects. At the end of the 20th century, the British scientist John B. Pendry proposed the theoretical design of artificial structures: the metal wires
[3] and split rings
[4]—that could respectively realize an effective negative permittivity and negative magnetic permeability. Later on, the American scientist David R. Smith constructed negative refractive index materials by using these two structures as a unit cell, successfully observing negative refraction experimentally for the first time
[5],
[6]. At this point, metamaterials were presented to the public as an art that subverts human cognition.
Metamaterials are artistic—not only because they usually have delicate structures but also because of their unique physical properties that originate from an artificially designed unit cell known as the “meta-atom.” As shown in
Fig. 1, metamaterials’ extraordinary physical properties stem from the intricate structures of the meta-atom rather than the intrinsic properties of their component materials. The realization of the metamaterials is full of design and creativity—the same artistic inspiration that gives humans an almost infinite ability to create ideas that are not found in nature, allowing us to utilize our imaginations to the extreme.
To realize negative refractive index metamaterials, a negative dielectric constant and negative permeability can be obtained by generating certain electromagnetic resonances through the design of artificial structures. This means that many extraordinary electromagnetic properties—such as large positive refractive index values, near-zero refractive index values, and high loss—can be achieved in the same way
[7],
[8],
[9], as shown in
Fig. 2 [6],
[8],
[9],
[10]. Thus, metamaterials with any desirable permittivity, permeability, and refractive index values can be realized with greater freedom than ever before. In addition to such extraordinary properties, the construction of a metamaterial with certain arrangements of meta-atoms may also give rise to new material properties. For example, by modifying the refractive index, in combination with a specific ordering of meta-atoms, it is possible to realize spatial transformations of propagating electromagnetic waves, which has given rise to a new field known as “transformation optics”
[11],
[12],
[13],
[14]. One of the most striking results of this field is the invisibility cloak
[10],
[15],
[16], which turns the idea of invisibility from literature and dramas into a reality.
3. Artistic development of metamaterials
Metamaterials were originally realized in microwave range
[5],
[6],
[10]; this was mostly due to the relatively easier realization in fabrication in that field, since the exotic properties of metamaterials are described by the effective medium theory, which requires the unit cell size to be deep sub-wavelength of the incident wave. Yet the fascinating exotic properties of metamaterials make this concept contagious throughout the entire physics community. Over the subsequent two decades of vigorous development, metamaterials have expanded to many fields, including optics
[17],
[18],
[19],
[20], mechanics
[21],
[22],
[23],
[24], acoustics
[25],
[26],
[27],
[28],
[29], and thermal sciences
[30],
[31],
[32],
[33]. Here, instead of reviewing the history of metamaterials based on conventional timelines or subject areas, we explore the unique artistry of metamaterials from the perspective of new designs and ideas. The key to designing metamaterials lies in understanding what makes them “meta.” In general, they can be thought of as possessing extraordinary properties, property reinforcement, and strong manipulation, among other unique features.
3.1. Extraordinary properties
In this context, “extraordinary properties” refer to special properties that do not exist in natural materials, such as negative refractive index
[5],
[6] and zero refractive index
[7],
[8]. These electromagnetic properties were widely studied in the microwave field initially and then extended to other fields involving wave propagation, such as optics and acoustics. In the field of electromagnetics and optics, negative refraction behavior and the resulting evanescent wave enhancement
[34], along with the reversed Doppler effect
[35],
[36] and anomalous Cherenkov effect
[37],
[38], were hot topics in the early days of metamaterials research. In negative index materials, since the wave vector is reversed, the electric field, magnetic field, and wave vector of the electromagnetic wave obey the left-hand rule. Thus, negative index metamaterials also appeared as “left-handed” metamaterials in the literature
[39],
[40],
[41],
[42]. The reversal of the wave vector causes evanescent waves—which usually experience exponential decay in conventional materials—to experience an exponential increase instead. This phenomenon allows for the creation of a flat lens with super-resolution capabilities: the “superlens”
[34],
[43],
[44],
[45]. Based on a principle similar to the negative refractive index, by selecting an appropriate frequency, a metamaterial with a refractive index close to zero can be obtained
[46],
[47],
[48]. Through careful design while considering the special energy band characteristics of photonic crystals, a zero index can also be achieved
[49],
[50],
[51],
[52]. With a zero index, the wavelength of electromagnetic waves tends to infinity, showing a tunneling-like effect and the ability to shape the wavefront
[53],
[54].
Similar to electromagnetic properties, anomalous mechanical properties can also exhibit negative values, such as a negative Poisson’s ratio
[55],
[56]. This concept was proposed much earlier and can be achieved through artificially purely designed structures, such as concave hexagonal honeycomb structures
[57]; certain natural materials, such as pyrite
[58] and zeolite
[59]; or composite materials, such as polymer foams
[60] and fibers
[61]. The concept of metamaterials combines both structural and material properties but from the materials perspective; thus, abnormal mechanical properties are realized through such structural designs. Negative Poisson’s ratio metamaterials exhibit unique mechanical properties such as high shear resistance
[62],
[63] and impact resistance
[64],
[65], and increased resistance to indentation
[66]. Making use of these unique properties, Ren et al.
[67] carried out a comprehensive study on how to design a high-performance auxetic nail, as shown in
Fig. 3(a). These types of metamaterials are lightweight and can be used for energy dissipation
[68],
[69], vibration isolation
[70],
[71], defense applications
[72],
[73], and structural support
[74],
[75], all of which have promising applications in the aerospace, military, and medical fields. This trend is not limited to Poisson’s ratio but extends to other mechanical properties as well, such as negative stiffness
[76],
[77] and zero stiffness
[78],
[79],
[80], which previously only existed as theoretical concepts but can now be achieved through metamaterials.
The special energy-transfer mechanism of negative stiffness metamaterials can also be used for energy dissipation. By combining this with the bi-stability mechanism, functionalities such as self-locking and reconfiguration can be designed, which are highly desired in soft robotics
[81],
[82]. Since negative stiffness materials can also produce sensations like that of a sudden collapse or a missed step, Zhang et al.
[83] at Westlake University applied this concept to provide multi-sensory feedback in virtual reality (VR) technology, greatly enhancing the immersive experience, as shown in
Fig. 3(b). Zero stiffness materials are mainly used for vibration isolation materials; similar to zero refractive index materials, they represent a theoretical absolute value. Therefore, for a long time, the concept of zero stiffness was viewed as a quasi-zero stiffness that only approached zero stiffness. However, Wu et al.
[84] successfully achieved true zero stiffness for the first time using a constant-force energy-circulation mechanism through capacity cycling. As shown in
Fig. 3(c) [84], metamaterials with absolutely zero stiffness can be used for energy shielding across the entire frequency range, thereby achieving truly perfect vibrational isolation.
3.2. Property reinforcement
The properties that are enhanced through reinforcement in the field of metamaterials are those that exist in natural materials but are insufficiently strong, which greatly limits their applications. The most typical of these is optical anisotropy, which is usually rather weak, given that the differences between the main elements in a dielectric tensor are mostly in the range of 0.01–0.50
[85],
[86],
[87],
[88],
[89],
[90],
[91]. By using metal/dielectric structures, such as multilayered structures
[92],
[93],
[94],
[95],
[96] or metal nanowire arrays
[97],
[98],
[99], permittivities along different orientations can vary greatly, such that the main elements in a dielectric tensor can have opposite signs, resulting in extreme anisotropy. Based on the form of the dielectric tensor in mathematics, which is defined as an indefinite tensor, this type of materials was originally referred to as “indefinite media”
[100]. Later on, they became widely referred to as “hyperbolic metamaterials,” since their isofrequency contour is hyperbolic
[101], as illustrated in
Fig. 4(a) [95]. It should also be noted that hyperbolic anisotropy can occur in magnetic properties, with an indefinite permeability tensor
[102],
[103]. Due to a strong anisotropy (either dielectric or magnetic), an all-angle negative refraction can be obtained regarding the energy flow (the Poynting vector), despite the refractive index (of the wave vector) still being positive.
The most significant effect of hyperbolic anisotropy is the ability to support the propagation of evanescent waves, which decay exponentially in conventional materials yet grow exponentially in left-handed materials, as discussed in Section 3.1
[101]. By combining this phenomenon with the control of the evanescent wave energy flow through strong anisotropy, hyperbolic metamaterials can transform evanescent waves into propagating waves below the diffraction limit, as shown in
Fig. 4(b) [104],
[105]. Therefore, optical lenses made of hyperbolic metamaterials, called “hyperlenses,” can be used to achieve super-resolution in optical microscopy
[96],
[101],
[104],
[106]. Hyperlens super-resolution imaging was first demonstrated by Liu et al.
[104] in the ultraviolet range, where 50 nm feature size patterns were successfully imaged using 365 nm illumination. In 2015, Sun et al.
[106] demonstrated a visible hyperlens with a slinky-like structure, which successfully enabled 80 nm resolution using a 780 nm illumination source. By using an inverse setup, a hyperlens can demagnify optical images to a scale below the diffraction limit, enabling non-diffraction-limited photolithography
[107],
[108]. Based on this theory, Sun and Litchinitser
[105] developed a visible photolithography method, achieving a 80 nm linewidth with h-line (405 nm) technology. Liu et al.
[109] realized a 55 nm linewidth under 365 nm illumination with a hyperlens.
Properties such as chirality, absorbance, and optical nonlinearity can also be greatly enhanced using metamaterials. Chirality is a ubiquitous feature in nature and has extremely important applications in biology, chemistry, optics, medicine, and other fields
[110],
[111],
[112]. Chirality in natural materials usually originates from chiral microstructures, including mirror-asymmetric molecular structures
[113],
[114],
[115],
[116] and crystal structures
[117]. However, because chiral molecules or supramolecular structures are much smaller than optical wavelengths and are randomly oriented, such materials’ overall chirality is weak. As shown in
Fig. 4(c) [118], by artificially constructing chiral structures and arranging them in the same orientation, strong chirality can be obtained by metamaterials in a direct way
[118],
[119],
[120],
[121],
[122],
[123]. Although absorption is a very common material property, 100% perfect absorption is a characteristic that natural materials do not have. As illustrated in
Fig. 4(d), Landy et al.
[124] proposed a scheme for metamaterials with high loss and impedance matching, achieved by designing meta-atoms with equal permittivity and permeability. Such materials can eliminate all incident electromagnetic waves within sub-wavelength distances and simultaneously ensure zero back reflection
[124],
[125],
[126]. This complete absorption of electromagnetic waves is extremely important in stealth technology.
Optical nonlinearity refers to nonlinear polarization behavior in materials under a strong electric field, accompanied by the excitations of high harmonics. Among such effects, due to the coupling between materials polarization and symmetry, even-order nonlinear effects can only be found in materials whose crystal structures lack central symmetries
[127]. Through the design of artificial structures, the magnetic field of the light can be enhanced and coupled with the optical electric field, simultaneously driving the carriers to produce second harmonic generations
[128],
[129], as shown in
Fig. 4(e). This design not only overcomes the limitations of the intrinsic crystal structure of a material but also provides a feasible way to obtain second harmonic generation in specific wavebands, such as the terahertz frequency band, where natural materials hardly show any second-order nonlinearity, since the intrinsic polarization effect of natural materials is rather weak
[130]. In addition to the great enhancements that have been achieved in the abovementioned attributes themselves, knowing how to broaden the working bandwidth of each attribute as much as possible is highly desired
[131]. These enhancements have paved the way for the design of many high-performance devices.
In mechanics, metamaterials with ultra-strong stiffness, ultra-strong toughness, ultra-light mass, and high energy dissipation have been widely studied
[132],
[133]. Titanium alloy metamaterials based on hollow pillar structures can achieve strength close to the Gibson–Ashby upper limit, with densities of only 1–1.8 g∙cm
−3. Combining negative Poisson’s ratio metamaterials with aluminum foam can greatly improve the energy absorption performance of the aluminum foam itself, nearly tripling the specific energy absorption
[134].
3.3. Strong manipulation of physical fields
Metamaterials’ strong control over physical fields originates from the significant influence they have on physical fields, such as the ability to confine the intensity distribution of electromagnetic waves or modulate the phase and polarization of light as it passes through a two-dimensional (2D) structure with an ultra-thin longitudinal scale. In general, there are two primary manifestations of metamaterials’ control: One is their strong control of electromagnetic wave propagation behavior, as shown in
Figs. 5(a)–(e) [135],
[136],
[137],
[138],
[139], and the other is their strong manipulation of the wave vector, polarization state, and phase, as shown in
Figs. 5(f)–(j) [140],
[141],
[142],
[143].
First, let us investigate the method of propagation control. Based on the polaritons generated by the strong interaction between the material interface and electromagnetic waves, the energy of the electromagnetic waves is localized at the interface, with its electric field attenuating exponentially in the direction away from the interface, making light an optical surface wave transmitted along the material interface. Surface plasmon polaritons (SPPs) are a commonly used type of surface wave based on interactions with metal interfaces
[135],
[136],
[144],
[145],
[146],
[147]. As shown in
Fig. 5(b), due to their 2D propagation properties, they can be used in the next generation of integrated photonic circuits with a high level of integration. Metallic nano-structures can also be used as resonators to generate surface plasmon resonance, which can significantly enhance the local field and has important applications in biological and chemical detection, sensors, and so on
[148],
[149],
[150],
[151],
[152],
[153]. In addition, anisotropic material interfaces that meet particular conditions can support the propagation of these surface waves
[154], as shown in
Figs. 5(c)–(e). For example, in the mid-to-far infrared band, hyperbolic polaritons are generated as a result of phonon resonance at the interface of van der Waals materials
[138],
[155],
[156],
[157]. Dyakonov surface waves (DSWs) are also observed at anisotropic crystal interfaces in the visible light band
[137],
[158],
[159]. Compared with the high loss in metals in the visible light band, the DSWs along transparent crystal interfaces can achieve nearly loss-free, highly directional 2D transmission, making them promising for use in 2D photonic circuits
[160],
[161].
Second, let us examine the method by which metasurfaces—that is, the 2D forms of metamaterials—realize the strong manipulation of wave vector, phase, and polarization states
[140],
[142],
[162],
[163],
[164]. Bulky devices based on conventional materials or metamaterials usually rely on geometric shapes to modulate the phase of a light beam or electromagnetic wave. However, fabrication challenges greatly limit the realization of a bulky metamaterial on its way to high frequency, especially in the optical range. Thus, the strong effect achieved by a thin metamaterial is always desirable, which has led to the emergence of metasurfaces. Through strong control of the wave phase by means of a single layer of meta-atoms, metasurfaces can achieve strong phase modulation with a uniform thickness of less than one wavelength, thereby realizing functions such as focusing, beam deflection, and the generation of orbital angular momentum. In 2011, Yu et al.
[140] at Harvard University proposed a concept based on the generalized Snell’s law and demonstrated how a gradient phase distribution of transmitted light could be obtained based on a single-layer metal nano-antenna array (Fig. 5(g)), achieving beam deflection and orbital angular momentum loading. Since then, the concept of metasurfaces has received increasingly widespread attention. Many behaviors related to optical phase modulation—such as lens focusing (
Fig. 5(h)), structured light generation (
Fig. 5(i)), holography (
Fig. 5(j)), and even cloaking—can be realized using metasurfaces
[141],
[143],
[165],
[166],
[167],
[168],
[169],
[170],
[171]. Physical mechanisms that can produce phase modulations, such as a geometric phase based on polarization conversion, a transmission phase based on scattering mechanisms, and the phase change in electromagnetic resonance, are widely used in the design of metasurfaces
[164],
[169],
[170],
[171]. This strong control of phase and polarization can greatly reduce the size of optical devices, making metasurfaces an important approach toward ultra-compact optical systems.
Another strong manipulation ability of metamaterials involves the strong confinement of a field, such as the bound states in the continuum phenomenon. An extremely high-
Q resonant mode can be obtained through metamaterials with specific periodic dielectric constant distribution conditions
[172],
[173],
[174],
[175]. In addition to the aforementioned control of the light field achieved through the metamaterials with specific distribution of refractive index to realize optical invisibility
[176],
[177], many other types of cloaks can be created using similar approaches; examples include the cloaking of acoustic waves to produce sonar invisibility, shown in
Fig. 6(a) [178],
[179],
[180],
[181]; the control of heat flow in efficient thermal management, shown in
Fig. 6(b) [182]; and the cloaking of seismic waves, which can be used to protect civil infrastructures in an earthquake, as shown in
Fig. 6(c) [183],
[184]. All of these examples perfectly illustrate the artistic manipulation of metamaterials.
4. Future trends in metamaterials
4.1. Using metamaterials to boost fundamental sciences
The construction of metamaterials in itself makes metamaterials an important platform in basic research. Phenomena and effects that previously existed only at the theoretical level or could only be observed under extreme experimental conditions can now be experimentally verified by constructing these specific conditions through metamaterials, which can be fully illustrated by the birth of the metamaterials itself. Given the synergy between metamaterials and various other disciplinary fields, metamaterials offer many ways to boost the progress of fundamental sciences, as shown in
Fig. 7 [185],
[186],
[187],
[188],
[189]. This is well presented in the field of optical sciences. In optical quantum science, the photonic spin Hall effect
[186],
[190],
[191],
[192], parity–time (PT) symmetry
[193],
[194],
[195],
[196],
[197], supersymmetry
[198],
[199], electromagnetically induced transparency (EIT)
[200],
[201], and the aforementioned bound states in the continuum
[172],
[173],
[174] can be obtained by constructing specific metamaterials. In topological photonics, metamaterials can be used to construct structures with specific topological photonic states. Concepts such as topological insulators
[187],
[202], Weyl crystals
[185],
[203], Moiré patterns
[188], and the polar skyrmions
[204],
[205] in solid-state physics can be transplanted into photonics and realized through metamaterials
[188]. The realization of these new concepts and effects has become one of the most important directions in the development of modern photonics and provides new ideas for the design and development of new devices.
4.2. Increasing intelligence in metamaterials
As early as in 2014, Professor Engheta at the University of Pennsylvania proposed the concept of computational metamaterials that realize computationally streamlined functions such as differentiation, integration, and convolution, as shown in
Fig. 8(a) [206]. In 2019, Engheta’s team started to experimentally implement metamaterials that could carry out calculation-based functions in the microwave band, which can be used to solve the Fredholm integral equation, as shown in
Fig. 8(b) [207]. Recently, this capability was successfully demonstrated in the optical frequency band as well. This design of combining metamaterials and waveguides can easily be integrated with an on-chip design
[208]. There are no intermediate steps, and no storage is required in the calculation process; moreover, it allows for photonic calculations to occur in parallel without any crosstalk. Thanks to these advantages, this design holds great significance in the development of a new generation of photonic chips.
At almost the same time, advances in metasurfaces were moving toward more intelligent design, too. Cui et al. at Southeast University proposed the concept of intelligent metasurfaces in 2014
[209]. Making the meta-atoms of a metasurface programmable enhances the metasurface’s capability for signal processing. Such a design integrates the sending, receiving, and processing of signals, thereby creating a so-called “information metasurface” for system-level applications, as shown in
Fig. 8(c) [210]. Currently, Cui’s team is working on single-antenna super-resolution imaging based on digital metamaterials, gigahertz-frame-rate programmable holographic imaging, and large-scale electromagnetic data mining
[211],
[212],
[213],
[214],
[215].
With the development of information technology and artificial intelligence (AI), the amount of data has increased sharply, leading to increased requirements for computational efficiency and energy consumption. An integrated storage and computing framework can avoid the cost caused by the transfer of data between storage and calculation components in traditional computing processes, thereby greatly reducing energy consumption and improving computational efficiency. The key device in a computer that integrates storage and calculations is a component that combines memory and processing functions. In an electronic computer, this is a memristor
[216],
[217],
[218]. The realization of such a component with memory functions through metamaterials is not limited to the memory of electrical signals but can also be extended to optical memory functionalities that directly participate in the calculation process
[219]. This is another important direction for the development of metamaterials.
Not only are electromagnetic/optical metamaterials being intelligentized, but mechanical metamaterials are also on the way. The approaches used to design programmable mechanical metamaterials can be quite artistic, such as the use of the traditional art of origami and kirigami to build exquisite architectures with paper.
Fig. 9 [220],
[221],
[222],
[223],
[224],
[225],
[226],
[227],
[228],
[229],
[230],
[231] illustrates the logic of the origami and kirigami used in metamaterials design. The paper is 2D, while the final architecture is three-dimensional (3D)—a transformation that is achieved by merely folding or cutting the paper. Moreover, through different ways of folding or cutting, miscellaneous 3D structures can be built from the same piece of paper. All these 3D structures are reversible, as they can be transformed back to the 2D form of the original paper. Such practices provide a valuable guideline for building 3D metamaterials that exhibit unique and programmable mechanical properties, such as shape morphing
[232], flexibility
[233], a tunable Poisson’s ratio
[229], tunable stiffness
[234], and multistability
[230].
When designing mechanical metamaterials through origami/kirigami, the starting material does not have to be paper; metals
[220],
[235],
[236], polymers
[237], hydrogels
[225],
[238], graphene
[226], and DNA
[222],
[223],
[224] have also been used, ranging from the macroscale to the microscale
[239] or even the nanoscale
[236]. The special properties of mechanical metamaterials grant them the capabilities of energy harvesting, sensing, actuation, self-adaptation, and even calculation and information processing, making them applicable in many fields, such as intelligent materials
[240],
[241],
[242],
[243], flexible electronics
[244],
[245],
[246],
[247], medical devices
[248], and robotics
[234],
[249],
[250],
[251],
[252],
[253].
Regarding intelligence in metamaterials, the compliant mechanisms of origami/kirigami greatly enhance metamaterials’ programmability and reconfigurability and are thus widely used in realizing computational functionalities mechanically
[254]. Ranging from logic gates—the most fundamental element (e.g., AND, OR, NOT)
[255]—and functional elements such as actuators
[256] to memories
[257], almost all types of components found in a conventional electronic computer can be realized through origami/kirigami metamaterials. These mechanical computers not only diversify how computation is performed but are also very helpful in carrying out the computations in severe environments, like cold weather, high radiation, or a lack of electrical power.
4.3. Artificial intelligence
AI, machine learning, and materials genome engineering have received widespread attention in traditional materials research. Through machine learning and big data analysis, materials design and performance development can be well guided from the microscopic composition level. Similarly, AI is becoming an important tool in metamaterials design. Traditional metamaterials design usually starts from theoretical physics research. After that, specific performance characteristics can be optimized through numerical simulation of the structural and geometric parameters of the meta-atoms. The main challenge in this design method lies in creating new metamaterial configurations based on physical mechanisms, which can be thought of as similar to a creation by a famous artist. Continuing with this analogy, most people are only able to follow and copy famous works. Similarly, most classic metamaterials—such as split-ring resonators (SRRs)
[5],
[6],
[9],
[10], cut-wires
[18], fishnet structures
[18],
[19], multilayer film structures
[92],
[95], and high-permittivity Mie scattering particles
[171]—were proposed by a few pioneer scientists in the early stages of the development of metamaterials. Most subsequent metamaterials have been developed based on these designs while being modified to meet various requirements. Taking certain structures as a starting point, enhanced performance can be obtained through optimization via numerical simulations; these are usually performed by parameter scanning and may consume a large amount of computational resources and time. As early as in 2011, Freitas et al.
[258] proposed a machine learning method that can accurately predict the dispersion behavior of a classic configuration of left-handed materials (SRR + metal wire) by means of a trained artificial neural network (ANN), for use in achieving structural optimizations of metamaterial primitives. For metamaterials or metasurfaces with relatively simple configurations and single functions, the advantages of machine learning tools are not yet obvious. Under normal circumstances, the functionality of metamaterials/metasurfaces is positively related to their complexity. For those metamaterials/metasurfaces containing a large number of meta-atoms with different shapes, the optimization efficiency is extremely low using the optimization method of trial and error, requiring a huge number of numerical simulations. This can be well explained in the design of achromatic metasurface lenses, as shown in
Fig. 10 [259]. The size of the meta-atoms in a metalens is generally at the scale of 1/10 of the working wavelength (
λ), and the overall size of a metalens is 40
λ–50
λ. According to its inherent symmetry, a metasurface lens may consist of about 20 configurations of meta-atoms and around 20 000 meta-atoms in total
[259]. If the configuration is known, the light-modulation capability (the Fresnel transmission coefficient in physics) of this configuration can be obtained by running these numerical simulations, where the determination from configuration to light-modulation functionality is a one-to-one relationship. In a metalens design, the desired phase and group delay are first calculated from achromatic focusing. There is no direct way to determine the configuration of the meta-atoms from the required phase and group delay. To solve this problem, one feasible way is to establish a data library of meta-atoms with as many configurations as possible, to aid in discovering desired effects through massive numerical simulations, such that meta-atoms with the required performance characteristics can be chosen from this library to construct an achromatic lens
[258],
[259],
[141],
[260],
[261],
[262],
[263],
[264].
Establishing a data library through numerical simulations consumes an unrealistic amount of computing power and time. If the accurate phase control capability obtained through numerical simulations of small-scale configurations is used as a training database to train machine learning tools, the trained machine learning tools can then generate a massive database in a very short time for use in metasurface design
[265],
[266],
[267],
[268]. As shown in
Fig. 11(a) [269], this method is known as forward design and is usually implemented via deep learning; it is widely used in the design of various optical devices, including metamaterials. Wang et al.
[268] carried out a study on the whole process of the design, fabrication, and characterization of a visible-light achromatic metalens based on machine learning. In their work, the time consumption at each step in the theoretical design (i.e., the establishment of the training database, training of machine learning tools, generation of a performance database, and configuration searching) was carefully analyzed, fully demonstrating the important role of machine learning tools in accelerating the design of metasurfaces. Their results showed that the fabricated metalens designed via machine learning had excellent achromatic performance, competitive with those of human-designed metalenses, as well as a configuration that is easier in nanofabrication.
In forward design, machine learning tools utilize highly efficient predictions to accelerate performance optimization; in inverse design, while machine learning tools based on the inverse design become the designer of the metamaterials, as shown in
Fig. 11(b) [269]. The pixelated configuration of meta-atoms can easily be digitally generated into patterns. A well-trained machine learning tool can theoretically predict the performance of all possible configurations by testing different pixel compositions, thereby establishing a data library for metasurface design
[269],
[270],
[271],
[272],
[273],
[274],
[275],
[276]. During this process, fabrication limits can also be considered, so that configurations that are too complex and difficult to fabricate can be removed to make the metasurface design more practical.
Thus far, numerical simulations are still required to establish a training database in both forward and inverse design, which still requires numerical simulations. Although the amount of calculation for a training database is affordable, it is the most time-consuming part of the design process
[269]. Further combining data-driven and physical models, instead of completely relying on the black box of data training, is a very promising method to overcome this bottleneck.
Aside from the widely used machine learning tools mentioned above, large language models (LLMs), which are primarily designed for natural language processing, have recently appeared in metamaterials design
[277]. LLMs are usually deep-learning-based models based on transformer architectures, such as generative pre-trained transformers (GPTs)
[278] and bidirectional encoder representations from transformer (BERTs)
[279]; they are trained on vast amounts of data and are thus capable of processing, generating, and understanding human language. For example, ChatGPT is now being used by the general public for tasks such as generating AI art. It is very likely that LLMs can greatly assist the development of metamaterials thanks to their powerful generative designs and properties predictions; they may also enable the further development of intelligent metamaterials/metasurfaces, as discussed in Section 4.2. This trend has recently been emerging in academic conferences (e.g., Society of Photo-Optical Instrumentation Engineers (SPIE) 2024 conference in San Diego)
[280],
[281].
4.4. Multi-property coupling and decoupling
The intersection of multiple fields in physics plays an important role in materials science. In conventional materials, properties such as mechanics, heat, light, electricity, and magnetism are coupled with each other, resulting in extremely important physical effects, including (inverse) piezoelectricity, thermoelectricity, and pyroelectricity; the electro-optic effect, magneto-optic effect, and photoelectric effect; electromagnetic induction (Faraday); and the Hall effect, among others. These effects cover almost all areas of modern science and technology. That said, due to the inherent limitations of natural materials, many expected properties are still being studied. For example, the working principle of light detection is based on the photoelectric effect caused by the particle nature of light. When materials’ band gaps are smaller than the incident photon energy, an electric signal can be generated through photocarriers, allowing the incident light to be detected. However, for long-wavelength bands, from mid- to far-infrared and even up to the terahertz range, the wave nature of light is stronger (where the photon energy is very tiny). With regards to materials, the band gap of semiconductor materials is very narrow; thus, the photoelectric effect is mostly hidden by the intrinsic carrier excitation of the material at room temperature. Therefore, despite its extremely fast response speed, detection technology based on semiconductor materials in the mid- and far-infrared bands (e.g., mercury cadmium telluride) can only work at low temperatures through a cooling system in order to suppress the noise caused by intrinsic thermal excitation
[282]. To solve this problem, Wen and Zhou
[283] proposed a completely new way of obtaining electric signals from the electric field in a light beam, resulting in an ultra-fast response in photoelectric detection without any cooling. This approach holds promise in the field of mid-infrared imaging and detection.
The decoupling of properties also holds great significance in materials design. The properties of a material originate from its microscopic composition and structure. Therefore, when a material exhibits one desired property due to its specific composition or structure, it can lead to limitations in other aspects. If the desired property can provide excellent performance in a certain device, while its other properties do not impede the device’s functionality, the performance of the device can be further improved by enhancing that property. In many cases, however, a dilemma occurs in which the material has a desired property that is inextricably coupled with an undesirable shortcoming. For example, a material with a high stiffness usually has limited ductility. As another example, an electric conductor is an excellent thermal conductor, but this property may seriously limit its efficiency in a thermoelectric device
[284],
[285],
[286],
[287],
[288]. If the two correlated (or even conflicting) properties are first decoupled—meaning that they are obtained independently through different meta-atom designs—and then re-coupled by combining the two meta-atoms together, a material with the required composite properties can be constructed artificially. This is analogous to a famous painting originally created by a master through professional control over the colors: Once the colors are discretized and pixelated, even a beginner can create a copy of the painting by filling in the right colors.
The design of left-handed materials is realized by combining structures with a negative dielectric constant and a negative magnetic permeability together to obtain a negative refractive index
[6]. The invisibility cloak mentioned earlier is constructed from meta-atoms with certain refractive indices as pixels, which enables transformation optics through the spatial arrangement of each meta-atom
[10]. The decoupling of material properties is very likely to realize the digitization and pixelation of material properties, making materials design similar to using a Lego set, as shown in
Fig. 12. This approach holds great promise for true on-demand customization and the ultimate development of an “omnipotent” material.
4.5. Engineering
With more than two decades of development, metamaterials are gradually moving from the realm of fundamental research to that of engineering. In this process, the advantage of metamaterials lies in their ability to “create” materials based on needs, making it possible to avoid the struggle of “discovering” materials based on needs, as in the traditional technological framework. When looking for materials for a specific purpose, we are always facing the challenges that suitable natural materials may not exist, or the material’s properties may not be good enough. In contrast, metamaterials can be customized to meet specific needs in order to solve critical challenges in engineering
[288]. Therefore, knowing how to transform the extraordinary properties of metamaterials into excellent device performance is a key step. A metamaterial created in the laboratory is similar to a work of art, with exquisite structures and extraordinary properties. The question of how to turn such an “artwork” into a “craft” suitable for mass production is the main obstacle hindering the widescale use of metamaterial-based devices in industry. The preparation of metamaterials—ranging from mechanical manufacturing and circuit printing to fine nanofabrication processing—requires a great deal of technological prowess and advanced skills. Although the properties of many different metamaterials have been fully demonstrated in laboratories, achieving the low-cost mass production of these materials has always been a barrier to their industrialization.
In the field of electromagnetic/optical metamaterials, the meta-atom size of a metamaterial is proportional to the working wavelength. Therefore, microwave, radio frequency, and longer band metamaterials can be realized through traditional processing techniques, and industrialization is developing rapidly in this area. One of the most well-developed applications is the electromagnetic antenna based on metamaterials. In 2017, the American company Kymeta Corporation launched a satellite antenna product. As shown in
Fig. 13(a) [289], the Kymeta u7 terminal, which operates in the Ku band, efficiently enables high-throughput communication between satellites and mobile platforms such as vehicles, ships, and aircrafts. Another successful metamaterial-based product is the radiofrequency (RF) coil, which is the essential component of enhancing magnetic resonance imaging (MRI) image in terms of the signal uniformity, signal-to-noise ratio, and image resolution. A cylindrical metasurface-based RF coil developed by the start-up TsingMeta, Ltd., incubated by Zhao’s research team at Tsinghua University
[290], can significantly enhance the RF magnetic field in commercial MRI equipment. In the clinical validation, a 1.5 T MRI with the metasurface coil can greatly improve the image, comparable to that supplied by a 3 T MRI. The device is wireless and passive, and do not need to establish a protocol interface with the commercial MRI. Besides of the use in a hospital, the products are also widely used in animal experiments, in order to fulfill the requirement of the strong magnetic field, aiming at 9.4 T or even higher, which is not available to the animal experiment yet, as shown in
Fig. 13(b) [291].
With advancements in communication technologies, the increase in operational frequency bands used in communication-system devices is resulting in a decrease in the polarization of materials, making it difficult to provide high-performance transmission, isolation, and reception of signals. At the same time, it is necessary to ensure the miniaturization and lightweight nature of these devices. These demands have prompted the industry to focus on metamaterials, with the aim of solving these problems through structural design.
Challenges in optical metamaterials mainly come from processing costs and inefficiencies in production. Metamaterials in research laboratories are mostly prepared through fine nanofabrication methods, such as electron beam lithography or ion beam etching. This type of processing method has extremely high precision but comes with a high cost
[18],
[19],
[141],
[143],
[165],
[166],
[167],
[168],
[169],
[170],
[259],
[260],
[261],
[263],
[264]. Furthermore, the low output and yield of such methods make mass production difficult to realize. At present, many universities and companies engaged in optical metamaterial research are trying to achieve mass production based on prototypes in laboratories by merging them with current existing semiconductor manufacturing processes. That said, even if high-end micro-/nano-processing technology is used, the limit of the feature size that can be obtained is on the scale of tens of nanometers. For visible light, such a feature size will still cause strong scattering losses, resulting in deterioration of the device performance.
Although mechanical metamaterials are large in scale, they typically include complex structures and rely on additive manufacturing for mold-less production, primarily through the use of 3D printing. The production of resin-based materials via 3D printing is relatively mature, but selective melting technologies for metals do not yet meet the requirements for mechanical metamaterial preparation. In addition, the low yield rate of 3D printing is a major bottleneck in the industrialization of mechanical metamaterials.
5. Conclusion and outlook
Metamaterials are artificial materials that can be designed and customized by humans but are also a new way for humans to understand nature at a high level. In the past, people were limited to the materials found in nature. When natural materials cannot satisfy human needs, it is necessary to break through the old ideological framework of searching and improving natural materials and move toward creating metamaterials through intelligent design. The ideal goal of metamaterials is to make huge progress in methodology, enabling materials science to greatly expand its borders.
Metamaterials design is a very creative study. Researchers can use their imagination and creativity to overcome challenges in realizing applications and achieving technological progress. At the same time, they can engage in scientific exploration and transform theoretical ideas, phenomena, and laws into tangible materials that allow people to gain a more direct understanding and perception, promoting progress in materials science.
In industry, metamaterials can bring advancements in technology and thereby lead to huge economic growth. With the entry of metamaterial products on the market, metamaterials are creating huge economic value. In 2023, the global metamaterials market size reached 1.4 billion USD; by 2030, this market size is expected to exceed 3.5 billion USD, with an expected compound annual growth rate reaching 57%
[292].
Metamaterials are changing human life: As an advanced science and technology, they improve people’s quality of life by promoting technological progress, including more convenient communication, medical advancements, increased traffic safety, and more. Metamaterials will eventually be fully integrated into human society to serve humanity.
Acknowledgments
This work was supported by the National Key Research and Development Program of China (2022YFB3806000) and the Key Program of National Natural Science Foundation of China (52332006).
We thank Mr. Youcheng Xu’s effort in formatting the references and Mr. Maxwell Wallace’s help with the language polishing.
Compliance with ethics guidelines
Jingbo Sun and Ji Zhou declare that they have no conflict of interest or financial conflicts to disclose.
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