Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Joonkyo Jung; Hyeonjin Park; Junhyung Park; Taeyong Chang; Jonghwa Shin

doi:10.1515/nanoph-2020-0111

Open Access Published by De Gruyter June 25, 2020

Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Joonkyo Jung , Hyeonjin Park , Junhyung Park , Taeyong Chang and Jonghwa Shin

From the journal Nanophotonics

https://doi.org/10.1515/nanoph-2020-0111

Abstract

Metamaterials can possess extraordinary properties not readily available in nature. While most of the early metamaterials had narrow frequency bandwidth of operation, many recent works have focused on how to implement exotic properties and functions over broad bandwidth for practical applications. Here, we provide two definitions of broadband operation in terms of effective material properties and device functionality, suitable for describing materials and devices, respectively, and overview existing broadband metamaterial designs in such two categories. Broadband metamaterials with nearly constant effective material properties are discussed in the materials part, and broadband absorbers, lens, and hologram devices based on metamaterials and metasurfaces are discussed in the devices part.

Keywords: broadband; broadband absorber; broadband metalens; constitutive parameter; metamaterial; metamaterial-based device

1 Introduction

Metamaterials are composite media with subwavelength-scale repetitive features (motifs) whose interaction with waves can be described by a set of homogenized material parameters. What differentiates metamaterials from ordinary composite media is that, with a careful design of motifs and their arrangement, new and tailored resonances are introduced to the system and the effective material properties such as electric permittivity and magnetic permeability can become extraordinary, attaining values that are very different from those of the constituent materials or any other material readily available in nature.

The suitability of a homogeneous effective medium description of metamaterials provides important benefits for metamaterial-related research and development. First, this homogenization allows simplification: macroscopic behaviors of metamaterials can be adequately described by just a few homogenized material properties, which can greatly simplify device design processes and can lessen the computational burden by several orders of magnitude because one does not have to solve Maxwell’s equations at the microscopic level repeatedly whenever the device configuration is changed. Second, the homogenization facilitates general applications: a developed metamaterial showing specific constitutive parameters can serve as a building block for a diverse range of applications. Split ring resonator metamaterials with controlled effective permeability [1], [2], [3], [4] and small-gap metamaterial with broadband high effective permittivity [5], [6], [7] are such examples. In this light, numerous studies (referred to as material-focused metamaterial research hereinafter) have concentrated on achieving extraordinary constitutive parameters themselves with metamaterials, often without presenting the explicit design of the actual devices using those metamaterials.

Most of the early metamaterials had very dispersive homogenized constitutive parameters that vary considerably as the frequency of the electromagnetic wave is changed around the target frequency. There were two main reasons for the strong dispersion. In some designs, the dispersion was a direct consequence of the dispersion of the constituent materials such as metals. More often, the dispersion originated from the principle of metamaterial itself, i.e., the introduction of new resonances to obtain exotic constitutive parameters. While the incorporation of tailored new resonances allowed easy access to much-expanded parameter space, the resulting strong dispersion and associated absorption loss were often very conspicuous [8], [9]. Although the dispersion and absorption may be tolerated or even desired in some applications, many other conventional optical systems such as refractive lenses call for transparent materials with low dispersions, presenting difficult challenges for metamaterials as a versatile building block. Thus, in material-focused broadband studies, considerable efforts have been focused on how to obtain homogenized constitutive parameters that are exotic but still nearly constant over a broad frequency range.

On the other hand, increasingly more research effort has been focusing on realizations of actual optical systems and devices with specific functionality based on metamaterials. In designing optical systems such as light absorbers, beam deflectors, and holograms, the main task is to optimize the choice of (meta-)materials and their spatial configurations for best device performance. To quantify the performance, one can define a set of numerical measures such as spectral absorptance, numerical aperture (NA), conversion efficiency, etc., which are of course dependent on the intended usage and functionality of the device, from perfect absorbers [10] to achromatic diffractive lenses for color imaging [11]. In some of the applications, broadband constitutive parameters at the level of the materials do not automatically result in broadband device performance as the spatial configurations can induce additional frequency dependence. Fluctuations of the transmission amplitude and phase as a function of frequency, also known as Fabry–Perot resonances, of a cavity filled with a non-dispersive, transparent medium is a classic example. For broadband functionality, in general, metamaterials should have a tailored frequency dispersion, specific to the target application and the actual device configuration, among which the zero-dispersion is the most important example but is not the only one.

In this review, we discuss metamaterials aimed for broadband operation in two sections targeting material-focused and device-focused works, respectively. We devote the first section to reviewing the specific strategies used to implement broadband effective medium parameters, namely, electric permittivity, magnetic permeability, and chirality parameter, and relevant examples. In the second section, we first clarify the definition of broad bandwidth at the device level and then discuss the strategies and examples used to achieve such broadband characteristics in three major applications: light absorbers, lenses, and holograms.

2 Nearly constant constitutive parameters over broad bandwidths

Quantitative modelling of electromagnetic materials with homogenized constitutive parameters allows understanding electromagnetic phenomena in a simple and intuitive way. Despite the complexity of materials at an atomic scale, the homogenized effective medium model can explain the interaction between waves and natural substances with good accuracy if the inhomogeneity of the material is at a much smaller length-scale than the scale of interest [12]. Composite media such as metamaterials can also be treated as homogeneous effective media if a second homogenization is conducted at the subwavelength-sized unit cell scale, in addition to the atomic-scale homogenization. More complex electromagnetic responses from the much larger unit cell structures, such as strong non-locality, make the second homogenization process not so trivial, but it is this very aspect that makes metamaterials more interesting [13], [14], [15], [16], [17]. In this section, we focus on one of the most commonly used constitutive relations for bulk metamaterials [18] as shown in Eq. (1), among several alternatives, and review its constitutive parameters.

(1A)D=ε0εE+(χ+iκ)μ0ε0H

(1B)B=(χ−iκ)μ0ε0E+μ0μH.

In Eq. (1), constitutive parameters, ε, μ, κ, and χ are relative permittivity, relative permeability, chirality parameter, and Tellegen parameter, respectively (we omit the term ‘relative’ for simplicity, hereafter) while ε₀ and μ₀ are the vacuum permittivity and permeability, respectively. We focus our discussion on the first three parameters because, while Tellegen media are being actively researched [18], [19], [20], there have been only few experimental realizations in the field [21].

In Eq. (2) and Figure 1, we show simple Lorentz models of effective constitutive parameters in order to review their dispersion characteristic,

(2A)ε(ω)=εb+pεω02ω02−ω2−iγω,

(2B)μ(ω)=μb+pμω2ω02−ω2−iγω,

(2C)κ(ω)=pκω0ωω02−ω2−iγω,

where ω₀, γ, and p_a (a ∈ {ε, μ, κ}) are the resonance frequency, damping factor, and oscillator strengths of a Lorentzian resonance introduced by the metamaterial, respectively [22]. Here, we assume that there is one prominent resonance near the frequency of interest and all other resonances are sufficiently far away in frequency such that their effect on permittivity and permeability are captured by dispersion-less background contributions. Resonances at far frequencies give minimal effect on the chirality parameter near the frequency of interest. These background values from the resonances at far away in frequencies are determined based on the asymptotic behaviors of resonances of each constitutive parameter, which will be discussed soon. Note that p_a can differ substantially from one another while ω₀ and γ are the same in Eqs. (2A–C). For example, a purely electric resonance would have non-zero p_ε and zero p_μ and p_κ. In general, for bi-anisotropic metamaterials, the constitutive parameters in Eq. (2) becomes tensors, of which each component may have different p_a.

Figure 1:

Lorentz oscillator models of effective constitutive parameters. (A) Effective electric permittivity, which converges to ε_b + p_ε at very low frequency. By tuning the resonance frequency, effective permittivity can be controlled from highly-negative to highly-positive values (blue, yellow, green curves). Damping factor, γ, is assumed as ω₀/10. Controllability based on adjusting resonance frequency can be applied to magnetic permeability and chirality parameter as well. (B) Effective magnetic permeability, which converges to μ_b − p_μ at high frequency regime. (C) Effective chirality parameter, which linearly increases as frequency increases with the slope of p_κ/ω₀ at low frequency regime.

Figure 1 illustrates that the constitutive parameters can vary widely in magnitude and can also change their signs near the resonance frequency, so one can in principle realize a wide range of constitutive parameters at a target frequency simply by adjusting the physical size of the resonant motif to shift its resonance frequency slightly, without redesigning the resonator from scratch for each desired constitutive parameter value. The achievable range of parameters, from their most negative values to their most positive values, increases as the damping factor decreases if the resonance frequency and oscillator strength are fixed. So, one can try to optimize the resonator design and its materials such that the damping factor, including the radiative loss and the absorptive loss of the resonance mode, diminishes to a very small value in order to obtain the largest possible range of effective parameters. However, this approach has a fundamental trade-off relationship between the range of the attainable parameter values and the frequency bandwidth: as the damping is reduced, the resonance becomes sharper and constitutive parameters become more dispersive, which narrows down its usable frequency bandwidth. Therefore, in order to realize constitutive parameters that are both “exotic” and nearly constant over a broad frequency range, a different approach is required.

The same equation, Eq. (2), which explains the trade-offs near the resonance frequency, provides clues to a broadband tuning of effective parameters as well. At the off-resonance regime, ε, μ, and κ show characteristic asymptotic behaviors. The Lorentz term in the ε expression adds an almost-constant, positive real value in the low frequency regime (ω ≪ ω₀, γ), while that in the μ expression adds a nearly-constant, negative real value between −1 and 0 in the high frequency regime (ω ≫ ω₀, γ). The resonance term in the chirality parameter expression exhibits ω dependence in the low frequency and 1/ω dependence in the high frequency regime. In the following subsections for each constitutive parameter, we will discuss how these characteristic properties are utilized to achieve broadband and exotic electromagnetic properties.

2.1 Electric permittivity

Prior to the study of metamaterials, quasi-static homogenization theories such as Maxwell-Garnett and Bruggeman mixing formula were utilized to investigate homogenized electric permittivity of composite media. These mixing theories provide a straightforward way to achieve broadband effective permittivity. As their mathematical expressions are not explicit functions of frequency, the resulting effective permittivity is also frequency independent as long as each constituent material is in its transparent regime with its own electric permittivity mostly real and constant within the frequency band of interest. The range of attainable quasi-static permittivities of composite media is confined to the enclosed area between linear Wiener bound (LWB) and circular Wiener bound (CWB) in the complex plane [23],

(3A)[∑Nfn/εn]−1(CWB)

(3B)∑Nfnεn(LWB)

where f_n and ε_n are volume fraction and electric permittivity of the nth constituent material. In Figure 2, we show several examples of effective permittivities of the composite medium of two different materials. It can be found that the attainable range of effective permittivity with two different low-loss dielectric material (0 < ε_1,2) is limited to value around ε₁ and ε₂ (Figure 2A). Nevertheless, fine tuning of dispersion-less effective permittivity based on this dielectric-dielectric mixing has been used in the field of transformation optics for applications such as carpet cloak [9], [24], [25] (Figure 3A) or graded refractive index lens [26].

$Figure 2: Wiener bounds of various composite materials. (A) Wiener bounds of a composite of two dielectric materials. Amorphous Al2O3 and crystalline Si near 800 nm wavelength are assumed. Effective permittivity can be realized only within the boundary between Circular Wiener Bound (CWB) and Linear Wiener Bound (LWB) (shaded region). (B) Wiener bounds of a composite material mixture of amorphous Al2O3 and Au at 500 nm (yellow), 520 nm (green), 540 nm (blue) wavelengths. Filled dots and asterisks are algebraic averages and harmonic averages of permittivities of Al2O3 and Au for the same volume ratio, respectively. (C) Wiener bounds of a composite material composed of gold and a model dielectric at 1, 10, 100 GHz frequencies (blue, green, yellow, respectively). For permittivity of a dielectric, 10 + 0.003i is assumed for all frequencies. Asterisks indicate harmonic averages of the conductor and the dielectric when volume fraction of the dielectric is 0.01, respectively. Homogenized permittivity based on the harmonic average (i.e. εeff ≈ 100εd) is nearly dispersion-less.$

Figure 2:

Wiener bounds of various composite materials. (A) Wiener bounds of a composite of two dielectric materials. Amorphous Al₂O₃ and crystalline Si near 800 nm wavelength are assumed. Effective permittivity can be realized only within the boundary between Circular Wiener Bound (CWB) and Linear Wiener Bound (LWB) (shaded region). (B) Wiener bounds of a composite material mixture of amorphous Al₂O₃ and Au at 500 nm (yellow), 520 nm (green), 540 nm (blue) wavelengths. Filled dots and asterisks are algebraic averages and harmonic averages of permittivities of Al₂O₃ and Au for the same volume ratio, respectively. (C) Wiener bounds of a composite material composed of gold and a model dielectric at 1, 10, 100 GHz frequencies (blue, green, yellow, respectively). For permittivity of a dielectric, 10 + 0.003i is assumed for all frequencies. Asterisks indicate harmonic averages of the conductor and the dielectric when volume fraction of the dielectric is 0.01, respectively. Homogenized permittivity based on the harmonic average (i.e. ε_eff ≈ 100ε_d) is nearly dispersion-less.

Figure 3:

Metamaterials with near dispersion-less effective electric permittivity. (A) A schematic of a carpet cloak and its broadband cloak performance. Adapted with permission from Ref. [9]. Copyright 2009, Springer Nature. (B) A schematic diagram of small-gap I-shaped metamaterial with broadband high permittivity (left). The capacitive coupling (strong local electric field in the small-gap region) is the origin of the enhanced effective permittivity. Adapted with permission from Ref. [7]. Copyright 2011, Springer Nature. (C) A schematic of a metal-nanocube array and local electric field distribution under light incidence, which shows enhanced permittivity at near-infrared frequency regime. Reproduced with permission [33]. Copyright 2015, Optical Society of America. (D) The principle of broadband polarization enhancement and measured dielectric constants. Adapted from Ref. [37]. Copyright 2016, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY).

Figure 2B shows a much larger area of achievable effective permittivity if the real parts of permittivities of two components have opposite signs, such as in the case of metal and dielectric. With this kind of disparate composites, a large positive, a near zero, or a large negative value can be realized. For example, effective permittivities of hyperbolic metamaterials such as wire medium [27], [28] and multi-layer stacking of metal and dielectric [29], [30] can be classified as this category. In particular for multi-layered structures, their out-of-plane (normal to their planar interfaces) and in-plane (parallel to the interfaces) permittivities are exactly on CWB and LWB owing to their structural symmetry. The effective permittivity can be tuned over the entire CWB and LWB curves between the permittivities of two constituent materials by changing the volume fractions of constituent materials. For the effective permittivities of metallic wire arrays (normal to the wire axis), metallic particle arrays with small dielectric gaps, or other similar variants are also close to CWB with slight geometric modification factors considering the exact shape of the metallic inclusions (e.g., cylindrical wire vs. Square prism) and fringe electric fields. Unfortunately, with typical metals, both LWB and CWB, and, hence, the effective permittivities of specific structures can be frequency dependent owing to the strong intrinsic frequency dispersion of metal’s permittivity as shown in Figure 2B.

However, the dispersion in the effective permittivity can be avoided if the metal’s volume fraction is kept below certain values. For CWB, [f_d/ε_d + f_m/ε_m]⁻¹ reduces to ε_d/f_d and becomes decoupled from ε_m’s dispersion if f_m ≪ f_d|ε_m/ε_d| where f_d (f_m) and ε_d (ε_m) are the volume fraction and permittivity of dielectric (metal), respectively. It is worth noting that the shape-dependent modification factors for wire and particle arrays mentioned above are also frequency-insensitive in the long-wavelength regime. Thus, their effective permittivity becomes linearly proportional to ε_d and the coefficient of proportionality is purely controlled by the volume fraction and geometry, with no influence from the strong dispersion of metal. As the absolute value of ε_m is typically very large (order of millions or even larger for microwaves and over 100 at the 1.55 µm optical communication wavelength), the condition of f_d/ε_d ≫ f_m/ε_m still can be fulfilled with a very small f_d, resulting in dispersion-less very high effective permittivities as shown in Figure 2C.

This dispersion-less enhancement of effective permittivity can be interpreted as the result of the capacitive coupling between the metallic inclusions [31], [32]. The effective permittivity of many metamaterials with strongly localized electric fields due to quasi-static boundary conditions, such as closely-packed metallic inclusion arrays [5], [33] and their planarized versions [6], [7], show this behavior. In Ref. [7], very high permittivity and refractive index over a broad terahertz frequency band were experimentally observed, demonstrating this principle (Figure 3B). Metamaterials of metallic nanoparticle array show enhanced effective permittivity in near-infrared and visible frequency regime [32], [33], [34], [35] (Figure 3C) and have been utilized in solar cell application [36].

Even though reducing the dielectric gap size in the aforementioned studies generally leads to higher effective permittivity, the amount of potential enhancement, in reality, is limited due to practical and fundamental reasons. As the gap size approaches nanometer scales, its fabrication becomes more challenging and dielectric breakdowns as well as current leakage through grain boundaries can present problems. Ultimately, at one nanometer or below, the electron tunneling will make the above model no longer valid. In Ref. [37], a new approach based on various staggered arrays of metal plates is used to overcome such limitations (Figure 3D). In previous “small-gap” approaches, intense electric fields appear only over a small fractional volume occupied by the dielectric gap material, which converges to zero as one decreases the gap size. By contrast, in staggered arrangements, the dielectric region with intense electric fields still occupies about half of the unit cell even in the vanishing gap limit as the unit cell thickness is shrunk at the same rate, so there is no trade-off between the degree of field enhancement and the volume fraction over which the enhancement occurs. Mathematically, this introduces another multiplication factor, M_p, to the effective permittivity, which is now expressed as ε_eff = M_pM_sε_d where M_s is the previously-known enhancement factor originating from electric field localization (the 1/f_d enhancement in previous cases). The factor M_p accounts for how large the macroscopic polarization is compared to the mesoscopic polarization formed in the dielectric gap and is also proportional to the geometric ratio between the lateral unit cell length and the gap size. As a result, ε_eff is proportional to the square of the geometric ratio, and a giant effective dielectric constant of one million can be obtained with a dielectric gap size of ∼1/1000 of the unit cell size for example [37]. Although the effective permittivity of staggered array metamaterials, as well as earlier “small-gap” metamaterials, is still within the Wiener bound in the long-wavelength regime, its analytic expression in terms of geometric parameters is not explained by well-known Maxwell-Garnett or Bruggeman formula since the interaction between metallic inclusions embedded in the dielectric matrix is very strong, necessitating new models [5], [31], [35], [37].

In addition to endeavors towards high-permittivity metamaterials, there has been a simultaneous effort on obtaining low or negative permittivity values resulting from negative electric susceptibility over a broad frequency [38], [39]. While metals themselves have permittivity whose real part is negative for a vast span of frequencies from DC to the optical range, its frequency dispersion is very strong due to the resistive damping and non-zero effective mass of conduction electrons. Instead, if one can incorporate active inclusions with resonant gain, it is expected that negative electric susceptibility over broadband in the off-resonance regime can be realized based on Kramers-Kronig relation [40]. If the resulting permittivity is small and positive, the effective refractive index becomes less than 1, and the superluminal phase and group velocity can manifest [39]. However, a complete removal of dispersion is impossible as information velocity cannot be faster than the speed of light in vacuum.

2.2 Magnetic permeability

Quasi-static homogenization theories for effective magnetic permeability can be formulated similarly as for effective electric permittivity [41], [42], [43]. As the effective permittivity can be tuned over broadband by varying the volume fractions in dielectric composites, it is possible to obtain the desired permeability (within CWB and LWB) over broadband by constructing composites of magnetic materials with non-zero intrinsic magnetic susceptibility in principle [41]. However, the spin of the electrons and magnetic moments in solid state materials cannot easily keep up with the oscillation of the electromagnetic waves at frequencies above a few gigahertz and magnetism from electronic spin almost disappears at higher infrared and optical frequencies [41], [44], [45]. Although studies to overcome this limitation have been carried out [46], [47], low-dispersion magnetic materials above the microwave regime are yet to be realized [4]. This absence of intrinsically-magnetic building blocks at high frequencies presents predicaments for constructing broadband magnetic metamaterials using similar mixing formulae as in dielectric composites because, in strict quasi-static assumptions (i.e.∇×E=0 and ∇×H=0) [48], where the electric and magnetic fields are decoupled, effective permeability other than unity is theoretically prohibited if only non-magnetic constituent materials are available.

However, in the relaxed quasi-static regime allowing Faraday induction [48], non-trivial magnetization can be achieved by induction current of conducting inclusions even if all of the constituent materials are non-magnetic. A representative example is the split-ring resonator-based metamaterial. The frequency-dependent effective permeability of this kind of metamaterial is given in Eq. (2B) and Figure 1B assuming that the response is dominated by a single resonance. In Eq. (2B), there is an ω² factor in the numerator unlike in the effective permittivity expression in Eq. (2A). This is because the electromotive force is associated with the temporal change of the magnetic flux (ω dependence), and the induced currents and magnetizations are related to the temporal change of the electromotive force (another ω dependence). Thus, the relative permeability due to Faraday induction converges to the dispersion-less value of 1 − p_μ at frequencies above the resonance frequency.

This shows that near dispersion-less effective permeability between zero and unity can be readily achieved by constructing composites out of metals and dielectrics. The magnitude of diamagnetism from Faraday induction can be controlled by adjusting the volume fractions and structural shapes of the metallic inclusions [31], [49], [50] (Figure 4A). In particular, the lower end of the frequency range of near dispersion-less diamagnetism can be lowered by reducing the resonance frequency. Closed rings, for example, can be considered as limiting cases of split rings that can be modelled with lumped circuit elements of a capacitor and an inductor. As the gap closes, the capacitance increases to infinity and the inductor-capacitor resonance frequency reduces to zero. However, even if the resonance frequency can be reduced to zero, the dispersion-less diamagnetism does not extend down to zero frequency if the constituent metal is lossy with a non-zero γ in Eq. (2B). This is due to the fact that the skin depth increases as the frequency decreases below the damping frequency in lossy-Drude type conductors, and the structure-induced effective diamagnetism reduces if the skin depth grows comparable to or larger than the size of metallic inclusions. A special case would be superconductors with vanishingly small γ [51], for which the diamagnetic effect can appear down to very low frequencies. Diamagnetic metamaterial in DC [8] and DC magnetic cloaking [52] are reported examples.

Figure 4:

Metamaterials with near dispersion-less effective magnetic permeability. (A) A μ-near-zero metamaterial composed of metallic cubes and measured permeability. Adapted with permission from Ref. [49]. Copyright 2013, AIP Publishing. (B) The principle of independent control of permittivity and permeability is illustrated through three motif designs. Each column corresponds to a different motif that produces a similar effective permittivity but progressively larger effective permeability from left to right. The first row shows induced surface charges from the capacitive coupling between metallic inclusions. The second row shows eddy currents and the third row shows magnetic field distribution. Adapted with permission from Ref. [5]. Copyright 2009, American Physical Society. (C) In the visible and near infrared regime, the size of nanoparticle and electromagnetic skin depth are comparable. By choosing a proper unit cell size and particle size, the permittivity and permeability can be independently controlled. Adapted with permission from Ref. [35]. Copyright 2016, AIP Publishing. (D) The phase difference of displacement currents within a slab gives an effective magnetization. It can be used for broadband optical magnetism. Adapted from Ref. [56]. Copyright 2018, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY).

On the other hand, this kind of diamagnetic effect by Faraday induction may be undesirable in some cases while one utilizes metallic inclusions to control effective permittivities to be uniformly high over broadband. For example, if a dispersion-less enhancement of effective refractive index is a final goal, reduced effective permeability due to metallic inclusions should be avoided since n=με where μ and ε are relative magnetic permeability and relative electric permittivity, respectively. Therefore, methods of maintaining an effective permeability close to unity in composite media even with metallic inclusions have been proposed in various frequency bands [5], [35]. In a more general sense, these works provide ways to control the electric permittivity and the magnetic permeability independently over a broad frequency range. In Ref. [5] (Figure 4B), it is shown that the effective permittivity and permeability are governed by different aspects of the shape of metallic inclusions in the quasi-static regime: the capacitive coupling between inclusions and the amount of area enclosed by eddy currents, respectively. Hence, the permittivity and permeability can be independently controlled over broadband just by changing the shape of the inclusions accordingly. This design strategy is experimentally verified in Ref. [53], [54] for microwaves. Also, a planarized version of the design is experimentally demonstrated at the terahertz regime showing a quasi-static high refractive index around 10 (around 40 near resonance) at THz frequencies [7] (Figure 3B). For infrared and visible light, the principle remains valid but fabrication of intricate designs may become challenging as the minimum feature size reduces to tens of nanometers or even smaller. Instead, at these high frequencies, an even simpler approach becomes available as the structural length scales are now comparable to the electromagnetic skin depth of constituent metals. Since Thomas-Fermi length of metal is very small, capacitive coupling between metallic inclusions maintains even for very small unit cell size. In Ref. [35], it is shown that the effective permittivity and the effective permeability can be independently controllable by adjusting the unit cell dimension and dielectric gap size (Figure 4C). In particular, arrays of sub-skin-depth sized metallic nanoparticles show a large refractive index in near-infrared and visible frequency regime without a significant diamagnetic effect [34], [55]. This is possible because the diamagnetic property of metallic particles changes drastically depending on whether the particle radii are larger or smaller than the skin depth. So, intricate designs are not needed to control the amount of eddy currents. On the other hand, Thomas-Fermi screening length for longitudinal electric fields inside metal is less than a nanometer and electric fields are still localized to tiny gaps between metallic inclusions like at microwaves or terahertz. So, simply by changing the gap size, one can control the capacitive coupling between inclusions and, hence, the effective permittivity.

Several studies have indicated that effective permeability can be negative or greater than one over broadband in various frequency regimes. Recently, it is reported that effective magnetization of dielectric slab based on the phase retardance within a slab can be utilized for non-trivial optical magnetism in dielectric-metal-dielectric multilayer structure [56] (Figure 4D), offering nearly constant effective permeability over visible to near-infrared regime. As an attempt to achieve nearly dispersion-less negative permeability, methods using gain medium [40] and nonlinearity [57] have been proposed.

2.3 Chirality

A chiral medium with a non-zero chirality parameter in Eq. (1) has left and right circularly polarized light as eigenwaves with different complex wavenumbers for the same frequency. The difference results in polarization rotation and circular dichroism [18], [58], [59]. A simple Lorentz model for conduction or displacement current-based chirality can be expressed as Eq. (2C) [22]. Unlike the permittivity and permeability, κ has ω or 1/ω dependence at frequencies below or above the resonant frequency, respectively (Figure 1C). This behavior is also observed in natural chiral materials, although their magnitudes are much smaller [60], [61]. With the ω or 1/ω dependence in the off-resonance regime, the chirality parameter as defined in Eq. (1) is dispersive at all frequencies.

In spite of this apparent frequency dispersion, nearly constant polarization rotation and circular dichroism may be achievable for some frequency range. Polarization rotation, measured as the total rotation angle of the plane of polarization of a linearly polarized light passing through a chiral medium with a refractive index n and thickness l, is expressed as nωlRe[κ]/c [22], [62]. Related, circular dichroism is the difference in absorbance between left and right circularly polarized light and its magnitude is captured by nωlIm[κ]/c. Because both quantities are linearly proportional to the thickness of the chiral medium, l, one can define per-unit-length rotation and dichroism by dividing them with l; then, these quantities can be regarded as intensive material properties of the medium. Owing to their additional ω dependence compared to the chirality parameter, they show nearly dispersion-less values in high frequency regime, while showing ω² dependence in low frequency regime, similar to the case of magnetic permeability if the dispersion of the refractive index is small.

In order to overcome the small chirality of natural chiral materials, many studies have considered chiral meta-atoms or meta-molecules. Since chirality originates from spatial dispersion owing to the nonlocal excitation of inclusions, meta-atoms and meta-molecules that are much larger than natural chiral molecules are promising building blocks for large chirality. In the initial stage, arrays of diatomic meta-molecules with two stacked identical meta-atoms in a twisted manner, such as stereo-metamaterials [63], were investigated. These structures succeeded attracting much attention toward chiral metamaterials and, while some early designs already showed broadband polarization rotation in the frequency region away from the resonance [64], the exploration for different configurations with stronger chirality over broader bandwidth continued. An interesting twist came in the form of meta-molecules that are composed of two layers of meta-atoms complementary to each other, an example of which can be seen in Figure 5A. In this configuration, polarization rotation can be relatively constant and large in magnitude in a wide frequency band above the resonance frequency [65], [66]. In addition, there is the advantage of a high transmittance owing to Babinet’s principle.

Figure 5:

Metamaterials with broadband optical activity or broadband circular dichroism. (A) An array of rotated complementary crosses. Transmission resonance occurs around 4.5 GHz (not shown). Adapted with permission from Ref. [66]. Copyright 2014, American Physical Society. (B) Three-dimensional metallic interconnection with Drude-like response. Adapted with permission from Ref. [67]. Copyright 2014, Springer Nature. (C) Two metallic layers with aligned slit tips are strongly magnetically coupled while the electric coupling is minimized. Adapted with permission from Ref. [69]. Copyright 2019, WILEY‐VCH. (D) A helical stack of highly anisotropic effective layers. Adapted with permission from Ref. [70]. Copyright 2012, Springer Nature. (E) Metallic helix array realized with direct laser writing. Adapted with permission from Ref. [71]. Copyright 2009, American Association for the Advancement of Science. (F) Similar structure realized by glancing angle deposition where their feature size is tens of nanometer scale. Adapted with permission from Ref. [73]. Copyright 2013, AIP Publishing.

A more drastic design change is based on the fact that, if the resonance frequency becomes zero and damping is negligible in Eq. (2C), the ω dependence of the polarization rotation and circular dichroism completely disappear. In Ref. [67], constant polarization rotation over a wide frequency range where the upper bound reaches around 42 GHz (limited by higher-order resonance frequencies) is obtained by the Drude-like response of meshed helical metamaterials (Figure 5B). This phenomenon may also be understood with successive mode conversions between free-space modes and transmission line modes occurring at the front and back interfaces, such as in Ref. [68], in which a frequency-independent geometric feature (e.g., the orientation of the out-coupling antenna) determines the orientation of the plane of polarization on the output side. In one recent study, even in the absence of complex 3D metallic structures, dispersion-less polarization rotation was achieved with magnetic coupling between two separate metal layers, while electric coupling was minimized (Figure 5C) [69].

A related phenomenon, broadband circular dichroism, can also be achieved by helical stacking of anisotropic layers; a classical example of this concept is cholesteric liquid crystals. One thing to note is that the chirality of the subwavelength-scale inclusion on each layer is not required. In this method, each layer can be achiral with mirror symmetries and their helical stacking induces chirality. In Ref. [70], broadband circular dichroism is demonstrated with a helical stack of gold nanorods (Figure 5D). Each layer of the stack is composed of aligned gold nanorods and can be considered as a homogeneous and anisotropic effective medium slab. Indeed, any lateral displacement of gold nanorods does not affect the circular dichroism significantly, which is a necessary condition for the validity of the homogeneous slab model and indicates that near-field coupling between inclusions of adjacent layers is not strong. Although the overall structure resembles those of cholesteric liquid crystals, the exact ways in which chirality manifests are different. For cholesteric liquid crystals, the anisotropy of each layer and the overall chirality are generally small, and the difference in the Fabry–Perot resonance condition for left and right circular polarizations is a major factor to the circular dichroism, which makes the circular dichroism dispersive. However, for a helical stack of gold nanorod arrays, the lattice effect—the separation and structural rotation angle between two layers—leads to the circular dichroism. By proper tuning of the subwavelength separation and the rotation angle, strong circular dichroism can be induced over almost the entire visible wavelength range. The gold helix array [71], [72] shown in Figure 5E also shows broadband circular dichroism. At first glance, these structures may look similar to other chiral metamaterials based on chiral inclusions or natural chiral materials due to the apparent chirality of the helical gold inclusions. However, a closer look reveals that the chirality in these studies has much in common with Ref. [70] because much higher-order localized resonances are at play rather than the fundamental resonance mode spanning the entire helix due to the vertical orientation and relatively large inclusion sizes. In other words, these systems share many properties with a stack of thin anisotropic layers. This view is supported by the fact that circular dichroism vanishes when the helix arrays are composed of mixed perfect electric conducting helixes with different pitch phases, which eliminate the anisotropy of each layer [72]. However, if the helix is composed of a lossy metal, the structural chirality of helix induces a nonzero optical chiral effect. These kinds of metallic helix arrays can be realized by direct laser writing [71] (Figure 5E) and glancing angle deposition [73] (Figure 5F).

3 Broadband metamaterial-based devices

In the previous section, it was discussed how exotic effective material properties can be maintained over a broad frequency band using several different approaches. In this section, the discussion will focus on metamaterial-based devices with broadband characteristics. While dispersion-less (meta-)materials help to achieve broadband device operation in many cases, there are also cases in which an intentional frequency dispersion is required for a larger operation bandwidth. To identify the optimal dispersion for maximum bandwidth, it is necessary to consider a specific target application and system configuration. Hence, in this section, the developments in the field are overviewed in three representative application areas of absorbers, beam deflectors/lenses, and holograms. These three are among the most popularly investigated applications of metamaterial-based devices and can benefit much if broad bandwidth can be obtained. The explicit conditions needed for broadband operation and the approaches so far proposed to achieve those will be explained in the following sub-sections for each application.

3.1 Broadband absorbers

When a wave is incident on a homogenous, flat surface, it is reflected, transmitted or absorbed. The goal of perfect absorbers is to minimize the reflection and transmission and to maximize the absorption and their common usages include avoiding detection [74], [75] or utilizing the absorbed energy []. While the transmission can be easily blocked over a very broad frequency range by just placing a metallic mirror, minimizing the reflection over a broad bandwidth is not a trivial task. In fact, there are some physical laws governing the amount of absorption that an absorber can attain once the constituent materials are fixed [79]. According to the theoretical derivation in [79], absorbers backed by a perfect reflector has a fundamental trade-off relationship between the amount of reduction in reflection in dB scale and its wavelength bandwidth if the absorber’s total thickness is fixed. Moreover, the upper bound of their product increases linearly with the total thickness. For example, a commercially available pyramidal microwave absorber with a high absorption rate over a broad frequency range is many times thicker than its target wavelength while absorbers with narrow bandwidth can be much thinner for the same target wavelength. However, commercially available designs are still far from the theoretical limit in the target wavelength range, due to parasitic absorption at other wavelengths. To realize ultimate absorbers whose performance within the target wavelength range approaches the theoretical limit, a proper engineering of the admittance and its frequency dispersion are required.

A metamaterial is a promising candidate to realize such an admittance with tailored dispersion. By using metamaterial-based absorbers, it is possible to achieve absorption performance that is closer to the theoretical limit compared to conventional absorbers, owing to the vast degree of freedom of metamaterial in controlling its constitutive parameters and their dispersion. Since the early work on metamaterial-based ultra-thin absorbers [2], many studies have been conducted on realizing high-performance absorbers with a very small thickness, much thinner than a single wavelength. On the other hand, there also have been studies on ultra-broadband absorbers at the expense of an increased thickness comparable to or larger than a wavelength. In both cases, the goal has been to approach the theoretical upper bound of extinction-bandwidth product for a given thickness.

Here, broadband meta-absorbers are classified according to their fundamental principles. The first class of broadband meta-absorbers can be easily understood in terms of admittance matching. Using metamaterial layers with tailored admittances, broadband admittance matching can be obtained between the absorber and the incident medium as shown in the first subsection. While the other class of absorbers can also be explained by admittance matching in principle, alternative explanations such as waveguide mode analysis provide more intuitive understanding as explained in the second subsection.

3.1.1 Thin meta-absorbers with admittance matching layers

A reflection coefficient can be expressed as a function of intrinsic admittance of a surrounding medium and input admittance of an absorber. The intrinsic admittance is an inherent parameter of a material, representing the (potentially frequency-dependent) ratio of the magnetic field phasor to the electric field phasor of a monochromatic uniform plane wave propagating within the material. In contrast, the input admittance is a system- and position-dependent parameter related to the total electric and magnetic field phasors at the given position and also a function of frequency. The complex reflection coefficient r and the reflectance R of an absorber are expressed as

(4A)r=Y0−YinY0+Yin

(4B)R=|r|2

where Y₀ is the intrinsic admittance of the surrounding medium (air in most cases)_,Y_in is the input admittance of an absorber. To reduce the reflectance over a broad bandwidth, it is apparent that Y_in should be close to Y₀ over the entire target frequency range, both in its real and imaginary parts. In many cases, especially for thin absorbers, matching between Y_in and Y₀ over a broad frequency range is a challenging task as will be discussed below.

In this section, absorbers that possess layers intentionally designed for broadband admittance-matching will be discussed. The most basic structure for the absorbers in this category is composed of three layers: a bottom metallic mirror, a dielectric spacer in the middle, and an admittance-matching layer at the top, as shown in Figure 6A. As an extension of this structure, additional layers can be added for better performance.

Figure 6:

A basic absorber structure in section 3.1.1 with a single admittance matching layer and a corresponding equivalent transmission line model. (A) A basic absorber structure is composed of three layers, which are an admittance matching layer, a dielectric spacer, and a metallic mirror. (B) An equivalent transmission line model of the basic absorber structure. The three layers are modelled with a shunt lumped element of admittance Y_M, a segment of transmission line whose characteristic admittance (Y_d) is same as the intrinsic admittance of the dielectric spacer material, and a short circuit, respectively. If the metallic mirror is not perfectly reflecting, it can be modelled with a finite lumped element admittance as well. The intrinsic admittance of air is denoted with Y₀.

For the flat absorbers, there are inward- and outward-propagating waves within the dielectric spacer and the admittance matching layer and the wave behavior inside the absorber can be analyzed with an equivalent transmission line model with a lumped circuit element as in Figure 6B. The input admittance is the ratio of total tangential magnetic and electric fields that are parallel to the absorber plane, contributed by both inward- and outward-propagating waves, each of which has an electric-magnetic field relation imposed by the intrinsic admittance of dielectric. If the bottom metal reflector is assumed to be a perfect mirror, the input admittance at the top of the dielectric spacer can be given as Yin,1=iYdcot(nωd/c) where Y_d, n, ω, d, and c are the intrinsic admittance of the dielectric spacer, refractive index of the spacer, angular frequency, thickness of the spacer, and the speed of light in free space, respectively. In absorbers with a very thin admittance matching layer with only electric effective conductivity, the input admittance at the top of the absorber, Y_in,2, is modelled as a parallel connection of two admittances, Y_M + Y_in,1, where Y_M is the effective admittance of the matching layer. Since the perfect absorption condition is Y₀ = Y_in,2, the ideal admittance for the matching layer becomes Y₀ − Y_in,1. Therefore, the ideal admittance of the matching layer depends strongly on the frequency due to the strong frequency dependence of Y_in,1.

The Salisbury screen is a classic absorber structure employing this admittance-matching technique [80]. With the Salisbury screen, it is possible to achieve perfect absorption at the target frequency. However, admittance-matching occurs only at the target frequency because the material used in the absorber generally cannot provide proper dispersive admittance for broadband operation, as shown in Figures 7A,7D. On the other hand, for many applications, reasonable absorption such as the −10 dB reflectance, which corresponds to 90% absorptance with no transmittance, over a broad bandwidth is preferred to perfect absorption at a single frequency.

Figure 7:

Concept of admittance matching for the structure in Figure 6A with λ/4-thick dielectric spacer. (A–C) Complex admittances required of the admittance-matching layer for perfect absorption are plotted as black dotted lines. Also shown are the actual admittance that can be realized by (A) top resistive layer of the Salisbury screen, (B) a double-resonance metasurface, and (C) a single-resonance metasurface. Top and bottom panels represent real and imaginary parts of admittances, respectively. In (A), blue dashed lines represent admittance of single resonance for comparison. In (B), blue and yellow dashed lines represent the contributions to the admittance from each resonance and the solid line corresponds to the combined admittance of the double-resonance metasurface. In (C), admittances attained from a single-resonance metasurface with different Q factors are plotted, showing that a proper quality factor of the resonator can be chosen to enlarge the bandwidth. (D–F) Reflectance of different absorber structures are compared: (D) Salisbury screen, (E) metal-backed metasurface with double resonance, and (F) metal-backed metasurface with single resonance. Red dashed lines represent −10 dB reflectance, which is a commonly used target in the literature.

There have been studies achieving broadband high absorptance using a simple thin film structure [81], [82]. For example, in [81], a thin chromium (Cr) layer is used as the admittance-matching layer. Since Cr shows proper admittance dispersion in the visible regime, the input admittance of the absorber can be close to the intrinsic admittance of air by using two dielectric spacers above and below the Cr layer. As a result, more than 99% absorption over 380–780 nm bandwidth is achieved. However, admittance-matching with a simple multilayer of natural materials has a limitation imposed by material’s intrinsic dispersion; if there is not a natural material with proper dispersion, it is hard to obtain an absorber with excellent performance.

By virtue of their design freedom, metamaterials can be an excellent choice of admittance-matching layer in absorbers. In particular, by adding artificial resonances in their effective permittivity, the required dispersion for broadband absorbers can be imitated by metamaterials. If the electric resonances are modelled with Lorentz oscillators, the expression for the effective admittance of the metamaterials can be easily found [83]. Figures 7A,7D show how a single artificial resonance can expand the −10 dB reflectance bandwidth of an absorber by admittance-matching.

The −10 dB reflectance bandwidth can be further improved using multiple resonances in a single metamaterial unit cell. In the equivalent transmission line model, multiple electric resonances can be modelled as multiple lumped elements connected in parallel; in this case, effective admittance of the metamaterial is the sum of the admittance of the constituting resonances. Figures 7B,7E show how double resonances can expand the absorption bandwidth. With more design parameters offered by double resonances, it is possible for the admittance-matching layer to approximate the required admittance over a broader frequency range. As a result, it provides a broader −10 dB reflectance bandwidth compared to that of the absorber with a single resonance. Continuing in the same direction, there have been studies using even more resonances to improve the absorber performance.

Metamaterials with multiple resonances can be made by placing components with spectrally close resonance frequencies in a single layer at the same time [84], which is known as resonance blending. One way of achieving resonance blending is using patterns with various shapes such as double rings [85], fractals [86], binaries [87] or doubly-periodic patterns [88]. In [89], metamaterials with multiple resonances are attained with a windmill pattern in the top layer (Figure 8A). In [90], continuous plasmon resonance is obtained from graphene with sinusoidal patterns. In [91], broadband absorption is achieved by using crossed trapezoidal patterns. In [92], a hierarchical structure is used to provide additional resonance to an existing resonance structure, mimicking the shape of a diatom frustule. A super-cell structure can also provide metamaterials with multiple resonances. In [93], 18 different resonators are arranged in a super-cell structure, resulting in high absorption over 450–950 nm wavelength range (Figure 8B).

Figure 8:

Various broadband absorber designs. (A) A windmill-patterned transparent broadband microwave absorber, and its measured absorptivity at different incident angles. Adapted with permission from Ref. [89]. Copyright 2017, AIP publishing. (B) A metasurface with a supercell composed of squares, circles, and crosses of different sizes. Each resonator is designed to possess a different resonance frequency, and the fabricated sample shows an average of 97% absorption in the 450–950 nm range. Adapted from Ref. [93]. Copyright 2018, The Authors, some rights reserved; exclusive licensee John Wiley and Sons. Distributed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC). (C) An absorber design with two chromium (Cr) rings of different sizes, vertically stacked with SiO₂ dielectric spacer layers. More than 80% absorption is achieved over 1–5 μm wavelength range. Adapted from Ref. [103]. Copyright 2017, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (D) An absorber using a titanium nanodisk array. Inset is a SEM image of a fabricated sample. Adapted from Ref. [109]. Copyright 2016, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (E) A porous plasmonic absorber. The structure shows ultra-broadband absorption for the wavelength range of 400 nm to 10 μm (black solid line). Adapted from Ref. [78]. Copyright 2016, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC). (F) A “metafluid” or a colloidal dispersion of tailored resonators. Adapted with permission from Ref. [116]. Copyright 2016, American Chemical Society.

As the meta-absorber field evolved, interesting designs with additional functionality have also emerged. Several studies have proposed optically transparent microwave absorbers by adopting a mesh grid [94], indium tin oxide [74], [89], water substrate [95], or standing-up ring resonators [96], demonstrating the applicability to important window stealth and other applications. Some studies have demonstrated broadband absorbers that are easy to fabricate [97], [98]. In particular, for absorbers working in the visible frequency regime, it is strongly desirable to have designs that are amenable to simple fabrication methods because the typical minimum feature size of optical metamaterials is in the order of tens of nanometers or even smaller. In [98], a randomly arranged gold nano-octahedra layer is used as a top layer of broadband absorbers. The proposed structure shows an averaged absorption of 85% in the visible spectral range. In several studies, it has been demonstrated that deposition of additional layers onto existing resonators can provide better admittance-matching, resulting in higher absorber performance [99], [100], [101]. In [100], silicon carbide and silicon dioxide (SiO₂) are used as anti-reflection layer on tungsten (W) cylinder array so that over 95% absorption at 200–900 nm wavelengths range can be achieved, which is much broader than the case of bare W cylinder array.

If the resonance blending is attained in a single layer, the broadband absorption can be obtained with absorbers with a simple layer configuration. However, because of the spatial constraint, it is difficult to expand bandwidth beyond a certain extent [86]. On the other hand, if the resonance blending can be achieved using vertically stacked structures, this constraint can be alleviated and absorption performance can be improved. In such a case, the input admittance can be matched by placing the resonators with different resonant frequencies in different layers and adjusting thickness of the dielectric spacer between them [102]. Compared to the single matching-layer absorber in which metamaterials require a complex shape for multiple resonances, in the vertically stacked structure, it is possible to obtain broadband absorption even with a relatively simple shape [102], [103], [104], [105]. In [103], broadband infrared absorber including two chromium ring layers is demonstrated (Figure 8C). In [104], a multiplexed broadband absorber that works simultaneously for the solar spectrum and microwaves is implemented by designing the broadband absorber in the microwave regime with multiple layers, including a material capable of absorbing solar radiation. In [105], multi-layer broadband absorber that contain metallic bars of various lengths are suggested. In [106], broadband absorption by stacking several layers of asymmetrically patterned graphene is demonstrated.

While it is easy to reduce the reflectance well below that of a perfect mirror over broad bandwidth (one can achieve it by placing on the mirror some combination of resonant structures made of lossy materials with varied resonance frequencies), it is not a straightforward problem, as attested by above examples, to maintain the reflectance below a small value (for example, 10%) at all frequencies within the band as would be required in real applications, due to the fact that the effective admittance should be closely matched to air over the entire frequency range. Matching the admittance involves matching both its real and imaginary parts. With a lossless dielectric spacer and a perfect mirror on the back, their contribution to the admittance, Y_in,1, is always imaginary. Therefore, matching the real part simply means that the admittance-matching layer should have the same real part of admittance as that of air, which is ∼ 1/377 S. The simplest solution is having a thin, homogeneous film of conductive material whose thickness is chosen such that its sheet resistance becomes 377 Ω. This is actually a Salisbury screen, in which the imaginary part is matched independently, albeit at only one frequency, by choosing a quarter-wavelength spacer. For implementing thinner absorbers, however, the problem is not so simple because one has to rely on the admittance-matching layer to match both the real part and the residual imaginary part simultaneously. Often a strategy adopted is to tune the quality factor (Q-factor) of the structural resonances. For example, Figures 7C,7F show that there is an optimal Q-factor for absorbers with a single resonance to achieve the broadest −10 dB operation bandwidth. There have been several studies that improve the performance of absorbers by manipulating optical losses (and, hence, the Q-factor) of resonances. Highly lossy metals such as refractory metals or lossy spacers can be used to obtain optimal optical loss [100], [107], [108], [109], [110], [111]. Figure 8D shows an absorber structure with a titanium (Ti) disk array [109]. The high loss of Ti causes the localized surface-plasmon polariton modes in this structure to have an optimized Q-factor. In [112], [113], [114], to manipulate the Q-factor, extra lumped circuit elements are added to metamaterials.

3.1.2 Dilute volumetric meta-absorbers

A drastically different approach to admittance matching is possible if one can allow the thickness of the admittance matching layer to be very thick such that the incident wave is sufficiently attenuated while propagating inside the layer and the wave reflected from the transmission-side boundary of the layer can be ignored when it reaches the incident-side boundary. In such cases, input admittance is identical to the absorbing material’s intrinsic admittance due to the lack of echoing wave’s influence. Thus, the reflectance becomes zero if and only if the material has the same intrinsic admittance as air. This is quite difficult to achieve in practice due to the lack of proper materials. In principle, a material’s admittance is the same as that of air if the ratio between its complex relative permittivity and relative permeability is the same as that of air in both real and imaginary parts. Finding proper lossy dielectric and lossy magnetic materials with this property over a broad frequency range is a challenging objective even at low frequencies. At optical frequencies, a lack of natural magnetic material makes this even more difficult.

Alternatively, one can try an approximate matching by using a very dilute, lossy dielectric material. Its relative permeability is unity and its relative permittivity is higher than that of air both in real and imaginary parts. So, strictly speaking, it is not admittance-matched to air. But, if the difference in permittivity is kept small (e.g., 0.1), the reflectance, which is roughly proportional to one-sixteenth of the square of the fractional difference, remains small (e.g., 0.000625). The drawback is that it requires the layer to be many wavelengths thick because of its small imaginary part of permittivity. Thus, there is again a trade-off relationship between extinction and thickness. There have been several studies based on this kind of intrinsic admittance-matching mechanism.

Vertically aligned carbon nanotube array (VANTA) structure [10], [115] is a representative example. In VANTA structure, carbon nanotubes, which are non-resonantly lossy over visible, are sparsely placed in air so that the effective intrinsic admittance of the air-nanotube composite material is close to that of air. In [77], high-efficiency solar steam generation with the VANTA forest is demonstrated. The carbon nanotube arrays with a 5% volume fraction and height of 280 μm show more than 98% absorption in the range of 0.2–200 μm. In [78], a nanoporous template with gold nanoparticles is used as a broadband absorber as shown in Figure 8E. Because of its high porosity, its effective intrinsic admittance can be approximately matched to that of air. Nearly 99% absorption can be realized over 400 nm to 10 μm due to the loss induced by the randomly sized gold nanoparticles within the porous template.

Another representative example is absorbing metafluid, which is a fluid with tailored light-absorbing particles dispersed in it. In [116], plasmonic or excitonic particles with various sizes are sparsely dispersed in water. The diversity of particle sizes provides broadband absorbing properties because different resonances of the particles can be superposed as shown in Figure 8F. In [117], gold super-particles, which are clusters of gold nanoparticles, are used as absorbing entities. From the superposition of multiple Mie resonances of colloidal gold super-particles with various sizes, broadband absorbing property can be achieved.

3.1.3 Alternative physical explanations for broadband meta-absorbers

Although there have been efforts to analyze multilayer absorbers using admittance-matching conditions [82], [104], absorber analysis based on admittance-matching becomes complicated and less intuitive when the number of constituting layers increases. In such cases, different physical explanations have been suggested to provide physical insights in understanding how these multilayer structures function as broadband absorbers.

In [118], an alternating metal/dielectric multilayered quadrangular frustum pyramids array is introduced (Figure 9A). The structure shows absorption higher than 90% in the range of 7.8–14.7 GHz. This is similar to other vertically stacked absorbers introduced in the earlier subsection, but authors of Ref. [118] also provided an alternative explanation of slowdown and trapping of an incident wave. Due to the tapered shape, the band-edge frequency of vertically propagating Bloch modes gradually increases with the height, and different frequency components are slowed down and trapped at a different height, resulting in broadband absorption as a whole. In [119], an analysis of similar tapered structures is provided in terms of hyperbolic metamaterials and resonant cavities. In [120], an array of nanotubes is used as a broadband absorber. The nanotube is concentric cylindrical shells of alternating layers of conductive aluminum-doped zinc oxide and insulating zinc oxide (Figure 9B), and has a height comparable to the target wavelength and small air gap (∼ one-tenth of the period) between adjacent tubes. So, the system is conceptually a denser and thinner version of vertically aligned carbon nanotubes introduced in the previous subsection, and both the maximum extinction and the bandwidth are smaller, in line with the general trend. Authors provide coalescence of modes resulting from hyperbolic dispersion as the key absorption mechanism. In [121], a broadband absorber possessing multiple surface plasmon-polariton modes is proposed. As shown in Figure 9C, one gold grating layer is placed on top to couple incoming waves to many in-plane guided modes of the underlying gold/silicon dioxide multilayer structure, which otherwise do not couple with incoming waves due to the translational symmetry of the system and the mismatch of the in-plane wave vector. Authors also provided a conceptual explanation based on a series of classical harmonic oscillators with only the outermost one coupled to the outside. Conceptually, it is similar to a slab of high-index lossy dielectric or semiconducting medium with high photonic density of states with scattering structures on the surface to couple outside modes to most of the internal modes, which otherwise cannot be probed due to wave vector mismatch, to reach an ergodic regime. In the same trend as other systems, the absorption bandwidth increases as the number of multilayer stacks and the total thickness of the system are increased. In [122], by replacing gold with iron in a similar structure, broadband absorption exceeding 92% for the 400–2000 nm range can be achieved. In [76], near 85% absorption in a large visible-infrared wavelength range is attained in a grating structure of alternating graphene/dielectric layers, on top of a spacer backed with a mirror (Figure 9D). Proper choice of the layer thicknesses and the filling factor of the grating is needed for large absorption of both input polarizations over broadband, which is attributed to the excitation of in-plane guided modes by the authors.

Figure 9:

Other broadband absorber designs. (A) A tapered metal/dielectric multilayer structure array, which shows broadband microwave absorption. Adapted with permission from Ref. [118]. Copyright 2012, AIP Publishing. (B) An array of hyperbolic metamaterial cylinders composed of ZnO and aluminum-doped ZnO concentric layers for infrared absorption. Adapted with permission from Ref [120]. Copyright 2017, National Academy of Sciences. (C) A visible light absorber composed of Au grating and Au/SiO₂ multilayer stack. Absorbers with more than five Au/SiO₂ pairs show average absorptions of more than 95% in visible regime. Adapted with permission from Ref. [121]. Copyright 2016, Optical Society of America. (D) Ultra-broadband light absorber composed of graphene and polydiallyldimethylammonium (PDDA) chloride multilayer grating. Waveguide mode coupling in grating contributed to broadband absorption of more than 80% in 300–2500 nm. Adapted with permission from Ref. [76]. Copyright 2019, Springer Nature.

3.2 Broadband meta-deflectors and metalenses

Unlike absorbers, which manipulate the intensity of reflected and transmitted light, the applications of beam deflection, focusing, and holography typically requires controlling the phase of light in a specific spatial pattern. A generalized Snell’s law captures the fact that incident light obtains additional in-plane momentum corresponding to the gradient of additional phase caused by the inhomogeneous material and geometry distribution on the surface [123]. Controlling the phase in spatial domain determines how a light beam is deflected or focused. Assuming that a device is in the x-O-y plane and the light is incident along the z-axis, the required phase distributions on the metamaterial for beam focusing and deflection are given as

(5A)ϕ(r,ω)=−ωc(r2+f2)+C(ω)

(5B)ϕ(x,ω)=ωcsinθ(x−x0)+C(ω)

where c, ω, f, r, θ, x, C(ω) are the speed of light, angular frequency, focal length, distance from the center of the lens (r=x2+y2), deflection angle, cartesian coordinate in the device plane, spectral degree of freedom, respectively [124].

Using metamaterials has the advantage that various phases can be realized with subwavelength spatial resolution. This controllability of phase relies on the design freedom of unit structures’ shape and size at different positions on the plane. By spatially arranging different structures, proper phase distribution like that indicated by Eq. (5) can be realized. Finding a good set of structures with satisfactory optical performance and ease of fabrication is the main design objective. In recent years, much metamaterial-based research for beam focusing and deflection has been conducted in various wavelength regimes from microwaves to visible light range. While it is relatively easy to design it for a single target wavelength due to multitudes of possible structural options, making it work for several different wavelengths at the same time, not to mention a continuous range of broadband wavelengths, is not a simple task.

Geometric phase has been much studied as a way to adjust the phase in broadband. When a circularly polarized wave is incident, full phase control from 0 to 2π of the cross-polarized output light that has the opposite handedness is possible by changing only the orientation of the unit structure. This phase is known as geometric phase or Pancharatnam-Berry phase. Because the structures are congruent in all positions, the phase can be manipulated while the amplitude remains uniform over the entire device, which makes the device design much simpler. The fact that the phase is purely determined by the geometric orientation results in identical phase distribution regardless of wavelength. One problem of this approach is that the amplitude, or the conversion efficiency, depends on the wavelength. This can be potentially mitigated by utilizing multiple resonances, as demonstrated by a high cross polarization conversion efficiency over broadband in Ref. [125]. However, a more fundamental problem is that, as can be expected from Eq. (5), the dispersion-less phase results in frequency dependence of the focal length or deflection angle for different wavelengths. In other words, for dispersion-less deflection angle and focusing performance, the device needs unit structure designs with properly dispersive phases.

Many studies have been conducted to overcome this single-wavelength limitation of early metalens designs. First, metalenses that can operate at multiple wavelengths have been proposed, taking advantage of the diversity of potential unit structure designs that can induce the same phase for a given wavelength. Second, some studies report broadband devices through dispersion engineering over a continuous wavelength band.

3.2.1 Multi-wavelength metalenses

For some applications, such as information displays using dual or triple lasers as light sources, independent controllability of light only at two or three wavelengths rather than in a continuous wavelength band is sufficient. In general, by introducing a larger number of different unit structure designs into the same device compared to a single-wavelength operation device, one can acquire enough degrees of freedom that allows manipulating light at different wavelengths independently, with the required number of different designs increasing rapidly with the number of target wavelengths. There are two main approaches of incorporating more designs into the same device. First, multi-wavelength operation enabled by spatially multiplexing the sub-arrays for each wavelength has been reported. Second, a method using a different unit structure design for each combination of different phases at each wavelength has been suggested. In this second case, light with each target wavelength still utilizes the entire device but sees different spatial phase profiles so that the same focal length or deflection angle can be achieved. Rather than trying to achieve the same function at each wavelength, both of these techniques can be modified to show very different device behavior for each wavelength on purpose such that the device acts as a convex lens for one wavelength and a concave lens for another or acts as a wavelength-based router for example.

Spatial multiplexing can be further categorized into in-plane and out-of-plane multiplexing. Figure 10A shows a double-wavelength metalens operating at 915 and 1550 nm using in-plane spatial multiplexing [126]. Metalenses are designed independently for each wavelength and then spatially multiplexed by dividing the lens aperture or interleaving both meta-atoms. Other approaches such as using meta-molecule composed of different combinations of meta-atoms [127], the shared aperture technique [128], and merging of sub-arrays composed of wavelength-selective meta-atoms [129], [130], [131] can be included in this category. On the other hand, Figure 10B shows the use of a multilayer metallic structure for spatial multiplexing in the out-of-plane direction [132]. Each layer acts as a Fresnel zone plate at the different target wavelength. A multi-wavelength metalens using a dielectric multilayer structure has also been reported [133], [134].

Figure 10:

Multiwavelength metalenses. (A) Dielectric metasurface with in-plane spatial multiplex. Left panels show two spatial multiplexing schemes: lens aperture division in top panel and interleaving of meta-atoms in bottom panel. Right panels show measured intensity profiles at two different wavelengths. Adapted from Ref. [126]. Copyright 2016, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (B) Metalens with out-of-plane spatial multiplexing. Left panels show the schematics and right panels illustrate intensity profiles at three target wavelengths. Adapted from Ref. [132]. Copyright 2017, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (C) Metalens with dispersion-engineered dielectric motifs. Top-left panel shows schematics of structure and required phases at different wavelengths. Remaining panels show intensity profiles at three target wavelengths. Adapted with permission from Ref. [135]. Copyright 2015, American Association for the Advancement of Science. (D) Metalens for tri-color routing. Left panel describes the application concept and middle panel shows how building blocks are arranged. Right figure shows measured results in focal plane. Adapted with permission from Ref. [129]. Copyright 2017, American Chemical Society. (E) Dual-wavelength metalens for two-photon microscopy [137]. Left panel provides working principle and right panels compare measured images for a conventional lens and dual-wavelength metalens. Adapted with permission from Ref. [137]. Copyright 2018, American Chemical Society.

A unit structure can be designed to have the required phase responses for several target wavelengths simultaneously because of its tailorable dispersive characteristics if enough design degrees of freedom are allowed. Several studies have been reported using these kinds of dispersive unit structures [135], [136], [137], [138]. Figure 10C shows a di-atomic unit structure made of dielectric cuboids that can independently control the phase at three wavelengths in the infrared regime [135]. The widths of each cuboid as well as their separation provide the design freedom. By virtue of the independent phase controllability of this structure, dispersion-less focusing and beam deflection have been realized by encoding different phase distribution for each wavelength in the same space.

The independent designability at each wavelength also leads to novel applications. Figure 10D shows a tri-color routing metalens enabled by the spatial multiplexing technique [129]. Taking advantage of the independent phase controllability, three wavelengths can be focused on the different positions, potentially eliminating the need for absorptive type of color filters that severely decreases the quantum efficiency of color image sensors. Figure 10E shows a dual-wavelength metalens used for two-photon microscopy [137]. This study demonstrates that the microscopy performance when using a metalens is comparable to that of conventional two-photon microscopy.

Using the multi-wavelength metalens discussed above, large-aperture lenses with relatively high NA can be more readily realized compared to the case of a white-light metalens that works over the entire visible wavelength range. However, some applications do require devices that perform well over a broad and continuous set of wavelengths, which will be discussed in the following subsection.

3.2.2 Continuous-band metalenses

For white-light imaging systems, conventional displays with broadband light sources, or any other application in which we cannot limit the illumination to a few narrow and discrete wavelength bands, a drastically different approach is required. Especially, typical white-light imaging setups necessitate the focal length of their lenses to remain almost constant over the entire visible spectrum. If the chromatic aberration is not well controlled, color fringing, loss of resolution, and other defects can manifest. In this section, studies that have suggested solutions to the above problem will be discussed.

First, we look at general requirements for a continuous-band metalens with a dispersion-less focal length over a broad wavelength range. The derivation is similar to that in Ref. [124] but with emphasis on how the metalens can overcome conventional lens’s limit. The broadband operation can be achieved if the phase and its dispersion for the target wavelength can be controlled. From Eq. (5A), the relation between the required phase and its first derivative at any spatial position on the metalens can be expressed as

(6)ϕ′(r,ω)−C′(ω)=1ω{ϕ(r,ω)−C(ω)}

where ϕ′(r, ω) and C′(ω) are (partial) derivative of ϕ(r, ω) and C(ω) with respect to ω, respectively. Higher order derivatives of ϕ should be identical to those of C(ω) according to Eq. (5) and affect higher order dispersion such as group delay dispersion. Please note that the second and higher-order partial derivatives of ϕ with respect to ω are only functions of the frequency with no position dependence. Therefore, all required phases and dispersions over every spatial point on metalens can be expressed on the ϕϕ′-plane, as shown in Figure 11A, implicitly assuming that other higher order terms are identical regardless of position on the metalens. For this ϕϕ′-plane, in which ϕ′ is normalized by h/c and corresponds to an effective group index (making visualization of conventional lens limits easier) and ϕ is represented with its principal angle between 0 and 2π, Eq. (6) is a straight line segment passing through point (C(ω), C′(ω)) with slope of c/(ωh), which is cut and shifted by 2π in ϕ whenever it hits the principal angle boundary. The starting and ending points of the line segment can be found from Eq. (5) if the size of the metalens and the focal length are given as the equation immediately shows the minimum (ϕ_min) and maximum (ϕ_max) unwrapped values of ϕ required, for a fixed C(ω). As ϕ′(r, ω) ‒ C′(ω) is proportional to ϕ(r, ω) ‒ C(ω), the starting point (ϕ_min) is the point with the minimum ϕ′ and the ending point, the maximum. Note that the principal angle of ϕ_min can be larger than that of ϕ_min due to 2π wrapping.

$Figure 11: ϕϕ′-plane. (A) Concept of ϕϕ′-plane. Black line segments show all possible combinations of ϕ and ϕ′ for conventional lenses made of dispersion-less dielectric materials with refractive index between nair (= 1) and nd (= 4), when the thickness is h = 7.54 c/ω (600 nm). Gray dashed line segments are guide for the eye. Blue dashed lines show the lower and upper bounds of thickness-normalized ϕ′ imposed by nair and nd. Red circle is the point corresponding to the dispersion represented by a red dashed line in Figure 11D. Blue circle corresponds to a different phase but the same first derivative with that of red circle. Red dashed line shows all points with the same ϕ′c/h as the red circle and can be implement with the same unit structure with proper rotation if geometric phases are utilized. (B) Schematics of a conventional lens (top) and its equivalent gradient index lens (bottom). (C) Dispersion relation of a quasi-static composite medium made of dispersion-less materials. Two dashed lines are light lines of component materials. (D) An example of dispersion relation of metamaterial. Red dashed line is a tangent line to the dispersion relation at the target frequency of 600 THz.$

Figure 11:

ϕϕ′-plane. (A) Concept of ϕϕ′-plane. Black line segments show all possible combinations of ϕ and ϕ′ for conventional lenses made of dispersion-less dielectric materials with refractive index between n_air (= 1) and n_d (= 4), when the thickness is h = 7.54 c/ω (600 nm). Gray dashed line segments are guide for the eye. Blue dashed lines show the lower and upper bounds of thickness-normalized ϕ′ imposed by n_air and n_d. Red circle is the point corresponding to the dispersion represented by a red dashed line in Figure 11D. Blue circle corresponds to a different phase but the same first derivative with that of red circle. Red dashed line shows all points with the same ϕ′c/h as the red circle and can be implement with the same unit structure with proper rotation if geometric phases are utilized. (B) Schematics of a conventional lens (top) and its equivalent gradient index lens (bottom). (C) Dispersion relation of a quasi-static composite medium made of dispersion-less materials. Two dashed lines are light lines of component materials. (D) An example of dispersion relation of metamaterial. Red dashed line is a tangent line to the dispersion relation at the target frequency of 600 THz.

Now one can realize a broadband metalens as long as one can find a corresponding unit structure design for each point on the above line segment on the ϕϕ′-plane, with identical higher order dispersion terms, and place those unit structures at the appropriate positions on the metalens. Since the choices of C(ω) and C′(ω) are arbitrary, one only needs to find such unit structures for any shifted version of the line segment on the ϕϕ′-plane. While the line segment has infinite number of points, a finite, discrete set of points would suffice in practice due to non-zero size of each unit structure. It is useful to note that broadband beam deflection can in principle be achieved with the identical line segment on the ϕϕ′-plane and, hence, identical unit structure designs, as with the broadband metalens if their ϕ range ϕ_max ‒ ϕ_min (equivalently, their ϕ′ range) and the thickness are the same, because Eq. (5B) has the same relation between the required ϕ and ϕ′. Of course, those unit structures will be placed on different positions on the device surface and the way a discrete set of points are chosen out of the continuous line segment can also be differentiated to optimize the efficiency and other performance parameters.

Conventional lenses, if their thickness is much smaller than the radius of curvature of their surfaces, bend light by imparting different amounts of propagation phase to the incident light depending on the position on the lens. Such lenses can be represented with equivalent gradient-index lenses composed of two materials (air as a low-index material and titanium dioxide as a high-index material, for example) forming composites with spatially varying volume fractions but with a uniform thickness, h, as shown in Figure 11B. While a direct comparison between conventional lenses and metalenses is also possible, the substitution of conventional lenses with equivalent gradient-index lenses can make intuitive understanding of metalenses easier due to their uniform thicknesses. If both of two constituent materials are in their transparent regime (loss-less and dispersion-less), their quasi-static composite with deep-subwavelength-sized motifs is also in a transparent regime if we ignore Rayleigh scattering and its dispersion relation appears as a straight line with a slope corresponding to the inverse of its effective index as shown in Figure 11C. As both constituent materials have real permittivities, CWB as well as LWB, introduced in the materials section, becomes a straight line segment between those two permittivities on a complex permittivity plane. Therefore, the effective index of the quasi-static composite is always between those of two constituent materials and its dispersion line lies between the light lines of the low and high-index materials (Figure 11C). A different choice of the volume ratio between two constituent materials results in a different slope of the dispersion line and can be mapped to a different point on the ϕϕ′-plane. The combinations of ϕ and ϕ′ realizable by the dispersion-less composite materials are represented as a (wrapped) black line segment with zero higher order phase derivative terms in Figure 11A; this line segment, when extended and properly wrapped, passes through the origin as shown with a gray dashed line and has a slope of c/(ωh). It shows, even though it is an obvious conclusion, that a conventional lens made of dispersion-less materials can work over broadband because it can realize all the required combinations of ϕ and ϕ′, if the full range of ϕ′c/h can be supported. However, in general, the dispersive nature of conventional optical materials inevitably induces chromatic aberration as the realizable points on the ϕϕ′-plane deviate from a perfect straight line.

More importantly, the above discussion illustrates why constructing a thin lens with high NA and large size has been a very challenging problem, both via conventional lens and metalens routes. To simultaneously achieve high NA and large size, the range of ϕ (and therefore the range of ϕ′c/h) should be wide. As thickness reduces, the required range of ϕ′c/h widens further, being inversely proportional to the thickness. For dispersion-less, quasi-static composites, however, this range is limited by the refractive index of the constituent materials. The straight dispersion line in Figure 11C indicates that the phase and its thickness-normalized derivative are simply ϕ = n_effωh/c and ϕ′c/h = n_eff, where n_eff is the effective refractive index of the composite and varies between that of the low-index material (n_air) and the high-index material (n_d). Therefore, the upper and lower limits of achievable ϕ′c/h for quasi-static composite-based graded index lenses are simply n_d and n_air, represented as blue dashed lines in Figure 11A. If silicon is used, n_d can reach 4 in the visible wavelength range, but it is quite dispersive and lossy. Practically realizable ϕ′c/h range for dispersion-less composites are well below three and this places the lower bound on h for a given NA and lens size.

However, if unit structures with engineered dispersions are utilized, this limitation can be overcome to certain degrees. A conceptually simple example is an array of high-index pillars, which can be considered as vertically aligned arrays of dielectric waveguides. Let’s assume that a hypothetical guided mode of the system propagating in the vertical direction has effective dispersion as shown in Figure 11D where β_eff = ϕ/h. The magnitude of ϕ′ can be seen from the slope of the red dashed line. These ϕ and ϕ′ are represented by a red circle in Figure 11A, which shows that it is possible to reach a higher ϕ′, beyond the limit imposed by the materials and the thickness. In other words, it is possible to make a lens with a thinner thickness with the same NA and size, or with larger NA and size with the same thickness. In addition, within the limit, more diverse combinations of ϕ and ϕ′ are possible such that the ϕϕ′-plane can be densely populated through various waveguide designs. However, it should be noted that all unit structures used in a metalens should have similar higher order derivatives of ϕ to enlarge the bandwidth as previously explained. Finding a set of such structures could still be a challenging procedure especially when strong dispersion is utilized to overcome the thickness limit of natural materials because an artificially large group index typically involves large higher-order dispersion terms as well. Thus, a practical design may require additional schemes such as adoption of geometric phases as in some of the works introduced below.

After the demonstration of the broadband metalens with 60 nm bandwidth in the visible regime [139], many studies on broadband metalenses have been conducted in various frequency regimes such as the visible [11], [140], [141], [142], [143], [144], infrared [124], [145], [146], [147], and terahertz regimes [148]. Figures 12A,B show visible broadband metalenses using titanium dioxide (TiO₂) and gallium nitride, respectively [11], [141]. It is noteworthy that the phase (ϕ) is controlled through the geometric phase and the phase dispersion (ϕ′) is controlled by the unit cell structure, so that ϕ and ϕ′ can be decoupled, which greatly reduces the diversity of the unit cell structure required for the achromatic metalens. This advantage of decoupling can be seen in Figure 11A. If the phase and the first derivative are coupled, the combinations of ϕ and ϕ′ indicated by the red and blue circles must have different unit cell structures. However, if they are decoupled and phase can be controlled simply by the orientation, all combinations of ϕ and ϕ′ on the red dotted line can be achieved with the same unit cell structure. In Figure 12A, a nearly constant focal length over visible regime is experimentally demonstrated using a unit cell structure having one or more TiO₂ nano-fin structures [11]. In the same study, it was also demonstrated that this broadband metalens technique can be used to reduce chromatic aberration of commercial lenses. In Figure 12B, GaN nano-posts and its inverse structures are used to realize various phase dispersions [141]. In addition to the aforementioned studies, visible metalenses with silicon nitride [142] or aluminum [144] have also been reported.

Figure 12:

Dispersion-engineered continuous-band metalens. (A–B) Visible metalens. (A) Metalens based on TiO₂ nano-fin structure. Left panel is SEM image of fabricated sample. Scale bar, 500 nm. Right panel shows measured intensity profiles. Adapted with permission from Ref. [11]. Copyright 2018, Springer Nature. (B) Metalens based on gallium nitride (GaN) nano-post and its inverse structure. Top panel is SEM image of fabricated sample. Scale bar, 500 nm. Bottom panel shows measured intensity profiles. Adapted with permission from Ref. [141]. Copyright 2018, Springer Nature. (C) Polarization-insensitive metalens with complex cross-sections. Left panel shows fabricated sample. Scale bar, 5 μm. Right panel shows measured intensity profiles. Adapted from Ref. [124]. Copyright 2018, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (D) Polarization-insensitive metalens with anisotropic structure. Left panel shows fabricated sample. Scale bar, 1 μm. Inset shows magnified and oblique view with scale bar of 500 nm. Adapted from Ref. [140]. Copyright 2019, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (E) Metalens array for light-field imaging. Top-left panel is schematics of light-field imaging using metalens. Bottom-left panels shows fabricated sample. Scale bars, 5 and 1 μm, respectively. Right panels show rendered images with focusing depths of 48.1, 58.2, and 65.3 cm, respectively. Adapted with permission from Ref. [143]. Copyright 2019, Springer Nature. (F) Broadband meta-corrector. Top-left panel shows complex optical system corrected by meta-corrector. Top-right panel shows required group delay and group delay dispersion. Bottom panels show results measured with and without meta-corrector. Adapted with permission from Ref. [149]. Copyright 2018, American Chemical Society.

While the geometric phase is a very useful tool, many metalens designs adopting the principle require a circularly polarized incident light and a polarizer on the output side to select the cross-polarized light. Figure 12C shows a polarization-insensitive achromatic metalens in the infrared regime [124]. Although such a polarization-insensitive metalens has already been reported [139], [147], the range of ϕ′ was small because of their simpler unit structures. In Figure 12C it can be seen that, with more complex cross-sections, a broader range of ϕ′ can be achieved so that the performance of the lens improves. Figure 12D shows a polarization-insensitive achromatic metalens with anisotropic unit cell structure [140]. Even if anisotropic meta-atoms are used, if every meta-atom is arranged at 0° or 90°, the geometric phase for both circular polarizations becomes identical and this metalens can be insensitive to the polarization of incident light. Using this approach, while meta-atoms benefit from a diversity of anisotropic structure, polarization-insensitive visible achromatic metalens can be realized.

Research on applications of metalenses has also been actively conducted in recent years. In the field of display, studies have been conducted using metalens arrays instead of microlens arrays for integral imaging [142] and light-field imaging [143]. In Figure 12E, it can be seen that for light-field imaging, a metalens array can replace a conventional microlens array which has the problem of chromatic aberration. Although it has already been suggested that metalenses can reduce chromatic aberration of commercial optics [11], Figure 12F shows the concept of a meta-corrector, which can improve the performance of much more complex optical systems by controlling the group delay and group delay dispersion [149].

Table 1 summarizes the performance of the broadband metalenses discussed above. In Figure 13, the experimental performances of the metalenses are compared. For comparison, a Figure of merit (FOM) for the performance, FOM = R⋅NA/(2h∆n), and the normalized wavelength bandwidth, ∆λ/λ_c, are used, where R is the radius of the device, h is the thickness, ∆n is the maximum index difference of the materials constituting the metalens, ∆λ is the usable bandwidth in wavelengths, and λ_c is the center wavelength. This FOM reflects the typical trade-off relationships between a conventional lens’s size and its NA for a given thickness and refractive index contrast. In conventional lenses, ϕ′ on the edge and at the center becomes, ϕ′_r=R = n_airh/c and ϕ′_r=0 = n_dh/c, respectively. Using these conditions and Eq. (5A), the FOM of a conventional lens converges to unity under small NA approximation. As can be seen in Figure 13, the achromatic metalens can overcome the limitation of the conventional lenses.

Table 1:

Summary of performance of broadband metalenses.

Year	Material	Diameter	NA	Efficiency	Wavelength range	Thickness**	Type	Reference
2017	TiO₂,SiO₂,Al	200 µm	0.2	～15%	490–550 nm	890 nm	Reflection	[140]
2017	Au,SiO₂	55.6 µm	0.268	～12%	1200–1680 nm	243 nm	Reflection	[146]
2017	Si,SiO₂,Al	500 µm	0.28	–	1450–1590 nm	1180 nm	Reflection	[148]
2018	TiO₂	26 µm	0.2	～20%	470–670 nm	600 nm	Transmission	[11]
2018	GaN	55.7 µm	0.106	～40%	400–660 nm	800 nm	Transmission	[142]
2018	Al,SiO₂	41.86 µm	0.124	～20%	420–650 nm	230 nm	Reflection	[145]
2018	Si	200 µm	0.13	～35%	1200–1650 nm	800 nm	Transmission	[125]a***
2018	Si	100 µm	0.85	–	1200–1400 nm	800 nm	Transmission	[125]b***
2019	TiO₂	26.4 µm	0.2	～30%	460–700 nm	600 nm	Transmission	[141]
2019	GaN	21.65 µm	0.216	～40%	400–660 nm	800 nm	Transmission	[144]
2019	Si₃N₄	14 µm	0.086	～47%	430–780 nm	400 nm	Transmission	[143]
2019	Si	10 µm	0.385	～50%	375–1000 nm	550 nm	Transmission	[149]
2019	Si	77.4 µm	0.82	～20%	3700–4500 nm	4000 nm	Transmission	[147]

* Approximated value.
** Thickness for a reflection type is total thickness including those of spacer and back metal mirror.
*** Different samples in same article.

$Figure 13: Comparison of experimentally demonstrated broadband metalenses. Figure of merit (FOM) and operating normalized bandwidth (∆λ/λc) of each metalens are graphically represented. FOM is represented in logarithmic scale. Red circles correspond to transmission type metalenses. Blue squares correspond to reflection type metalenses. Black dotted line shows FOM of conventional lens with dispersion-less refractive indices. For calculation of ∆n in FOMs, which is defined as ∆n = n1− n2, representative indices for each band were chosen and then were assumed to be dispersion-less over the band. Utilized refractive indices for each data point are as following. For [11], n1 = 2.65 (TiO2), n2 = 1 (air). For [124], n1 = 3.5 (Si), n2 = 1 (air). For [139], n1 = 2.65 (TiO2), n2 = 1 (air). For [140], n1 = 2.65 (TiO2), n2 = 1 (air). For [141], n1 = 2.41 (GaN), n2 = 1 (air). For [142], n1 = 2 (Si3N4), n2 = 1 (air). For [143], n1 = 2.41 (GaN), n2 = 1 (air). For [144], n1 = 1.45 (SiO2), n2 = 1 (air). For [145], n1 = 1.45 (SiO2), n2 = 0.52 (Au). For [147], n1 = 3.5 (Si), n2 = 1 (air). For [148], n1 = 3.45 (Si), n2 = 1 (air).$

Figure 13:

Comparison of experimentally demonstrated broadband metalenses. Figure of merit (FOM) and operating normalized bandwidth (∆λ/λ_c) of each metalens are graphically represented. FOM is represented in logarithmic scale. Red circles correspond to transmission type metalenses. Blue squares correspond to reflection type metalenses. Black dotted line shows FOM of conventional lens with dispersion-less refractive indices. For calculation of ∆n in FOMs, which is defined as ∆n = n₁− n₂, representative indices for each band were chosen and then were assumed to be dispersion-less over the band. Utilized refractive indices for each data point are as following. For [11], n₁ = 2.65 (TiO₂), n₂ = 1 (air). For [124], n₁ = 3.5 (Si), n₂ = 1 (air). For [139], n₁ = 2.65 (TiO₂), n₂ = 1 (air). For [140], n₁ = 2.65 (TiO₂), n₂ = 1 (air). For [141], n₁ = 2.41 (GaN), n₂ = 1 (air). For [142], n₁ = 2 (Si₃N₄), n₂ = 1 (air). For [143], n₁ = 2.41 (GaN), n₂ = 1 (air). For [144], n₁ = 1.45 (SiO₂), n₂ = 1 (air). For [145], n₁ = 1.45 (SiO₂), n₂ = 0.52 (Au). For [147], n₁ = 3.5 (Si), n₂ = 1 (air). For [148], n₁ = 3.45 (Si), n₂ = 1 (air).

3.3 Multi-color meta-holograms

Holography is a three-dimensional imaging technique that can record and reconstruct wavefronts scattered from a target object. It has been researched as a potential direction for next generation displays. Technically, holography involves encoding spatially varying phase and/or amplitude information in the hologram plane to obtain, through a reference beam, a holographic image in the imaging plane. In principle, the spatial modulation required in the hologram plane can be obtained inversely from the light fields to be generated at the imaging plane if both amplitude and phase are known. By virtue of the strong capability of manipulation of light waves with subwavelength resolution, metamaterials can be used as spatial modulators to achieve high quality holograms suppressing unwanted diffraction orders and having large field of view.

In case of far-field holograms, the images directly reflect the intensity distribution in the spatial frequency domain (k-space), which can be obtained by two-dimensional Fourier transform of the spatial profile of electromagnetic fields in the hologram plane. If dispersion-less phase modulation can be imparted on a uniform plane wave incident at the hologram plane, it will produce the same intensity distribution at all wavelengths in the in-plane spatial frequency domain (k_∥-space). However, the same tangential wavevector (k_∥) results in different normal wavenumbers (k_⟂) at different wavelengths as the length of the total wave vector (k₀ = |k|) is inversely proportional to the wavelength in air. Thus, the angular size of an image in the far-field region, determined by the direction (k/k₀) of the wave vectors, becomes different at different wavelengths, as shown in Figure 14A. On the other hand, for dispersion-less images, the phase modulation profile at each wavelength must be scaled in the spatial domain. If the phase has a linear dependence (ϕ = αx where α is the slope) on the spatial domain, scaling the space with the factor ω₁/ω₂ (unchanged ϕ, x→ x⋅ω₁/ω₂) is the same operation as scaling the phase at each position with the factor ω₂/ω₁ (ϕ→ϕ⋅ω₂/ω₁, unchanged x). For this simple spatially linear phase distribution, a dispersion-less beam deflection in the continuous wavelength bandwidth has been achieved. However, in general, realizing a complex dispersion-less hologram over a broad and continuous band is even more challenging than broadband lenses, which can be regarded as a simple, specialized case of hologram with a Gaussian profile as the image, because it requires very wide range of ϕ′ and good control on higher order derivatives to realize something like Figure 14B.

Figure 14:

Concept of broadband hologram. (A) Dispersion-less phase hologram. Blue and red colors correspond to high and low frequencies, respectively. Left figures show dispersion-less phase distributions over the spatial domain in which phase distributions for red and blue frequencies are identical. Right figures show resulting images in normalized spatial frequency domain. (B) Dispersion-less image hologram. Left figures show required phase distributions, which are scaled with respect to frequency, for images with identical size. Right figures show resulting dispersion-less images in normalized spatial frequency domain.

Holograms with dispersion-less phase are widely studied even though they give different sized image for various wavelengths. There have been studies demonstrating broadband operation by encoding the dispersion-less phase using the geometric phase or detour phase. In such cases, if the efficiency is high enough over the frequency band, images of the same shape, albeit with different sizes, can be produced with a broadband light source. Using dispersive unit structures, it has been reported that meta-holograms can achieve congruent holographic images at discrete target wavelengths [150]. Such multi-wavelength holograms can be generalized to produce intentionally different images for three monochromatic light sources, and are known as full-color holograms. In this section, main research related to the above technologies will be discussed.

3.3.1 Meta-holograms with dispersion-less phase modulation

The first way to make a dispersion-less phase is to use the aforementioned geometric phase. Since the geometric phase has the advantage that any phase distribution can be simply implemented, it has been widely used to realize meta-holograms [151], [152], [153], [154], [155], [156]. Figure 15A shows a reflection type meta-hologram with gold nano-rod structures [151]. It is working over the visible-near infrared regime. Recently, dielectric-based meta-holograms that can operate over the full visible wavelength have been reported [155].

$Figure 15: Meta-hologram. (A–C) Dispersion-less phase meta-hologram. (A) Meta-hologram with geometric phase. Adapted with permission from Ref. [151]. Copyright 2015, Springer Nature. (B) Conceptual explanation of detour phase. (C) Polarization multiplexed meta-hologram with detour phase. Left panel shows fabricated sample. Scale bar, 1 μm. Inset is zoomed-in view with scale bar of 200 nm. Right panels show captured holographic images. Adapted from Ref. [158]. Copyright 2018, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (D–G) Full-color meta-hologram. (D) Meta-hologram with polyatomic unit cell structure. Top-left panel shows schematic of polyatomic unit cell. Top-right panel shows fabricated sample. Scale bar, 1 μm. Bottom-left panel shows diffraction efficiency of resonators for three primary colors. Bottom-right panel shows captured colorful image. Adapted with permission from Ref. [150]. Copyright 2016, American Chemical Society. (E) In-plane image-multiplexed meta-hologram. Left panel shows working principle. Right panel shows simulated result. Since red dotted line corresponds to light line of free space, only center image can be propagated to the far-field region. Adapted from Ref. [168]. Copyright 2016, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC). (F) Out-of-plane image-multiplexed meta-hologram. Left panels show the working principle included in the supplementary information of [173]. Top-left panel shows images generated when incident light is left-circularly polarized. Bottom-left panel shows images generated when incident light is right-circularly polarized. Right panel shows schematic of proposed meta-hologram with six independent channels. Adapted with permission from Ref. [173]. Copyright 2018, American Chemical Society. (G) Meta-hologram with desired dispersion. Left panel shows fabricated sample. Right panel shows simulated images. Adapted with permission from Ref. [176]. Copyright 2018, American Chemical Society.$

Figure 15:

Meta-hologram. (A–C) Dispersion-less phase meta-hologram. (A) Meta-hologram with geometric phase. Adapted with permission from Ref. [151]. Copyright 2015, Springer Nature. (B) Conceptual explanation of detour phase. (C) Polarization multiplexed meta-hologram with detour phase. Left panel shows fabricated sample. Scale bar, 1 μm. Inset is zoomed-in view with scale bar of 200 nm. Right panels show captured holographic images. Adapted from Ref. [158]. Copyright 2018, The Authors. Distributed under a Creative Commons Attribution 4.0 International License (CC BY). (D–G) Full-color meta-hologram. (D) Meta-hologram with polyatomic unit cell structure. Top-left panel shows schematic of polyatomic unit cell. Top-right panel shows fabricated sample. Scale bar, 1 μm. Bottom-left panel shows diffraction efficiency of resonators for three primary colors. Bottom-right panel shows captured colorful image. Adapted with permission from Ref. [150]. Copyright 2016, American Chemical Society. (E) In-plane image-multiplexed meta-hologram. Left panel shows working principle. Right panel shows simulated result. Since red dotted line corresponds to light line of free space, only center image can be propagated to the far-field region. Adapted from Ref. [168]. Copyright 2016, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC). (F) Out-of-plane image-multiplexed meta-hologram. Left panels show the working principle included in the supplementary information of [173]. Top-left panel shows images generated when incident light is left-circularly polarized. Bottom-left panel shows images generated when incident light is right-circularly polarized. Right panel shows schematic of proposed meta-hologram with six independent channels. Adapted with permission from Ref. [173]. Copyright 2018, American Chemical Society. (G) Meta-hologram with desired dispersion. Left panel shows fabricated sample. Right panel shows simulated images. Adapted with permission from Ref. [176]. Copyright 2018, American Chemical Society.

The detour phase also exhibits dispersion-less phase characteristics. If an aperture is slightly displaced from its original position in an otherwise regularly arranged, diffracting aperture array, the contribution to a non-zeroth order diffracted light from that particular aperture has an additional phase factor controlled by the amount of displacement [157]. The additional phase, named a detour phase, is expressed as ∆ϕ = 2πD/Λ for the first-order diffraction, where D is the displacement from the original position and Λ is the period of the unperturbed aperture array (Figure 15B). Studies have been conducted to replace apertures using nanostructured scatterers []. In Figure 15C,A meta-hologram is achieved in the visible-near infrared regime by using the detour phase [158]. Because of its anisotropic unit structure shape, it possesses a polarization-sensitive response, which can be used to encode different holographic images for two orthogonal linear polarizations.

To improve the quality of holograms by reducing speckle noises and to increase the information capacity of the hologram, studies using additional properties such as amplitude and polarization have also been suggested. To manipulate both phase and amplitude, X-shaped meta-atoms have been utilized in [160]. Since amplitude is also controlled by geometry, the design provides well-controlled phase and amplitude modulation over broadband. By using diatomic meta-molecules, it is demonstrated that the polarization state of the image can also be controlled [161]. In [153], by designing a chiral meta-atom, independent phase encoding is implemented for orthogonal circular polarizations. Since the stepped aperture shows different transmittance values depending on the helicity of the incident light, it is possible to make a helicity-selective meta-hologram. Using a phase change material such as germanium-antimony-tellurium (GST), meta-holograms that can switch holographic images are also proposed [156]. These studies have been able to encode more information on the single meta-hologram.

3.3.2 Full-color meta-holograms

Most of modern commercial displays express various colors through a combination of three primary colors. A color image can be converted to three grayscale images, each representing the intensity distribution of each primary color. Conversely, from a device perspective, if three wavelengths of light can be spatially modulated independently, the addition of those three spatially modulated light waves will generate a colorful image. In this respect, metasurface-based full-color hologram technology has attracted much attention recently. To span the three-dimensional color space pixel-wise, the metasurface should be able to generate independent images in three wavelengths. To date, proposed methods are divided into three categories: spatial multiplexing, image multiplexing, and tri-color unit structures.

The first category is spatial multiplexing, in which three subarrays coexist on the same hologram plane. Each subarray has hologram information corresponding to one of the three primary colors. Unlike the case of a dispersion-less phase hologram, in meta-holograms in this category the unit structures must be highly wavelength-selective to prevent crosstalk between colors. “Color-block” configurations [162], [163] and “polyatomic” configurations [150], [] have been suggested. In color-block systems, the surface area is divided into small, repeated blocks of three kinds, and each block acts as single-color holographic metasurface composed of an array of unit structures whose scattering efficiency is high only near the target wavelength. This configuration greatly simplifies the design process since one do not have to worry about color cross-talks as long as the scattering efficiencies are narrow-banded, but there is a problem that unwanted images are generated due to block-size induced diffraction. On the other hand, several recent studies take the polyatomic approach and includes those three different kinds of unit structures, each scattering a narrow band of wavelengths, in a single unit cell. If the polyatomic unit cell size is still sub-wavelength, there is no additional diffraction unwantedly introduced. However, care must be taken such that the near-field coupling between sub-units is minimized to avoid color cross-talks. Figure 15D shows a full-color meta-hologram generated by a polyatomic structure [150]. Since the mode is well-confined in the individual high index dielectric structure, crosstalk between color channels is small, resulting in a clear image. However, both of these multiplexing methods through spatial mixing have the disadvantage that the maximum efficiency is reduced as the number of color channels increases [167].

The second category is image multiplexing, in which intensity profiles of three colors are all encoded into the same metasurface and each monochromatic light incident on it generates all three intensity images at different locations. By designing the metasurface and the illumination such that the correct set of three images are formed at the target location, one can realize a full-color image. Commonly, a dispersion-less phase modulation method, usually by using the geometric phase, is used. Image multiplexing is divided into in-plane [168], [169], [170] and out-of-plane [164], [171], [172], [173], [174], [175] schemes depending on where those three intensity images appear with respect to one another for a monochromatic illumination. For in-plane image multiplexing, the hologram is encoded such that the images for the three colors (for example, R, G, and B letters in Figure 15E) are located at different positions on the imaging plane [168]. Note that all three images may appear for each monochromatic illumination. When three monochromatic illuminations are used, the relative positions of these three sets of three images in the imaging plane can be further controlled as the incident angle of each color source changes. In other words, if each color source is illuminated at the designed angle, the desired colorful image can be reconstructed on a specific part of the imaging area. Out-of-plane image multiplexing can be used within the Fresnel diffraction region. Unlike the far-field region, the Fresnel diffraction region allows different images to be formed depending on the location of the imaging plane in relation to the hologram plane. If the wavelength of incident light is changed, the distance between the imaging plane where each image is formed and the hologram plane is also changed. This is graphically represented in Figure 15F [173]. One thing to note is that in the Fresnel diffraction region, geometric phase can produce different images for orthogonal circular polarizations. This is because focusing is required to form an image in this region. For example, when the image for right circular polarization is focused, then the image for left circular polarization diverges, such that it does not appear as an image. In [173], six independent hologram channels are realized by out-of-plane image multiplexing.

In the last category, the designable phase dispersion of unit structure is fully utilized to provide a way to implement all the necessary phases at three wavelengths in the same unit structure. This can be understood as an extension of a multi-wavelength metalens. In [176], a highly dispersive dielectric unit structure is realized using guided mode resonances. Since the phase can be adjusted independently, the required phase distribution can be generated for each wavelength.

Like the dispersion-less phase holograms, various research directions in full-color holograms have also been pursued in attempts to increase their information capacity or to obtain more functionality. In [164], a hologram showing different colorful images depending on the location of the imaging plane has been proposed using a combination of spatial multiplexing and out-of-plane image multiplexing. In [169], it has been demonstrated that with two-step (on and off) amplitude manipulation it is possible to reduce speckle noise, an intrinsic problem of phase-only holograms. By combining a color filter and a meta-hologram, meta-hologram with microprint functionality is presented [177], [178], [179]. Particularly, in [177], a color filter and meta-hologram are realized on a single metamaterial. While most studies have assumed either the reflection mode or the transmission mode of operation, in [170], a meta-hologram that simultaneously generates different images on the reflection and transmission sides has also been proposed.

4 Conclusion

In this review, we surveyed recent studies on electromagnetic metamaterials that have attempted to achieve either exotic properties as materials or outstanding performance as devices, uniformly over a broad frequency range. Results can be summarized as follows.

For broadband electric permittivity, capacitive coupling between metallic inclusions is mainly utilized to achieve nearly dispersion-less values in a broad frequency range below the resonance frequency. For broadband magnetic permeability, the main mechanism is Faraday induction of currents inside inclusions and the low-dispersion regime appears above the resonance frequency. Broadband optical activity and polarization rotation can also be achieved in frequency regimes higher than the resonance frequency and remnant dispersion can be further suppressed when the resonance frequency is sent to zero.

In order to achieve broadband device performance, an elaborate control of dispersion is required. For broadband absorption with thin meta-absorbers, a high degree of design freedom of the dispersive sheet admittance of incorporated metamaterial layers is the key ingredient in matching the input admittance of the meta-absorber to the intrinsic admittance of the incident-side medium over a broad frequency range. Alternatively, if applications allow the use of absorbers that are more than several wavelengths thick, a diluted volumetric meta-absorber with weakly absorbing inclusions can show very high absorption over broad frequency ranges. Regarding broadband lenses and holograms, maintaining the same focal length and holographic images, respectively, over a broad wavelength range are the objectives. While broadband meta-lenses have been realized mainly by control of the transmission or reflection phase and its first-order dispersion, white-light holograms are much more challenging because they require extreme dispersions with precise control on higher order terms. However, meta-holograms designed to work at a few discrete narrowband wavelength ranges (e.g. red, green, and blue) instead of the entire visible spectrum may be sufficient for applications such as color displays, in which one can control the illumination.

There are several issues to overcome for wide use of broadband metamaterials and broadband metamaterial-based devices. First, optical loss due to conductive inclusions should be minimized. Although all-dielectric metamaterials are also promising and could be a more suitable solution for certain applications, metals are still popular choice for metamaterials because the opposite signs of the real part of permittivity of metal and dielectric enable exotic forms of dispersion and effective material properties. The optical loss can be mitigated by development of better materials as well as novel designs with strategic use of metals and dielectrics together. Second, high-yield manufacturing methods should be developed. Owing to the subwavelength scale unit cell sizes and even smaller minimum feature sizes, slow but high-resolution serial writing techniques such as electron beam lithography and focused ion beam milling are commonly used in laboratory. Fabrication of three-dimensional metamaterials is usually even more challenging. Nevertheless, it has been shown that bottom-up processes such as block-copolymer lithography or particle synthesis and assembly and parallel processes such as glancing angle deposition are promising techniques for complex structure fabrication.

Broadband electromagnetic properties and functionalities are under active investigation, with many important but unexplored topics remaining. Specifically, efforts to realize near dispersion-less properties can be expanded to nonlinear or general bianisotropic constitutive parameters. In addition to the previous demonstrations of broadband cloaks and solar energy applications, broadband enhancement of general light–matter interaction can be used in other areas such as efficient sensing of various substances with different interaction spectrums, metamaterial achromatic refractive optics, and many others. Regarding device-focused metamaterial research, novel strategies for broadband functionality and demonstrations with serious consideration on their practicality are increasing in numbers. In particular, achromatic lens and hologram related works are developing rapidly and may see commercial applications in near future. We anticipate that the broadband metamaterials and metamaterial-based devices can provide ground-breaking solutions for the current issues in state-of-the art electromagnetic platforms.

Corresponding authors: Taeyong Chang and Jonghwa Shin, Department of Materials Science and Engineering, KAIST, Daejeon, 34141, Republic of Korea, E-mail: taeyong08@kaist.ac.kr (Taeyong Chang); qubit@kaist.ac.kr (Jonghwa Shin)

Joonkyo Jung, Hyeonjin Park, and Junhyung Park: These authors contributed equally to this work.

Acknowledgments

This work is supported by National Research Foundation (NRF) grants (NRF-2019M3A6B3031046, NRF-2018M3D1A1058998) funded by the Ministry of Science and ICT (MSIT), Republic of Korea.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-02-13

Accepted: 2020-04-28

Published Online: 2020-06-25

This work is licensed under the Creative Commons Attribution 4.0 International License.

Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Abstract

1 Introduction

2 Nearly constant constitutive parameters over broad bandwidths

2.1 Electric permittivity

2.2 Magnetic permeability

2.3 Chirality

3 Broadband metamaterial-based devices

3.1 Broadband absorbers

3.1.1 Thin meta-absorbers with admittance matching layers

3.1.2 Dilute volumetric meta-absorbers

3.1.3 Alternative physical explanations for broadband meta-absorbers

3.2 Broadband meta-deflectors and metalenses

3.2.1 Multi-wavelength metalenses

3.2.2 Continuous-band metalenses

3.3 Multi-color meta-holograms

3.3.1 Meta-holograms with dispersion-less phase modulation

3.3.2 Full-color meta-holograms

4 Conclusion

Acknowledgments

References

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