## Abstract

The rapid advent of radio-frequency (RF) and microwave technologies and systems have given rise to serious electromagnetic pollution, interference and jamming for high-precision detection devices, and even threats to human health. To mitigate these negative impacts, electromagnetic interference (EMI) shielding materials and structures have been widely deployed to isolate sophisticated instruments or human settlements from potential EMI sources growing every day. We discuss recent advances in lightweight, low-profile electromagnetic absorbing media, such as metamaterials, metasurfaces, and nanomaterial-based solutions, which may provide a relatively easy solution for EMI shielding and suppressing unwanted RF and microwave noises. We present a general review of the recent progress on theories, designs, modeling techniques, fabrication, and performance comparison for these emerging EMI and electromagnetic compatibility (EMC) media.

### Keywords

- EMI
- EMC
- metamaterials
- metasurfaces
- perfect electromagnetic absorbers

## 1. Introduction

Electromagnetic absorbers have important applications in a plethora of applications, including but not limited to electromagnetic interferences and electromagnetic compatibility [1, 2, 3, 4, 5], stealth [6, 7, 8, 9], camouflage [10], shielding [11, 12, 13], energy harvesting [14, 15], as well as antenna and optical measurements [2, 16, 17, 18]. Recently, the scientific interest has focused on EMC and EMI shielding that studies how to suppress noise or interference in various electronic appliances and radiative damage to humans caused by unintended EM signals. In these applications, electromagnetic absorbers play an essential role. As one of the representative examples, a high-performance and cost-effective anechoic chamber, which can provide a zero-reflection environment mimicking free space, is of paramount importance for EMC test, antenna, and scattering measurements, among many other applications. As illustrated in Figure 1(a), in an anechoic chamber, the entire inner surfaces (walls, ceiling, and floor) are properly covered with absorbers to absorb waves propagating toward them and thus eliminate multipath interferences. Hence, a simple and well-defined propagation channel can be obtained between the transmitting source and receiving antennas or a scattering object for radar cross-section (RCS) measurements. Nearly perfect absorption, realized with an ultrathin, lightweight, and low-cost manner, makes the artificial surfaces and media (i.e., metamaterials and metasurfaces) advantageous over the conventional electromagnetic absorbers made of natural materials. Ever since the first perfect metamaterial absorber was proposed by Landy * et al.*[19], numerous designs have been proposed for metamaterial or metasurface absorbers over a wide range of frequencies [20, 21, 22, 23, 24, 25] and even with multiband operation [1, 26, 27, 28].

The applications include RCS reduction and stealth [29], EMI shielding [12, 13], sensing [30, 31, 32, 33], terahertz imaging [34, 35, 36], energy harvesting, etc. A representative modern application of metamaterial absorbers may be the enhanced isolation in the multiple-input-multiple-output (MIMO) antenna system [37, 38], as depicted in Figure 1(b). With the growing demand for miniaturization of telecommunication devices, reducing the mutual coupling or cross-talk among the antenna elements has been a challenging task in MIMO systems. A specifically designed metamaterial absorber mostly consisting of periodic resonators can help improve the isolation among antenna elements and further enhance the efficiency of a MIMO system since it can significantly absorb the unwanted interferences among antennas.

The impedance of a material is defined as

In the same vein, although the intrinsic optical loss of metals is a major limitation in the performance of these devices, it is beneficial in improving light absorption. In 2008, Landy * et al.*first proposed a perfect metamaterial absorber with near-perfect absorption by simultaneously exciting electric and magnetic resonances to achieve impedance matching with free space [19]. Soon after, important absorber designs based on different physical mechanisms have been demonstrated theoretically and experimentally in a broad spectral range, which can be classified into two categories: narrowband absorbers [57, 58] and broadband absorbers [59, 60] in terms of their absorption bandwidth. While broadband absorbers are typically used in thermo-photovoltaic systems [61], perfect narrowband absorbers may be used for absorption filters [36], tailoring thermal radiation [62], and sensing [30, 32]. For the important sensing and detection applications, the experimentally performed refractive index (RI) sensor based on infrared coherent perfect absorber (CPA) shows that a narrow bandwidth and a large modulation depth are required for better performance [32, 33]. The three-layered configuration of metal–insulator–metal (MIM) employed was widely applied to the following SPP absorbers, where a thin dielectric spacer is sandwiched to allow for strong plasmonic coupling between the top resonators and the bottom metallic reflector as discussed in depth in [22, 59]. This class of CPA designs may also be intuitively treated as a single input transmission line (TL) coupled to a plasmonic resonator, where the thickness of the insulating spacer affects the radiative damping rates as well as the resonance frequency bandwidth.

## 2. Generalized theory for perfect electromagnetic absorbers

In this section, we will discuss the basic principles of extremely thin electromagnetic absorbers composed of an infinite two-dimensional array of electric dipoles, magnetic dipoles, or both. According to the optical theorem, when the scatterer interacts with the incident fields, the power depleted from the incident fields is the sum of the absorbed and scattered powers, i.e.,

where

Finally, the total incident power flowing through the surface * S*is zero

From Eqs. (1)-(3), the total extracted power (power extinction) is given by the cross-terms

The forward scattering sum rule is valid for any arbitrary absorbers, for which the scattered power

The absorbed power

Assuming that there are no grating sidelobes, the power extinction -

This can be seen as the optical theorem for infinite two-dimensional (2D) planar structures, such as metascreens or an ultrathin absorptive film. We know from Eqs. (5)-(7) that when the forward scattered power represents the total scattered power, i.e., no backward scattered (reflected) waves, the total absorption of the incident radiation can be achieved. In this case, the scattered power equals the absorbed power,

Consider an infinite 2D electric dipole array, separated from a PEC ground plane by a distance * k*is the wavenumber of the uniform background medium. For brevity, we consider an isotropic periodic grid that can be conveniently modeled by a scalar surface impedance

where * S*is the area of a unit-cell. This scattering problem can be solved using the image theory, which removes the ground plane and places an image source of

where

For an arbitrary value

or from Eqs. (8), (9), and (12), we obtain the optimum (lossy and capacitive) surface impedance

When the distance between the array plane and the ground plane

In the following, we briefly discuss how to design and synthesize the grid array that provides the required surface impedance. It is instructive to study a metamaterial surface or metasurface formed by a 2D array of meta-atoms excited by an external electric field _{ext} with the TE polarization (Figure 2a). The collective behavior of electric dipole moments induced in electric meta-atoms will result in a homogenous sheet current. The total averaged polarization related to the local field is responsible for the

where

where

where the area of the metasurface lattice S = * d*. This is an accurate description of the array’s electromagnetic properties, as long as the periods are small enough to ensure that only one Floquet harmonic could exist. The average surface impedance of metasurface, as the ratio of the local electric field to the surface current density, can be expressed as

_{x}d

_{y}

Under the lossless and low frequency condition, the polarizability is approximately given by

So, Eq. (17) can be further reduced to

For a subwavelength lattice, i.e.,

where

where

where

This can be achieved by tailoring the size, shape, and material property (i.e., dispersion of the complex permittivity) of the elementary inclusion (i.e., meta-atom) in the metasurface unit-cell. For a Salisbury-type absorber with

The first condition implies an individual scatterer is at its self-resonance, which considers the cancelation of a general sense, the maximum absorption cross-section of each inclusion in densely packed arrays * a*and

*is its radius. In the extreme case, the polarizability of a 1D conducting rod with a deeply subwavelength radius*a

*and height*a

*, aligned parallel to the electric field of the incident wave, has only the*h

where * A*is the amplitude.

Figures 4 and 5 show metasurface absorbers based on 2D arrays of plasmonic disks [78] and electric ring resonators [79], respectively. It is clearly seen that the ultrathin and low-profile metasurface absorbers can significantly absorb the incident wave in the frequency band of interest. We note that these electric resonant inclusions can be equivalent to a 2D array of electric dipoles discussed above.

It is also possible to exploit a metasurface constituted by magnetic or magnetoelectric meta-atoms [9, 19, 22, 23] to build a perfect electromagnetic absorber. For example, Figure 2(c) and (d) consider a magnetic dipole array over a ground plane and the image. When a plane wave normally incident on the structure, the magnetic current density is induced:

and

where

The total averaged fields on the metasurface can be expressed as

where the surface impedances are given by

If the reader is interested in learning details about anisotropic magnetoelectric metasurfaces, please see Refs. [80, 81, 82].

Figure 6 shows an ultrathin electromagnetic absorber based on resonant magnetic structures. Under the excitation of a plane wave, a magnetic dipole array can be induced, and at resonance, the incident power can be absorbed, analogous to the function of the electric dipole array discussed above. The experimental results reported an absorption efficiency above 93% at 1.74 GHz at illumination angles up to 60 degrees [83]. Moreover, this absorber is 98% lighter than traditional microwave absorbers made of natural materials working at the same frequencies. As an alternative explanation, this structure can be seen as a metal-backed magnetic-near-zero (MNZ) metamaterial slab [84]. For an ultrathin metal-backed MNZ absorber, the permeability * t*is the thickness of the metamaterial slab. This magnetic metamaterial absorber can achieve zero backward scattering (

*= 0) and a large forward scattering (*R

*= 0), i.e.,*T

On the contrary, if symmetric designs are considered (e.g., a suspended resistive film with optimal sheet impedance

## 3. Hyperbolic metamaterial absorbers

Hyperbolic metamaterials (HMMs) (see Figure 8) are known for their isofrequency contour and broadband singularity in the density of photonic states, which have led to many new photonic and optical applications, including the substrate for molding spontaneous emissions into a directional beam and the “rainbow trapping” structure for broadband light absorption [25, 86, 87, 88]. The effective medium theory can describe the effective permittivity of such an artificial anisotropic medium as:

where * th*constituent materials, and

Therefore, for an anisotropic medium with extreme material properties, i.e.,

Figure 9a considers a trenched HMM slab with a periodicity * P*and air slots with width

*, illuminated by a TM-polarized plane wave. The trenched HMM substrate is, in some sense, similar to a periodic array of air/HMM/air waveguides, for which a guided mode propagating along the waveguide axis can exhibit a near-zero group velocity, i.e.,*W

where * th*mode, are evanescent. The scattering and absorption properties of this HMM-based device can be solved using the TL model (TLM) and the transfer matrix method (TMM), as shown in Figure 9. For the TM-wave illumination normally incident upon the HMM substrate, the characteristic impedance per unit length can be expressed as

*imposed by the discontinuous fields [92].*B

and

Figure 9b shows the calculated dispersion diagram of a periodically trenched HMM slab constituted by stacked silver (Ag) and copper (Cu) thin-films with thickness t_{metal}, separated by 1 nm-thick niobium oxide (Nb_{2}O_{5}) insulating layers, of which the periodicity and air gap size are 300 nm and 150 nm, respectively. The realistic material properties extracted from experiments are used [89]. It can be seen from Figure 9b that near-zero group velocity can be achieved at certain wavelengths, resulting in the slow light effect and light trapping and absorption in the lossy (dissipative plasmon loss) and anisotropic HMM region. Figure 9c presents the associated contour plot of absorptance as a function of metal thickness _{metal} [nm] and wavelength λ [μm]. We find excellent agreement between the wavelengths of maximum absorption in Figure 9c and the near-zero group velocity points in the dispersion diagram plotted in Figure 9b. We note that total HMM size is still subwavelength since the large value of

Additionally, the absorption spectrum can be readily tailored by varying the volume fraction of metal, which determines the permittivity tensor elements of HMM. Although a linear HMM-based absorber can exhibit a high and angle-independent optical absorption, its bandwidth is limited around the slow-wave modes. This limitation can be mitigated by exploiting a tapered-HMM, as shown in Figure 10a, which has been proposed to realize wideband photodetection and solar energy harvesting applications [88, 89, 90, 91]. Using tapered geometry, the bandwidth is expected to increase due to the superposition of multiple slow-wave modes. Figure 10b shows the contour plot of absorptance as a function of the photon energy and the angle of incidence. It is evidently seen that a broadband (1 eV to 1.6 eV) and wide-angle (0^{o} to grazing angle) optical absorption can be obtained with the tapered HMM substrate backed by a metallic mirror (50 nm Ag thin-film). The capability to effectively trap photons over a wide range of photon energies and illumination angles is essential for building efficient hot-electron energy harvesters or photodetectors. Finally, we note that the general limitation on the maximum bandwidth of a ground-backed absorber should always obey the passivity and causality [93], following the physical bound * th*layer of the multilayered absorptive slab. For an effective non-magnetic medium, we can define Rozanov’s limiting factor as

*is the total thickness of the absorber.*t

Similarly, an ultra-broadband HMM absorber can be realized in the RF and microwave regions by integrating two different-sized tapered HMM waveguides, as shown in Figure 11a [94], each of which has wide but different absorption bands, leading to a broadband slow-light response. By properly selecting the geometrical parameters for each waveguide in the HMM, multiple absorption bands can be achieved with different waveguides, as shown in Figure 11b. Such an approach can effectively widen the total absorption bandwidth. Experimental results in Ref. [94] validate the theoretical results, showing a very large absorption bandwidth ranging from 2.3 GHz to 40 GHz.

## 4. Future trends: reconfigurable absorbers based on plasmonic, graphene, and beyond

Electromagnetic wave absorbers are mainly utilized as boundary structures to prevent the scattering of electromagnetic fields. They can be divided into two main categories based on their operating bandwidth, i.e., resonant and broadband absorbers [95, 96]. Resonant absorbers typically depend on the designed material assemblies interrelating with the incident waves around certain resonance frequencies [96]. On the other hand, the wideband absorbers rely on material damping characteristics that are largely independent of electromagnetic frequencies and typically made of lossy dispersive materials [96]. Such broadband absorbing materials along with structural transition are commonly used in anechoic chambers to effectively emulate a non-reflecting unbounded medium suitable for testing radiating antenna elements [95]. Lately, there is an emphasis in the scientific community to design efficient plasmonic metamaterial-based absorbers. Light matter interaction in subwavelength metamaterial structures allowed various other applications including perfect lenses [45, 97], chiral surfaces [98, 99], transformational surfaces [100, 101], optical cloaking [100, 102, 103], spatial light switching [104, 105] and IR camouflage and microwave antennas because of certain useful characteristics [96]. In addition to these applications, the perfect metamaterial absorber (PMA) is designed as a tool to efficiently absorb electromagnetic waves utilizing plasmonic resonator elements embedded within its assembly.

Generally, metamaterial absorbers are composed of a patterned metal film over a continuous thin metallic film with a dielectric substrate sandwiched between them [96]. It should be noted that the definition of total absorptivity considers reflected electric field vector, i.e.,

The response of PMA is often described as an effective medium and characterized by properties such as complex electric permittivity (ε) and magnetic permeability (μ) [109]. Although much of the work on effective medium properties of metamaterials has been focused on the real part of ε and μ, as it contributes to negative refractive index properties, it is equally important to reduce losses represented by the imaginary part of ε and μ for practical applications related to wave propagation within negative refractive index medium [110, 111]. In contrast, the metamaterial absorbers rely on high material losses (large value of imaginary parts of ε and μ) and impedance matching with the background medium. Landy et al. provided the first experimental demonstration of near perfect metasurface absorption at GHz frequencies. The working principle of PMA relies on impedance matching between effective medium forming metasurface with dielectric and background medium to the free space background, rejecting the reflection and therefore efficiently absorbing the incident EM wave [19, 20]. Ever since, the design of PMAs has attracted significant attention ranging from microwave to optical frequencies [112, 113]. Apart from resonant absorption characteristics, the plasmonic effects also provide tremendous near field enhancement to improve the efficiency of solar cells [114], support for sensing [31], and enhanced thermal emission and photo-detection [115].

Recently, the electro-optic tunability of resonant absorption spectrum at THz frequencies is made possible by varying the frequency dependent conductivity of plasmonic materials through the use of graphene metasurface [22, 59]. The frequency dependent optical properties of graphene in the THz frequency range are controlled by its optoelectronic properties. The permittivity (

Here,

The surface conductivity of graphene (

Here, * v*[m/s] is the Fermi velocity, and

_{f}

*[cm*μ

^{2}/Vs] is the electron mobility,

*is temperature,*T

The real-time tunability of Graphene Surface Plasmons (GSPs) is a distinct feature offered by graphene metasurface when compared to traditional noble metals. In addition, GSPs offer other benefits such as tighter mode volume confinement and lower intrinsic losses compared to conventional surface plasmon materials. The unique electro-optic tunability of graphene conductivity within the THz band makes it an attractive candidate for plasmonic metamaterial applications. Therefore, graphene enabled the research in surface plasmons to be redirected toward reconfigurable THz wave optics applications, including GSPP waveguides [116], modulators [24], THz cloaks [117], THz antennas [118], Fourier optics [119], photonic crystal nano-cavities [120], and biochemical sensors [31, 121]. The reconfigurable response of resonant absorption can offer additional functionalities, including wave modulation, polarization conversion, and sensing.

Here, we discuss a few selected applications of reconfigurable THz metasurface absorbers, as shown in Figure 13. Figure 13(a) shows graphene micro-ribbon metasurface design capable of efficiently absorbing THz radiation [22]. The chemical potential (* i.e.*, 6.9 THz bandwidth is obtained for over 90% normalized absorption. Figure 13(c) shows a schematic illustration of the design of graphene metasurface supporting polarization state modulation with high spectral efficiency [98]. The structural chirality of metasurface is utilized to generate chiral reflection along with highly dispersive Fano resonance. Several polarization states, including two orthogonal linearly polarized, right-and left-handed circular polarized reflections, are demonstrated for a narrow electro-optic tuning range of chemical potentials between 500 and 700 meV. By exploiting these properties, highly efficient modulation stages of modern communication systems can be designed. Figure 13(d) shows a polarization-state sensing setup to distinguish closely resembling optical properties of biomolecules such as viruses [31]. The measurement consists of a plasmonic metasurface with chiral unit cells, and the polarization properties of reflected fields can determine the optical characteristics of the analyte. It is shown that the proposed sensor can distinguish three closely resembling influenza virus strains i.e., H1N1, H5N2, and H9N2 based on the variation of the reflected polarization states.

## 5. Conclusion

In this chapter, we have reviewed the most recent advances in the field of metamaterial and metasurface-based electromagnetic perfect absorbers. We have first provided a thorough theoretical investigation describing the material and geometrical conditions that may lead to a near-perfect absorption of light. Based on the well-known optical theorem, this analysis gives a power balance and clarifies the design process in the microwaves and terahertz. Next, we have discussed a peculiar and interesting class of perfect absorbers that are hyperbolic metamaterial absorbers. These devices exploit a particular dispersion of hyperbolic media and lead to robust and tunable absorbers. We finally have discussed the newly proposed graphene plasmonics based absorbers, which exploit the high conductivity and tunable optical properties of this 2D material to build some of the most appealing and versatile absorbers, with applications spanning energy harvesting, biosensing, or light polarization manipulation. This chapter can be helpful to theorists and experimentalists alike, working on the design of novel absorbers of light or even other types of waves.

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