**4. Broadband metamaterial absorbers**

Various techniques have been developed for expanding the bandwidth of metamaterial absorbers. The major techniques for bandwidth enhancement includes the use of multi-layer stacked structures [39, 40], a co-planar arrangement of multiple resonant cells [56, 57], as well as adding lumped elements [58]. Highly lossy dielectrics or semiconductors have also been

**Figure 4.** Schematic view of the saw-toothed metamaterial absorber and its absorption spectrum. Reproduced from [39] with permission.

thickness of the substrate. Inspired by this pioneer work, great amounts of efforts have been devoted to the realization of metamaterial absorbers in different spectral ranges [30–40].

**Figure 3.** (a) Unit cell of dendritic metamaterial absorber and (b) simulated and measured absorptivity spectra.

The initial metamaterial absorbers are polarization sensitive because of anisotropic unit cells [29, 51]. Planar metamaterial absorbers with highly symmetric structures were developed later, such as annular and circular patch arrays [52] and snowflake cells [53, 54]. In 2009, we developed a metamaterial absorber composed of dendritic unit cells [50]. As shown in **Figure 3(a)**, the periodical array of metallic dendritic cells is on one side of the FR-4 substrate and a full ground plane on the other side. It is shown in **Figure 3(b)** that both the simulation and experiment, in accordance with each other, show over 95% absorptivity at the frequency of 10.26 GHz. Such a metamaterial absorber has an excellence of planar isotropy, which shows equal absorption performance for an incident wave with arbitrary polarizations. When scaling down the size of the dendritic metamaterial absorber to the nanoscale, it is able to achieve perfect absorption in

Metamaterials, including those metamaterial absorbers, are commonly made of periodically arranged unit cells. The imperfection in manufacture will, to some extent, affects the performance of the metamaterial. This is particularly significant in an optical regime where the unit cells of the metamaterials are of nano-scale. To study this effect, the impact of disorder in the unit-cell arrangement in the metamaterial absorber was further studied [55]. It was found that absorptivity decreases and the absorption frequency gets red-shift as the unit cells become more disorderly. However, the metamaterial absorber with random unit cells still presents

Various techniques have been developed for expanding the bandwidth of metamaterial absorbers. The major techniques for bandwidth enhancement includes the use of multi-layer stacked structures [39, 40], a co-planar arrangement of multiple resonant cells [56, 57], as well as adding lumped elements [58]. Highly lossy dielectrics or semiconductors have also been

the optical regime, which was also confirmed with numerical simulation [50].

over 95% absorptivity for a reasonable level of disorder.

**4. Broadband metamaterial absorbers**

Reproduced from [50] with permission.

138 Metamaterials and Metasurfaces

widely used for designing broadband metamaterial absorbers [59, 60]. In this section, some typical approaches for designing bandwidth-enhanced absorbers are discussed.

One of the most effective approaches for designing broadband metamaterial absorber is to stack resonant patches of different sizes. Cui et al. [39] proposed a multi-layer saw-toothed anisotropic metamaterial absorber at infrared wavelengths, as shown in **Figure 4**. Although such a metamaterial absorber is made of 21 layers of metal patches, its total thickness is still reasonably thin compared to the operating wavelength. Particularly, they demonstrated that the relative full absorptivity width at half maximum could be achieved to a figure as high as 86%. The ultra-broad bandwidth in such a layered metamaterial absorber is realized by the overlapping of multiple resonances according to the metal patches at different layers. Electromagnetic waves of higher frequencies are absorbed at the upper parts, while those of lower frequencies are trapped at the lower parts.

Intrinsic high loss in dielectrics or semiconductors can also be utilized for designing wideband absorption in simple structures [59, 60]. For example, water is a highly lossy dielectric at microwave frequencies, whose permittivity could be well described by the Debye formula [62]. **Figure 5** shows the metamaterial absorber made of a water layer (with periodical holes) placed in a resin container, which is backed with a metallic ground plane at the bottom. With such a structure, Xie et al. [61] experimentally demonstrated an ultra-broadband absorption with absorptivity higher than 90% in the entire frequency band from 12 to 29.6 GHz. To figure out whether the broadband absorption in such a water metamaterial absorber is predominantly because of the intrinsic high loss of water, they also compared the absorption spectra for the case when the full water layer without holes and the case when the resin container is empty of water. As shown in **Figure 5(d)**, they found that the absorptivity of a full water layer

**5. Frequency tunable metamaterial absorbers**

Although metamaterials, in principle, can be designed for having arbitrary electromagnetic properties, these properties are generally fixed after the design of the metamaterials [65–68]. This is also true for metamaterial-based absorbers, whose operating frequencies are very much fixed, restricting their practical applications. Therefore, metamaterial absorbers with frequencytunable characteristics are highly desirable, which allows more fruitful applications. To enable the tunability in a metamaterial absorber, one may integrate a medium with adjustable material properties into a traditional passive metamaterial absorber. Some of the proven methods include having elements, such as varactor diodes [69], ferroelectrics [70], ferrites [71], graphene

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Mechanical bending or shifting was also studied for tunable metamaterial absorbers [74–78]. Zhang et al. [76] experimentally presented a mechanically stretchable metamaterial absorber, which is composed of dielectric resonators on a thin conductive rubber layer, as shown in **Figure 7**. A nearly 100% absorption was found, along with strong localized electric field confinement due to the Mie-type resonance of the dielectric resonators. When stretching the metamaterial absorber under uniaxial stress, the space between dielectric bricks increases gradually, and therefore the resonance frequency undergoes a red-shift of 410 MHz in the X band (see **Figure 7**). Zhu et al. [78] experimentally demonstrated a metamaterial absorber whose resonance frequency can be shifted by mechanical means. The shift was achieved by

**Figure 7.** (a) Experimental and (b) simulated absorptivity spectra of the mechanically stretchable dielectric metamaterial absorber. (c) Schematic of stretching the dielectric resonators on a thin conductive rubber layer. (d) Magnetic field

distribution at the resonance frequency. Reproduced from [76] with permission.

[72, 73], anisotropic liquid crystals [74], and phase-transition materials [75].

**Figure 5.** (a) Schematic view of the water metamaterial absorber, (b) layer by layer view of the unit cell, and (c) cut plane view of the water layer. (d) Absorptivity spectra of the water metamaterial absorber, the full water layer backed by a metal ground, and the metamaterial without water. Reproduced from [61] with permission.

is only around 35–40%, while the absorptivity of the metamaterial absorber reduces to be only around 20–40% when the water is emptied. These results confirm that the ultra-broadband absorption mainly contributes to localized resonances in the structured water resonators.

Highly doped silicon has relatively low resistivity and behaves as a lossy dielectric at terahertz frequencies, which was employed for achieving broadband absorption [59]. Using a lossy patterned silicon substrate, Yin et al. [64] also experimentally demonstrated a metamaterial absorber with an operating band from 0.9 to 2.5 THz. A silicon-based metamaterial absorber, as shown in **Figure 6(a)**, was proposed for broadband high absorption at visible wavelengths [63]. Such a metamaterial absorber has three functional layers: a subwavelength silicon layer with periodic truncated conical holes, a subwavelength silicon dioxide spacer, and a thick gold substrate. As seen from the numerical results in **Figure 6(c)**, the silicon metamaterial absorber with truncated conical holes has higher absorptivity and wider bandwidth at the frequency band of interest.

**Figure 6.** (a) Schematic view of the silicon-based metamaterial absorber and (b) its unit cell. (c) Absorptivity spectra of silicon-based metamaterials with conical and circular holes. Reproduced from [63] with permission.
