**3. Narrowband metamaterial absorbers**

transmission coefficients. On the other hand, the highly conductive ground plane works as a perfect reflector, offering a phase delay of 180° to the electromagnetic wave reflecting on it.

**Figure 1.** Multiple reflections and interference model of metamaterial absorber. The yellow dashed line refers the

As shown in **Figure 1**, the front meta-layer resides at the interface between air and the dielectric substrate. The incident electromagnetic wave is partially reflected back to air with

reaching the metallic ground plane. The complex propagation constant inside the dielectric

tric substrate. At the ground plane, a total reflection occurs with a reflection coefficient of −1.

and transmission occur again at the front interface. The corresponding reflection and trans-

that multiple reflections and transmissions exist inside the dielectric substrate, and the totally output energy at the left side of the metamaterial is the superposition of reflections of all

where the first term in the right is the reflection directly from the meta-layer, and the second term is the contribution of the superposition of the multiple higher-order reflections. As long

in those metamaterial absorbers with metallic grounds and also provide an alternative under-

It is worth noting that the above analysis is fully based on the assumption that the incident wave is normal to the metamaterial. For the case when an electromagnetic wave incident is

21(*ω*)*ei<sup>θ</sup>*21(*ω*)

*\_\_\_\_\_\_\_\_\_\_\_* 1 *+ r ~* 21*(ω)e*2*i<sup>β</sup>*

~, the absorption spectrum of the metamaterial absorber could

. The interference theory can well explain the features observed

 and *t* ~ <sup>21</sup>(*ω*) = *t*

and partially transmitted into the substrate with a

. The transmitted wave will propagate further until

is the wavenumber of free space, *d* is the thickness of

refers to the absorption in the dielec-

, respectively. It is worth noting

*<sup>~</sup> ,* (5)

<sup>~</sup>, partial reflection

a reflection coefficient *r*

136 Metamaterials and Metasurfaces

transmission coefficient *t*

mission coefficients are *r*

as we know the total reflection *r*

be obtained by *A*(*ω*) = 1 −|*r*

<sup>~</sup> <sup>=</sup> *<sup>β</sup>*<sup>1</sup> <sup>+</sup> *<sup>i</sup> <sup>β</sup>*<sup>2</sup> <sup>=</sup> <sup>√</sup>

substrate is *β*

orders:

the substrate, *β*<sup>1</sup>

~

resonator array. Reproduced from [47] with permission.

~ <sup>12</sup>(*ω*) = *t*

\_\_

~

~(*ω*)| 2

<sup>12</sup>(*ω*) = *r*12(*ω*)*ei<sup>ϕ</sup>*12(*ω*)

*<sup>ε</sup><sup>d</sup> <sup>k</sup>*<sup>0</sup> *<sup>d</sup>*, where *k*<sup>0</sup>

<sup>21</sup>(*ω*) = *r*21(*ω*)*ei<sup>ϕ</sup>*21(*ω*)

*r <sup>~</sup>(ω) <sup>=</sup> <sup>r</sup> ~* <sup>12</sup>*(ω) <sup>−</sup> <sup>t</sup> ~* <sup>12</sup>*(ω) t ~* 21*(ω)e*2*i<sup>β</sup> ~*

standing of the origin and underlying physics of metamaterial absorbers.

12(*ω*)*ei<sup>θ</sup>*12(*ω*)

represents the propagation phase, and *β*<sup>2</sup>

After direct mirror reflection and an additional propagation phase delay *β*

The first metamaterial absorber was theoretically investigated in 2006, consisting of an array of split ring resonators (SRRs)-backed with a resistive sheet [49]. The incident wave is parallel to the SRR plane with magnetic field being perpendicular to the SRR array. Such an SRR array is placed on a resistive sheet having a resistance of 377 Ω for impedance matching with free space, similar to a Salisbury screen. Both the reflection and transmission are below −20 dB at the vicinity of 2 GHz as numerically found. This is due to the strong resonances in this structure, where nearly perfect absorption was achieved at this frequency. However, due to the standing arrangement of the SRR array, this structure is not of low profile as compared with planar structures, which also increase its complexity in the manufacture. The bandwidth of absorption is also very limited. Nevertheless, the design of this metamaterial absorption motivates further research in these kinds of absorbers.

In 2008, Landy et al. [29] proposed a planar sandwiched structure that consists of electric ring resonators and cut wires separated by an FR-4 substrate, as shown in **Figure 2**. This is the first-reported metamaterial absorber with a planar and deeply subwavelength structure. The absorptivity observed is as high as 96% at 11.65 GHz in simulation and 88% at 11.5 GHz in experiment. The relative bandwidth of full width half maximum (FWHM) is around 4%. The front electric ring resonators couple strongly to the incident electric field and contribute electric response, while the circulating flow of antiparallel surface currents at the front and back metallic layers contributed a magnetic response. The absorption intensity and frequency could be controlled by adjusting the geometric parameters of electric ring resonators or the

**Figure 2.** (a) Unit cell of the first planar metamaterial absorber, (b) simulated reflection, transmission, and absorptance at microwave frequency. Reproduced from [29] with permission.

**Figure 3.** (a) Unit cell of dendritic metamaterial absorber and (b) simulated and measured absorptivity spectra. Reproduced from [50] 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].

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

widely used for designing broadband metamaterial absorbers [59, 60]. In this section, some

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

Electromagnetic Metamaterial Absorbers: From Narrowband to Broadband

http://dx.doi.org/10.5772/intechopen.78581

139

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

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

typical approaches for designing bandwidth-enhanced absorbers are discussed.

lower frequencies are trapped at the lower parts.

with permission.

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 over 95% absorptivity for a reasonable level of disorder.
