Metamaterials have emerged as a class of advanced materials that have made significant contributions to the ongoing progress in science and technology [1]. These materials are artificially-engineered, comprising elemental unit cells with dimensions smaller than the operating wavelength, arranged periodically [2]. The constituent elements of metamaterial structures exhibit distinct electrical and magnetic resonance properties within specific frequency ranges [3]. Consequently, within these resonant frequency ranges, metamaterials manifest extraordinary electromagnetic characteristics which are not obtained with natural materials. Examples of such unique properties include negative refractive index [4], inverse Doppler effect [5], cloaking [6], and electromagnetically-induced transparency (EIT) [7]. The ability to manipulate the resonance properties of each element in the metamaterial structure or to modify the interconnections between these elements allows us precise control over the resultant properties of metamaterial ^{[8][9][10][11]}[8,9,10,11]. This facilitates the tailoring of the material’s behavior according to the specific requirements and desires of the designer. By strategically adjusting the resonance properties or modifying the structural arrangement, the metamaterials can be engineered to exhibit the desired electromagnetic responses, paving the way for innovative applications in various fields of science and technology ^[12][13][14][12,13,14].

Metamaterials have garnered significant attention due to their unique and promising properties, one of which is their capability to exhibit the perfect absorption of electromagnetic waves [15]. This intriguing property was demonstrated first by Landy et al., wherein the metamaterial structure was able to absorb electromagnetic waves with a near-perfect efficiency, exhibiting minimal transmission, reflection, and scattering [16]. The unique properties of metamaterial absorbers have led to their adoption in various applications. For instance, in the field of sensing, metamaterial absorbers have been utilized to develop highly-sensitive sensors capable of detecting tiny changes in the environment [17]. In energy harvesting, these absorbers have been employed to capture and convert electromagnetic energy into electrical energy [18]. Moreover, they have also been utilized to develop high-performance bolometers and photo-detectors, with potential applications in imaging and sensing technologies ^[19][20][19,20]. The metamaterial absorbers are essentially ultrathin structures with dimensions smaller than one-tenth of the operating wavelength [21]. These structures are lightweight and highly flexible, making them easily integrated into existing electronic systems and devices ^[22][23][22,23]. Additionally, the fabrication process for metamaterial absorbers is highly versatile, allowing us to produce structures with varying shapes, sizes and properties ^{[24][25][26][27]}[24,25,26,27]. As a result, these absorbers can be tailored to suit the specific application requirements [28].

2. The Principles of the Metamaterial Absorbers in Controlling Single-Peak/Multiple-Peaks/Tailored-Band/Broadband

2.1. Interference Theory

Interference theory is a widely accepted method for determining the absorption properties of metamaterial absorbers. This approach relies on the accumulation of reflections between the top metallic layer and the bottom metallic plate of the absorber ^[29][44]. Specifically, when the wave directly reflected on the resonator surface interferes destructively with that from multiple reflections, the wave is trapped within the metamaterial structure, leading to a high absorption. This phenomenon results from the constructive and destructive interference of waves, which can be explained by the interference model presented in Figure 1. The model illustrates how the incident wave is reflected off the top metallic layer, creating a reflected wave that interferes with the incident wave. The interference between these waves can be either constructive or destructive, depending on the distance between the top layer and the bottom metallic plate. When the distance is such that destructive interference occurs, it leads to the absorption of waves within the metamaterial structure. By understanding this physical mechanism, researchers can design and optimize the metamaterial absorbers for various applications, including sensing, imaging, and energy harvesting.

2.2. Impedance Matching Theory

Metamaterials are distinguished by their complex electric permittivity (ε = ε₁ + iε₂) and magnetic permeability (μ = μ₁ + iμ₂). By manipulating the resonance of ε and μ independently, absorption can be achieved for both electric and magnetic fields. Additionally, when ε and μ are matched properly, a metamaterial absorber can be impedance-matched to the free space, effectively minimizing the reflection of waves [16]. The absorption characteristics of metamaterial absorbers, specifically, their ability to achieve perfect absorption within a specific wavelength range, can be elucidated by using the theory of impedance matching ^[30][45]. This theory enables us to evaluate and determine the frequency at which the reflection is minimized ^[31][46]. By employing the reflection coefficient S₁₁(ω) and transmission coefficient S₂₁(ω), the researchers can calculate the effective impedance of the metamaterial absorber ^[30][45]: Figure 2a shows a metamaterial absorber, which is a composite structure composed of a dielectric substrate, an array of metallic patterns, and a highly-conductive metallic layer on the back surface. In order to analyze the behavior of a metamaterial structure, it is common to represent it in terms of an equivalent electrical circuit, as illustrated in Figure 2b, in conjunction with the transmission line theory. The resonator structure located on the top surface of the metamaterial, which includes lumped resistors, can be effectively represented by a series RLC circuit. On the other hand, the metallic component on the back surface can be modeled as a short circuit. The free space and dielectric layer are conceptualized as a transmission line. By applying the transmission line theory, the researchers can derive the reflection coefficient of a metamaterial structure: The calculation of the input impedance (𝑍_𝑖𝑛) of a metamaterial structure is dependent on its design. Perfect absorption occurs when the reflection coefficient (ΓΓ) is equal to zero, which corresponds to the condition that 𝑍_𝑖𝑛 is equal to the free space impedance (Z₀).

2.3. Controling the Absorption Bandwidth

The tunability of metamaterial absorbers refers to their remarkable capability to adjust and tailor the absorption properties across a wide range of frequencies. This characteristic is achieved through the strategic incorporation of tunable elements within the structure of a metamaterial absorber. By integrating these tunable components, the absorber becomes responsive to external control, allowing for dynamic and real-time adjustments to optimize the performance. Tunable metamaterial absorbers have emerged as a highly promising and versatile solution for controlling and effectively manipulating electromagnetic waves across various frequency bands. Their capability to adapt and modify the absorption characteristics makes them valuable in a multitude of applications, particularly, in the fields of energy harvesting, telecommunication, and sensing ^{[32][33][34][35][36][37]}[47,48,49,50,51,52]. The principles of tailoring the bandwidth of a metamaterial absorber include manipulating the structural design and material properties of the absorber to achieve the desired absorption characteristics within a specific frequency range. This is made by engineering the resonant properties of the structure, which comprises adjusting the geometry and material composition of the metamaterial unit cell. By enabling the shift of resonant frequency, the tunable structure provides the remarkable capability of achieving absorption at various specific frequencies. This feature allows us to control precisely the absorption bandwidth of the metamaterial absorber. With this capability to adjust the resonant frequency, the absorber can be fine-tuned to target and absorb electromagnetic energy at the desired frequencies. The development of tunable metamaterial absorbers needs the consideration of desired frequency range, tuning mechanism, and overall performance specifications. The successful realization of these absorbers has required the integration of various tuning mechanisms, such as optical ^[32][47] (Figure 3a), temperature ^[33][48] (Figure 3b), magnetical ^[34][49] (Figure 3c), electrical ^[35][50] (Figure 3d), and mechanical tuning mechanisms ^[36][51] (Figure 3e), in the metamaterial structure to achieve the desired level of tunability, as shown in Figure 3. The selection of a suitable tuning mechanism depends on several factors, such as the desired frequency range, required level of tunability, and practical constraints associated with the specific application. For instance, the optical tuning mechanism might be preferred for applications that require high-speed modulation and low-power consumption ^[32][47]. On the other hand, temperature and electrical tunings are more appropriate for applications which need precise and stable tuning over an extended period ^[33][35][48,50]. Similarly, the magnetical and mechanical tuning mechanisms also have their own special application purposes ^[34][36][49,51]. The integration of different tuning mechanisms within the metamaterial structure should be accompanied by the careful consideration of the design and fabrication process. This includes the selection of appropriate materials, the optimization of structural parameters, and the implementation of suitable fabrication techniques. The successful implementation of these processes is crucial to achieve the desired level of tunability and overall performance of the metamaterial absorber.