An Application-Based Study on Electromagnetic Absorber Using Metamaterial

Abstract

In recent years, metamaterials (MMs) have attracted researchers due to their geometrical and structural uniqueness that make these materials to absorb, block, and enhance electromagnetic (EM) waves, which is not possible with conventional materials found in nature. These artificially engineered materials derive the EM properties (effective values of permittivity ε∼eff and permeability μ∼eff less than zero) from the shape, size, orientation, and periodicity of unit cells rather inheriting those from material composition. The study on MMs has been diversified from the radio frequency range to the optical frequency range, with potential applications in realization of novel devices such as perfect lenses, EM, and MM based microwave patch antennas. For the past few years, the concept of MMs has been widely used to develop and design metamaterial perfect absorbers (MPAs). The proposed chapter mainly focuses on the classification of materials on the basis of permittivity and permeability; MPAs; applications of MPAs; experimental demonstrations of first single-band MPAs in microwave, THz, mid-IR and near IR regimes; conditions for complete absorption of EM waves; MPA as perfectly matched layer (PML); attenuation mechanism of EM waves inside the MPA; calculation of MM parameters; measurement and testing process, followed by a case study on multi-band MPA.

1. Introduction

The electromagnetic (EM) properties of materials are characterized on the basis of negative or positive values of permittivity $\stackrel{\sim }{\epsilon }$ or permeability $\stackrel{\sim }{\mu }$. Most of the materials that are found in nature have positive values of permittivity $\stackrel{\sim }{\epsilon }$ and permeability $\stackrel{\sim }{\mu }$, and hence, they are termed as “double-positive” (DPS) materials [1, 2]. Materials exhibiting negative values of permittivity or permeability are termed as “single-negative” (SNG) and these materials are further classified into two sub-categories “epsilon-negative” (ENG) and “mu-negative” (MNG) [1, 2]. If these quantities, permittivity $\stackrel{\sim }{\epsilon }$ and permeability $\stackrel{\sim }{\mu }$ are negative, they are called “double-negative” (DNG) [1, 2]. The energy flux carried by the EM wave is determined by the Poynting vector $\overline{S}$, given by Eq. (1) [1].

$$\overline{\mathrm{S}}=\frac{\mathrm{c}}{4\mathrm{\pi }}\left(\overline{\mathrm{E}}\mathrm{X}\overline{\mathrm{H}}\right)$$E1

For DPS materials the vectors, $\overline{E}$ (electric field vector), $\overline{H}$ (magnetic field vector), and $\overline{k}$ (propagation vector) form a right handed set of vectors, where $\overline{S}$ (Poynting vector) and $\overline{k}$ are co-directional. The DPS materials are also termed as “right-handed materials” (RHMs). For DNG materials, the same set of vectors forms left-handed set of vectors, but vectors $\overline{S}$ and $\overline{k}$ are in opposite directions. The DNG materials are also termed as “left- handed materials” (LHMs). The LHMs are also termed as substances with negative group velocity which means that the phase velocity is in opposite direction to that of energy flux.

The electric and magnetic fields are associated with each other, however the permittivity $\stackrel{\sim }{\epsilon }$ and the permeability $\stackrel{\sim }{\mu }$ control electric and magnetic fields in a medium. Negative permeability results in orientation of magnetic dipoles in reverse direction so as to oppose the external applied magnetic field (diamagnetic materials, anti-ferro magnetic materials), similarly the concept of negative permittivity results in the polarization of electric dipoles in reverse direction. Thus, by making both the permittivity $\stackrel{\sim }{\epsilon }$ and the permeability $\stackrel{\sim }{\mu }$ negative, the direction of flow of energy inside the material is made to change in contradiction to the conventional direction of flow of energy. The natural materials do not possess simultaneous negative values of permittivity $\stackrel{\sim }{\epsilon }$ and permeability$\stackrel{\sim }{\mu }$, hence they must be created artificially (Figure 1).

Figure 1.

Classification of known materials on the basis of $\stackrel{\sim }{\epsilon }$ and $\stackrel{\sim }{\mu }$ with the realization of metamaterials (MMs) [1].

MMs are artificially engineered new class of materials that are not found in nature. These artificial materials possess unusual EM properties with values of effective permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$and effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$less than zero [3]. The geometry, the periodic arrangement and the orientation of the structural units give rise to unusual EM properties. These unusual EM properties are not inherited from the material composition. So, MMs can be defined as periodic arrangement or irregular periodic arrangement of sub-wavelength metallic structures which derive EM material properties from their geometry rather than inheriting them directly from the material composition or band structure.

In 1968 Veselago [1] gave theoretical concept of these new class of materials that can possess unusual properties like negative index of refraction, opposite phase and group velocity, reverse Doppler shift, reverse Cerenkov radiations. The absence of the natural occurrence of materials with these properties led to neglect of the subject until 1996 when Pendry et al. [4] explained the design and behavior of artificial material termed as metallic microstructures comprising of periodic structure of infinite wires arranged in cubic lattice and exhibiting negative permittivity $\stackrel{\sim }{\epsilon }$ and split ring resonator (SRR) structures exhibiting negative permeability $\stackrel{\sim }{\mu }$. In 1999 Smith et al. [3] demonstrated a composite medium exhibiting simultaneous negative values of effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$ and permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$ comprised of periodic array of SRRs and continuous micro-structured wires in microwave region, forming left-handed medium (Figure 2). With this demonstration the concept of materials with negative values of ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$ and ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$ given by Veselago way back in 1968 came into existence and a whole new field of research came into limelight to be known as ‘Metamaterials’. Word ‘Metamaterial’ is derived from Greek word ‘meta’ which means ‘beyond’. The term metamaterial was first introduced by Walser [5].

Figure 2.

Experimental demonstration of composite medium by Shelby et al. [2].

The geometrical and structural uniqueness of MM makes these materials capable to bend [6, 7], absorb [8, 9], block [10, 11], and enhance [12] EM waves which is not possible with conventional materials found in nature [1]. In recent years the study of MMs has been diversified from radio frequency range to optical frequency range.

The MMs find applications to realize perfect-lens [6], super-lens [7], EM cloak [10, 11], EM concentrators [12], EM band gap based microwave circuit design [13], multi-band MNG resonators [14], MM-based and MM inspired efficient, electrically small antennas [15], MM-based patch and leaky-wave antennas [16], MM-based perfect absorbers [8, 9, 17].

2. EM wave absorber

An EM wave absorber is a device which absorbs all the EM radiation incident on it under perfectly matched conditions. American engineer Salisbury and another scientist J. Jaunmann [18] invented EM absorbers independently to improve the performance of radar and to provide stealth technology. Salisbury [18] developed the Salisbury screen. The basic structure of EM wave absorber consists of a resistive sheet and metal laminated ground plane both separated by some lossless dielectric of thickness (λ_o/4) as shown in Figure 3. When EM waves are incident on the Salisbury screen, the waves pass through the resistive sheet without any reflections and the EM waves get reflected by the continuous metallic surface. The waves travel back λ/2 distance with phase change by 180^o and result in destructive interference with incident EM waves.

Figure 3.

Salisbury screen [18].

The performance of Salisbury screen is limited firstly because of the bulky size. The thickness increases for broad-band absorption due to cascading of dielectric lossy layers. To satisfy the complete destructive interference the thickness of dielectric layer must be $\left(\frac{\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\eta }\right).$ If wavelength (λ) of EM wave is large then the dielectric layer has to be very thick. Secondly, the performance of Salisbury screen is limited to microwave frequencies due to impedance matching conditions.

3. Metamaterial perfect absorber

Conventional metamaterial perfect absorber (MPA) is a three-layered structure [8]. It consists of top layer that is periodic array of unit cells, constituting MM high impedance surface, a middle layer that is lossy or lossless dielectric layer, and a bottom layer that is metal laminated ground plane. Figure 4 shows the layered structure of MPA. The shape, size, periodicity, and orientation of the unit cells are optimized to match the normalized impedance of the top layer of MPA with that of the impedance of free space. Under normalized impedance matched conditions, the incident EM waves at certain frequency bands propagates through the high impedance layer without any reflections. The continuous metal laminated bottom layer completely blocks the EM waves and reflects back the EM waves.

Figure 4.

Layered structure of MPA [17].

The dielectric layer provides space to the incident EM waves to stay and get absorbed inside the material. The dielectric layer should have high permittivity as it results in reduction of thickness maintaining the optical path. The dielectric layer should also have high loss tangent (tan δ) value. The MPA must offer high values of imaginary part of effective permittivity and effective permeability to attenuate the EM waves inside the MPA.

The complete absorption of the incident microwave radiation from free space on a microwave absorber surface requires the fulfillment of the following conditions:

1. The complete transfer of the incident microwave radiation into the surface of the microwave absorber which can be achieved by perfect impedance matching of the free space and the front surface of the microwave absorber known as perfectly matched condition.

2. The transferred microwave radiation into the microwave absorber should be completely absorbed within the microwave absorber which can be achieved by high attenuation constant for the incident microwave radiation inside the microwave absorber.

3.1 Metamaterial perfect absorber as perfectly matched layer

A conventional MPA structure consisted of three-layered structure, the uppermost high impedance layer described by effective impedance ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) = [${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f)/${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f)]^1/2, the middle dielectric layer described by effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) and effective permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and lowermost continuous metal laminated ground layer. Berenger in 1994 [19], gave the idea of artificial absorbing layer which can be frequency and angle of incident independent described as perfectly matched layer (PML). The PML has the characteristic of no reflection at the interface and maximum absorption inside the medium. To achieve this characteristic, the PML has its effective impedance matched with that of free space. i.e. ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) = 1.

According to the Fresnel’s equations [20], the reflectance (R) and reflection coefficient (γ) of the interface separating free space (with impedance, permeability, permittivity and, refractive index: Z_o, μ_o, ε_o, η_o, respectively) and medium (with impedance, permeability, permittivity and, refractive index: $\stackrel{\sim }{\mathit{Z}}$, $\stackrel{\sim }{\mu }$_r, $\stackrel{\sim }{\epsilon }$_r, $\stackrel{\sim }{\eta }$, respectively shown in Figure 5) for TE and TM polarized wave is given by Eq. (2) and Eq. (3), respectively [20].

Figure 5.

Incident (I), transmitted (T) and reflected (R) EM wave.

The impedance $\stackrel{\sim }{Z}$, permeability $\stackrel{\sim }{\mu }$, permittivity $\stackrel{\sim }{\epsilon }$, and refractive index $\stackrel{\sim }{\eta }$ of the media are complex quantities [21] defined by Eq. (4), Eq. (5), Eq. (6), and Eq. (7), respectively, and the effective impedance ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$, permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$, permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$, and refractive index ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$of the media are defined by Eq. (8), Eq. (9), Eq. (10), and Eq. (11), respectively.

$$R_{\mathrm{TE}}={\left|{\gamma }_{\mathrm{TE}}\right|}^2={\left|\frac{\mathrm{Cos}{\theta }_i-{\stackrel{\sim }{\mu }}_r^{-1}\sqrt{{\stackrel{\sim }{\eta }}^2-\mathrm{Sin}{{\theta }_i}^2}}{\mathrm{Cos}{\theta }_i+{\stackrel{\sim }{\mu }}_r^{-1}\sqrt{{\stackrel{\sim }{\eta }}^2-\mathrm{Sin}{{\theta }_i}^2}}\right|}^2$$E2

$$R_{\mathit{TM}}={\left|{\gamma }_{\mathit{TM}}\right|}^2={\left|\frac{{\stackrel{\sim }{\epsilon }}_r\mathrm{Cos}{\theta }_i-\sqrt{{\stackrel{\sim }{\eta }}^2-\mathrm{Sin}{{\theta }_i}^2}}{{\stackrel{\sim }{\epsilon }}_r\mathrm{Cos}{\theta }_i+\sqrt{{\stackrel{\sim }{\eta }}^2-\mathrm{Sin}{{\theta }_i}^2}}\right|}^2$$E3

where θ_i is the angle of incidence and $\stackrel{\sim }{\eta }=\sqrt{{\stackrel{\sim }{\mu }}_r{\stackrel{\sim }{\epsilon }}_r}$ is the refractive index of the dielectric medium.

$$\stackrel{\sim }{Z}=Z^{\prime }\left(f\right)+{\mathit{jZ}}^{\prime \prime }\left(f\right)$$E4

$$\stackrel{\sim }{\mu }={\mu }^{\prime }\left(f\right)+{\mathit{j\mu }}^{\prime \prime }\left(f\right)$$E5

$$\stackrel{\sim }{\epsilon }={\epsilon }^{\prime }\left(f\right)+{\mathit{j\epsilon }}^{\prime \prime }\left(f\right)$$E6

$$\stackrel{\sim }{\eta }={\eta }^{\prime }\left(f\right)+{\mathit{j\eta }}^{\prime \prime }\left(f\right)$$E7

$${\stackrel{\sim }{Z}}_{\mathrm{eff}}=\frac{\stackrel{\sim }{Z}}{Z_o}$$E8

$${\stackrel{\sim }{\mu }}_{\mathrm{eff}}=\frac{\stackrel{\sim }{\mu }}{{\mu }_o}$$E9

$${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}=\frac{\stackrel{\sim }{\epsilon }}{{\epsilon }_o}$$E10

$${\stackrel{\sim }{\eta }}_{\mathrm{eff}}=\frac{\stackrel{\sim }{\eta }}{{\eta }_o}$$E11

where $Z^{\prime }\left(f\right)$, ${\mu }^{\prime }\left(f\right)$, ${\epsilon }^{\prime }\left(f\right)$ and ${\eta }^{\prime }\left(f\right)$ are the real part and $Z{\prime }^{\prime }\left(f\right)$, $\mu {\prime }^{\prime }\left(f\right)$, $\epsilon {\prime }^{\prime }\left(f\right)$ and ${\eta }^{\prime \prime }\left(f\right)$ are the imaginary part of impedance, permeability, permittivity, and refractive index of the medium, respectively. For normal angle of incidence θ_i = 0 degree, the Eq. (2) and Eq. (3) reduced to Eq. (12).

$$R={\left|\frac{\stackrel{\sim }{Z}-Z_o}{\stackrel{\sim }{Z}+Z_o}\right|}^2$$E12

$\text{where}\stackrel{\sim }{Z}=\sqrt{\frac{\stackrel{\sim }{\mu }}{\stackrel{\sim }{\epsilon }}}\text{and that of free space is}{Z}_o=\sqrt{\frac{{\mu }_o}{{\epsilon }_o}}.$

The absorptance, A = [1 – R – T], where R is the reflectance and T is the transmittance. Due to the presence of the bottom ground layer, T is reduced to zero and absorptance A = [1 – R]. For perfect absorption, i.e., A = 1, the reflectance R should be zero which can be achieved if, $\stackrel{\sim }{Z}=Z_{\mathrm{o}}.$ This condition is referred to as perfect matched condition [8, 9].

Attainment of perfectly matched condition so as to have minimum reflection from the material and maximum dissipation of EM waves inside the material led to a new field of research identified as MPAs. To achieve the perfect absorption of incident EM wave radiation researchers explored MM design concept to achieve a material having absorptance of ‘Unity’, i.e., MPA. After the first experimental demonstration of MPA [8], advanced research has been carried out in the field of MPA from radio spectrum to optical spectrum at microwaves, mm wave, THz, infrared, and optical range. The advancement and improvement in designing MPAs to maximize the absorptance over a wide frequency band contributes to narrow-band MPAs, dual-band and multi-band MPAs, broad-band MPAs, polarization insensitive MPAs, and wide angle MPAs. MPAs find potential applications in reducing radar cross section (RCS) [22], in improving antenna radiation pattern [16], and in reducing electromagnetic interference (EMI) [21]. Future applications include the use of MPA as selective thermal emitters [23] and wavelength sensitive sensors [24].

3.2 Metamaterial parameters

Under impedance matched conditions, the MPA structure is considered to be a single homogeneous layer with dispersive effective permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f). To study the absorptance of incident EM waves through frequency selective top layer of MPA, the effective impedance ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f), the effective permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f), the effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f), and the effective refractive index ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f) is calculated.

According to Nicolson-Ross-Weir (NRW) method [25], the effective impedance ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) is calculated using Eq. (17) given as:

$${\stackrel{\sim }{Z}}_{\mathrm{eff}}\left(f\right)=\frac{1+S_{11}\left(f\right)}{1-{\mathrm{S}}_{11}\left(f\right)}$$E13

The effective permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) is calculated using Eq. (18) given as:

$${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}\left(f\right)=\frac{2}{\mathrm{j}{\mathrm{k}}_{\mathrm{o}}\mathrm{d}}\left(\frac{1-S_{11}\left(f\right)-{\mathrm{S}}_{21}\left(f\right)}{1+{\mathrm{S}}_{11}\left(f\right)+{\mathrm{S}}_{21}\left(f\right)}\right)$$E14

The effective permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) is calculated using Eq. (19) given as:

$${\stackrel{\sim }{\mu }}_{\mathrm{eff}}\left(f\right)=\frac{2}{\mathrm{j}{\mathrm{k}}_{\mathrm{o}}\mathrm{d}}\left(\frac{1+S_{11}\left(f\right)-{\mathrm{S}}_{21}\left(f\right)}{1-{\mathrm{S}}_{11}\left(f\right)+{\mathrm{S}}_{21}\left(f\right)}\right)$$E15

The effective refractive index ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f) is calculated using Eq. (20) given as:

$${\stackrel{\sim }{\eta }}_{\mathrm{eff}}\left(f\right)=\sqrt{{\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}\left(f\right)\ast {\stackrel{\sim }{\mu }}_{\mathrm{eff}}\left(f\right)}$$E16

In an MPA, under perfectly matched conditions, at the maximum absorptance frequency (f_o), the real and imaginary parts of effective impedance of MPA matches with that of free space. ${\left.{\stackrel{\sim }{Z}}_{\mathrm{eff}}\left(f\right)\right|}_{f=f_{\mathrm{o}}}=Z_{\mathrm{eff}}^{\prime }\left(f_{\mathrm{o}}\right)+i{Z}_{\mathrm{eff}}^{\prime \prime }\left(f_{\mathrm{o}}\right)$ = 1. It implies that the normalized real value of ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) is equal to 1 and the imaginary value of ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) is equal to zero.

$$Re{\left[{\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}\left(f\right)\right]}_{f=f_o}=\mathit{Re}{\left[{\stackrel{\sim }{\mu }}_{\mathrm{eff}}\left(f\right)\right]}_{f=f_{\mathrm{o}}}\text{and}Im{\left[{\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}\left(f\right)\right]}_{f=f_{\mathrm{o}}}=Im{\left[{\stackrel{\sim }{\mu }}_{\mathrm{eff}}\left(f\right)\right]}_{f=f_{\mathrm{o}}}$$

In case of MM behavior, the real part of ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) shows the Lorentzian oscillation at or within the vicinity of maximum absorptance frequency band. The imaginary part of ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) attains appreciable high values as compared to real part. Under perfectly matched condition ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f) = 1, the point at which the real values of ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) crosses ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f)=1, the imaginary values of ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) and ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) attains appreciable high values as shown in Figure 6a and b.

Figure 6.

Real and imaginary values of (a) ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) (b) ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f) at or within maximum absorptance frequency band [17].

3.3 Measurement and testing of metamaterial absorber

The measurement and testing setup consisted of anechoic chamber, transmitting, and receiving horn antennas, and vector network analyzer (VNA) as shown Figure 7. The measurement process is calibrated in order to reduce the measurement errors. The measurement process is carried out in two different steps as described below.

1. In first step the MPA structure is placed in front of transmitting and receiving horn antennas with copper laminated ground plane of MPA structure facing the horn antennas in an anechoic chamber as shown in Figure 7. The transmitting horn antenna is connected to port 1 of VNA and the receiving horn antenna is connected to the port 2 of the VNA as shown in Figure 7. The transmitting horn antenna transmits 1 mW EM radiation towards the copper laminated ground plane of MPA. The reflected radiation from the copper laminated ground plane of MPA is received by the receiving horn antenna. The VNA measures the reflection coefficients corresponding to the reflected power.

2. In second step the MPA structure is rotated by 180^o such that the unit cells structured side of MPA faces the transmitting and receiving horn antennas. The reflected radiation from the structure side of MPA is received by the receiving horn antenna. The VNA again measures the reflection coefficients corresponding to the reflected power. The difference of the two measurements gives the calibrated measured values.

Figure 7.

Block diagram of the experimental set up.

The two-step measuring process is used to measure absorptance for normal incidence, for variation in angle of incidence θ, and variation in E-field and H-field orientations Φ of the incident EM waves. For taking measurements of reflection coefficients S₁₁ at different angles of incident of EM waves, the MPA structure sample placed on a circular scale is rotated along the y-axis by the desired angle and measurements were recorded in two steps as described. Similarly for taking measurements of reflection coefficients S₁₁ at different angles of E-field and H-field of EM waves, the MPA structure sample is rozztated along the z-axis by the desired angle.

4. First reported single-band metamaterial perfect absorbers

The first narrow single-band MPA was experimentally demonstrated in 2008 by Landy et al. [8]. The unit cell consisted of electric ring resonator (ERR) over micro-structured cut wired section separated by dielectric layer as shown in Figure 8. The dielectric layer was of FR-4 substrate of 0.2 mm thickness. The top-layered ERR and bottom-layered micro-structured cut wired section was etched out of 17 μm thick copper layers shown in Figure 8. The MMA structure consisted of two-dimensional arrays of unit cells with separation of 0.72 mm. The MPA was fabricated using photosensitized method. The results simulated in finite difference time domain (FDTD) solver, computer simulation technology (CST) microwave studio showed absorptance of 96% at 11.48 GHz whereas experimentally achieved absorptance was 88% at 11.5 GHz. The difference in the simulated and experimental values was mainly explained due to fabrication errors. The top layer comprising of ERR and the bottom layer comprising of micro-structured cut wire section strongly coupled the incident EM waves at the resonance frequency 11.48 GHz thereby generating strong electric response. The anti-parallel currents induced in the ERR and the micro-structured cut wire section was responsible for magnetic coupling. Thus, the combined effect of ERR and the micro-structured cut wire section was responsible for electric and magnetic responses. It was explained by the authors that the variation in geometry of ERR resulted in fine variation in absorptance frequency strength of resonance whereas varying the spacing between the two metallic structures ERR top layer and the bottom micro-structured cut wire section layer resulted in modification of magnetic response. The proposed MPA was reported to have potential application in devices such as bolometers.

Figure 8.

Top view of narrow band MPA experimentally demonstrated in 2008 by Landy et al. [8].

After the first experimental demonstration of narrow single-band MPA in microwave region, the same work was extended in THz region [9] with MPA dimensions in μm and replacing FR-4 substrate layer with polyamide dielectric substrate layer as indicated in Table 1. The simulated results in CST microwave studio showed absorptance of 98% at 1.12 THz as compared to experimental results with 70% absorptance at 1.3 THz with potential application as low thermal mass absorber with thermal sensing.

Type of absorber →	Microwave absorber (dimensions in mm)	THz absorber (dimensions in μm)
Resonance frequency	11.48 GHz	1.3 THz
Absorptance	88%	70%
a1	4.2	34
a2	12	50
t	0.6	3
t1	0.6	3
G	0.6	3
W	4	30
W1	4	30
H	1.7	4
L	11.8	48
Type of substrate	FR-4	Polyamide
Thickness of ERR and cut wire section	0.017	0.2
Thickness of substrate	0.2	8

Table 1.

Dimensional comparison of first experimentally demonstrated MPA in μW and THz regime.

The MPA structure was fabricated using surface micro-machining process with the deposition of 200 nm thick cut wire layer of Au/Ti ground plane on GaAs wafer followed by deposition of 8 μm thick layer of polyamide as dielectric substrate and on the top a 200 nm-thick Au/Ti layer as ERR.

The first single-band MPA in mid-IR regime was experimentally demonstrated in 2010 by Liu et al. [24]. The 140 × 140 μm MPA structure was fabricated with the deposition of 100 nm thick gold layer ground plane on silicon substrate followed by 185 nm thick layer of Al₂O₃ as dielectric substrate and on the top a 100 nm thick layer of gold in the cross wired shape (plus shape) as shown in Figure 9a and b. The simulated and measured absorptance was 97% at 6 μm and the absorptance band has FWHM of 1 μm. The proposed MPA has potential application in hyper-spectral imaging cameras.

Figure 9.

Schematic of first single- band MPA in mid-IR regime experimentally demonstrated in 2010 by Liu et al. [24] (a) Top view. (b) Side view.

The plus-shaped cross wired structure acted as ERR and it was responsible for coupling of E-field and the combination of ERR and ground plane for coupling of H-field from the incident EM radiation.

With the impedance of MPA matched to that of free space and the width of ground plane exceeding the penetration depth in mid-IR led to maximum EM radiation absorption with zero transmission through MPA.

The first experimental demonstrations for MPAs in NIR regime were reported by Hao et al. [26] and Liu et al. [27] separately in 2010. The MPA structure design by Liu et al. consisted of top layer of gold disks of 352 nm in diameter and 20 nm in height and gold lamination ground plane of 200 nm separated by MgF₂ dielectric of 30 nm thickness as shown in Figure 10b. The entire MPA structure was grown over glass substrate. The MPA structure was measured to be 99% polarization insensitive and to have wide angular absorptance at 1.6 μm with application as plasmonic sensor for refractive index sensing. The MPA structure design by Hao et al. consisted of top layer of rectangular patches of gold of 170 nm by 170 nm by 40 nm and gold lamination ground plane of 310 × 310 × 50 nm separated by Al₂O₃ dielectric of 10 nm thickness as shown in Figure 10a. The simulated absorptance was found to be greater than 97% at 1.58 and 1.95 μm for TM and TE radiation modes respectively. The ultra-thin MPA structure was measured to have 88% wide angular absorptance at 1.58 μm for TM mode radiations and 83% absorptance at 1.95 μm for TE mode radiations. The proposed MPA has micro technological applications including micro-bolometers, photo detectors, coherent thermal emitters, and solar cells. Anti-parallel surface currents induced in gold disks (or gold patches) and the ground plane gold layer resulting in magnetic resonance where the magnetic moment due to circulating currents strongly interact with magnetic field of incident EM radiation. At resonance the strong localized EM field enhanced between the two gold layers is confined in the dielectric layer and led to minimum reflectance and maximum absorptance of incident EM radiations (Table 2).

Figure 10.

(a) Schematic of first single-band MPA in NIR regime experimentally demonstrated in 2010 by Hao et al. [26]. (b) Schematic of first single-band MPA in NIR regime experimentally demonstrated in 2010 by Liu et al. [27].

Reference	Unit cell design	Frequency/wavelength		Absorption bandwidth	Absorptance
		Sim.	Exp.		Sim.	Exp.
[8]	Electric ring resonator (ERR) with back-to-back connected two split rings and a micro-structured split wire.	11.4 GHz	11.5 GHz	—	96%	88%
[9]	Electric ring resonator (ERR) with back-to-back connected two split rings and a micro-structured split wire. The dimensions of unit cell were in μm.	1.12 THz	1.3 THz	—	98%	70%
[24]	ERR as cross ring resonator (plus shape).	—	6 μm	FWHM :1 μm	—	97%
[26]	Rectangular patches of gold with gold laminated ground plane separated by Al2O3 dielectric.	1.58 μm	1.58 μm	—	97%	88%
[27]	Gold disks with gold laminated ground plane separated by MgF2 dielectric.	—	1.6 μm	—	—	99%

Table 2.

Experimental demonstrations of first single-band MPAs in microwave, THz, mid-IR and near IR regime.

5. Case study: multi-band metamaterial absorber-simulation, fabrication, testing

The multi-band metamaterial absorbers (MMAs) are practically more useful when they are capable of exhibiting high absorptance at many resonance frequencies. The potential applications of multi-band microwave absorbers increase manifolds if they are insensitive to state of polarization and wide angular incident microwaves. The case study in this section is based on description of the MMA design, MM behavior, comparison of measured reflection coefficient and absorptance with the simulated results of a MMA with frequency selective surface consists of concentric continuous rings (CCRs) [28]. The concentric rings are of different widths and radius and exhibits high degree of symmetry that makes the MM absorber insensitive to wide incidence angle and polarization state of incident EM waves.

5.1 Optimized design of metamaterial absorber

Figure 11 shows the optimized design of a MMA and the optimized dimensions of the unit cell and the rings are depicted in Tables 3 and 4, respectively. The design is optimized by parametric analysis of the dimensions of the unit cell wherein anyone parameter is varied and rest all other parameters are kept constant. This process is repeated for each and every parameter and the effect on the absorptance is observed.

Figure 11.

The 3-D perspective view of the geometry of the unit cell with dimensions of the subcells.

Design parameter	r1	r2	r3	r4	r5	r6	r7	r8	w	w1	w2	a	t
Dimension (mm)	3.93	3.68	2.35	2.10	3.20	2.85	2.35	1.93	0.25	0.35	0.42	18	1.5

Table 3.

Optimized dimensions of the unit cell.

Structure	OR-1	IR-1	OR-2	IR-2
Width of ring	0.25 mm	0.25 mm	0.35 mm	0.42 mm
Mean radius of ring	rm(OR-1) 3.80 mm	rm(IR-1) 2.22 mm	rm(OR-2) 3.02 mm	rm(IR-2) 2.14 mm

Table 4.

Optimized dimensions of the rings.

5.2 Simulation of metamaterial absorber

The optimized design of the multi-band MMA is simulated to study the response of the MMA at different frequency bands depicted in Figure 12.

Figure 12.

Reflection coefficient S₁₁(f), Transmission coefficient S₂₁(f) and Absorptance A(f) of the proposed MMA structure at 7.06, 9.18, 12.62 and 13 GHz.

The simulated reflection coefficients and absorptance is depicted in Table 5. The absorptance is estimated from simulated values of reflectance |S₁₁(f)|² and transmittance |S₂₁(f)|² using the Eq. (21) [8, 9, 24, 25]. The presence of continuous metallic bottom layer blocks the transmission of incident EM waves thereby making transmittance (S₂₁) zero shown in Figure 12.

Resonance frequency	7.06 GHz	9.18 GHz	12.62 GHz	13 GHz
Reflection coefficients	−6.5 dB	−36 dB	−21.5 dB	−27.5 dB
Absorptance	78%	99.9%	99.2%	99.8%

Table 5.

Effective resonance frequencies, reflection coefficients, and absorptance.

$$A\left(f\right)=1–\left|S_{11}\right(f){|}^2–|S_{21}\left(f\right){|}^2$$E17

To better understand the contribution of CCRs towards the resonance frequencies, the surface current distributions are investigated at different resonance frequencies. When an EM radiation is applied along the axis of the CCRs, depending upon the resonant properties of CCRs strong surface currents are induced either opposes or enhances the incident EM field. Figure 13 shows the surface current induced on the surface [29] of CCRs on the top layer of MMA structure. The arrowhead indicates the direction of current induced and the density of arrows shows the magnitude of surface current induced. Each continuous ring acts as a resonator and contributes towards absorption of incident EM radiation by resonating at a particular frequency shown in Figure 13. The two-dimensional periodic array of unit cells that consisted of four pair of CCRs in MMA structure resulted in strong coupling of CCRs in the MMA structure that further contributed to high absorptance of incident EM radiation.

Figure 13.

Surface current distributions at resonance frequencies (a) 7.06 GHz. (b) 9.18 GHz. (c) 12.62 GHz. (d) 13 GHz.

The circulating anti-parallel surface currents are induced from magnetic response whereas the circulating parallel surface currents are induced from electric response [29]. The surface currents resulted in coupling of incident EM radiation field with that of electric and magnetic responses and hence enhancement of localized EM field is established at resonance frequencies. At resonance frequencies the simultaneous magnetic as well as electric resonance results in complete absorptance of incident EM radiation under normalized impedance matching conditions (impedance matching of MMA with that of free space). Therefore, the incident EM radiation ranging from 5-15 GHz got confined within the MMA structure with minimum reflection and maximum absorptance.

With the incident EM radiation, the localized E-field is concentrated in x-direction along the CCRs as shown in Figure 14, and the localized H-field is concentrated in y-direction along the CCRs as shown in Figure 15. The metallic patch of CCR acts as inductive element on which the magnetic field gets concentrated. The inductive element is responsible for magnetic resonance. The electric field is concentrated in between the metallic patch of CCRs where the gaps between the metallic patches act as capacitive elements, responsible for electric resonance [3]. Thus, the magnetic and electric resonance at each CCR contributes to the absorptance peak at a particular resonance frequency. The concentration of surface current, E-field, and H-fields along a CCR indicates the responsiveness of that CCR for absorptance at a distinct resonance frequency [3]. From Figures 13–15, it is evident that the surface current and field distribution, is concentrated along the outer ring OR-1 and therefore it contributes to the absorptance at first resonance frequency 7.06 GHz. For second resonance frequency at 9.18 GHz the surface current and field distribution is concentrated along the outer ring OR-2 which contributes to high absorptance greater than 99%. Third and fourth resonance frequencies merged to generate the absorptance band from 12.62 to 13 GHz where the surface current and field distribution is concentrated along the inner rings IR-1 and IR-2 which contributes to absorptance greater than 99%.

Figure 14.

E-field distributions at resonance frequencies (a) 7.06 GHz. (b) 9.18 GHz. (c) 12.62 GHz. (d) 13 GHz.

Figure 15.

H-field distributions at resonance frequencies (a) 7.06 GHz. (b) 9.18 GHz. (c) 12.62 GHz. (d) 13 GHz.

5.3 Metamaterial properties of metamaterial absorber

To verify the maximum absorptance under perfectly matched conditions and dissipation of EM waves inside the MMA structure, the values of effective impedance ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f), permittivity ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f), permeability ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) and refractive index ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f) are retrieved from S₁₁ and S₂₁ parameters using standard methods of retrieval like NRW method [25], direct refractive index (DRI) method [30].

Therefore ${\stackrel{\sim }{Z}}_{\mathrm{eff}}\left(f\right)=\sqrt{\frac{{\stackrel{\sim }{\mu }}_{\mathrm{eff}}\left(f\right)}{{\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}\left(f\right)}}$ = 1 at maximum absorptance frequencies. The incident EM waves propagate through the top layer of MMA with no reflections under perfectly matched conditions and blocked by the continuous metallic ground layer. The MMA structure exhibits the large value of imaginary part of effective ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f) with respect to value of real part of effective $\stackrel{\sim }{\eta }$_eff (f) [${\eta }_{\mathrm{eff}}^{\prime \prime }\left(f\right)\gg {\eta }_{\mathrm{eff}}^{\prime }\left(f\right)$], which results in exponential decay of EM waves inside the MMA (Table 6).

Parameter	7.06 GHz	9.18 GHz	12.62 GHz	13 GHz
${\stackrel{\sim }{Z}}_{\mathrm{eff}}$(f)	0.41 − j0.15	0.95 + j0.04	1.15 + j0.04	0.94 + j0.04
${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f)	1.59 + j6.42	0.04 + j4.01	−0.12 + j4.44	0.22 + j3.34
${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f)	−0.188 + j2.45	−0.03 + j3.99	0.17 + j4.58	−0.17 + j3.32
${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f)	0.2107 + j3.98	0.0288 + j4.00	0.188 + j4.51	0.0244 + j3.33

Table 6.

Values of ${\stackrel{\sim }{Z}}_{\mathrm{eff}}$ (f), ${\stackrel{\sim }{\epsilon }}_{\mathrm{eff}}$(f), ${\stackrel{\sim }{\mu }}_{\mathrm{eff}}$(f) and ${\stackrel{\sim }{\eta }}_{\mathrm{eff}}$(f) at 7.06, 9.18, 12.62 and 13 GHz [28].

5.4 Measured reflection coefficient and absorptance of metamaterial absorber

A 10 × 10 two-dimensional periodic array consisting of 100 unit cells was fabricated on FR-4 substrate (ε_r = 4.4, tan δ = 0.02) of thickness 1.5 mm by UV photolithography method and wet etching process is shown in Figure 16a. The experimental process is calibrated, and the measurements recorded for the calibration process are shown Figure 16b. The calibrated reflected power is the difference of reflected power measured from the bottom copper laminated side and the reflected power measured from the top layer comprising of CCRs by the VNA through receiving antenna in terms of (S₁₁) parameter as described in Section 3.3.

Figure 16.

(a) Fabricated MMA structure with two-dimensional periodic array comprising of 100 unit cells within 180 mm by 180 mm. (b) Measured reflected power as a difference of reflected power from bottom copper laminated layer and top layer with CCRs of MMA structure from 5 to 15 GHz.

The measured resonance frequencies, the reflection coefficients S₁₁ and the absorptance peaks at these resonance frequencies are in close approximation with the simulated values. The reflection coefficients in terms of S₁₁ parameter are measured experimentally and it is found that at first resonance frequency (7.20 GHz) the S₁₁ value is −12.7 dB. At second resonance frequency (9.3 GHz) the S₁₁ value is measured to be −17.4 dB. At third resonance frequency (12.61 GHz) the S₁₁ value is measured to be −13.1 dB. At fourth resonance frequency (13.07 GHz) the S₁₁ value is measured to be −21.8 dB shown in Figure 17a. Figure 17b shows the comparison of estimated simulated and measured absorptance at resonance frequencies. The estimated absorptance at first resonance frequency from measured reflection coefficients is 94.5%. At second resonance frequency the measured absorptance is 97.9%. At third resonance frequency the measured absorptance is 95.1%. At fourth resonance frequency the measured absorptance is 99.3%. The third and fourth resonance peaks merged together to generate a 3 dB broad-band of bandwidth 1.2 GHz that lies in Ku-band. The measured resonance frequencies are found to be slightly shifted towards right (at higher frequency) as compared to the simulated resonance frequencies. This slight variation is contributed by fractional variation in the width of the CCRs structure fabricated on an area of 180 × 180 mm by UV photolithography and wet etched process as compared to dry etched process of fabrication.

Figure 17.

(a) Comparison between simulated and experimentally measured values of reflection coefficient S₁₁(f). (b) Estimated simulated and measured absorptance at resonance frequencies for MMA at 7.20, 9.3, 12.61 and 13.07 GHz.

6. Conclusions

MMs are artificially engineered materials that exhibit negative permittivity and permeability. These materials possess unusual EM properties that make these materials unique. The interest in MMs increased with first demonstration of MM absorber by Landy et al. in 2008. The conventional EM absorbers were limited in performance due to their bulky size and the performance is limited to microwave frequencies due to impedance matching conditions. One of the application domains of MMs is a MPA. The frequency selective top layer of conventional MPA has matched impedance with that of the free space. Under perfectly matched conditions the incident EM waves are absorbed with minimum reflections and get attenuated inside the substrate. The MM design, MM behavior, impedance matched conditions, and absorptance of EM waves under perfectly matched conditions are explained with a case study of a multi-band MPA that finds application in stealth technology.