Introduction
In contrast to natural materials, metamaterials possess exclusive properties that are unattainable using conventional materials. For example, their permittivity and permeability can be tailored to display highly dispersive or negative characteristics. These qualities can be achieved through the utilization of periodic arrays of resonators, such as split ring resonators (SRR) [Reference Sabah, Dincer, Karaaslan, Akgol, Demirel and Unal1, Reference Duan, Tang, Wang, Zhang, Chen, Chen and Gong2]. Owing to their exceptional capabilities, they find applications in various fields like biomedicine [Reference Fang, Lee, Sun and Zhang3], super lenses [Reference Ramesh and Vakula4], cloaking technology [Reference Schurig, Mock, Justice, Cummer, Pendry, Starr and Smith5], and the absorption of electromagnetic waves [Reference Baqir and Choudhury6, Reference Bilal, Baqir, Choudhury, Naveed, Ali and Rahim7].
EM wave absorbers are utilized in numerous applications, such as energy harvesting [Reference Oudich and Li8], reduction of radar cross-section, imaging [Reference Fallahi, Yahaghi, Benedickter, Abiri, Shahabadi and Hafner9], heat production [Reference Salek, Celep, Weimann, Stokes, Shang, Phung, Kuhlmann, Skinner and Wang10], detection sensitivity enhancement [Reference Ghasemi, Roostaei, Sohrabi, Hamidi and Choudhury11, Reference Amugothu and Damera12], solar panels [Reference Li, Zhao, Liu, You, Chu, Tian, Chen, Li, An, Cui and Zhang13], and photodetectors [Reference Wu, Wang, Lai, Zhu and Gu14]. One of the interesting and exciting applications of metamaterials is their ability to act as EM wave absorbers.
To elaborate, microwave metamaterial absorbers have proven advantageous in reducing radar cross-section (RCS) and mitigating electromagnetic interference (EMI) [Reference Wang, Feng, Xu, Wu and Hu15]. The absorption capabilities of metamaterials can be amplified through the incorporation of ferrites [Reference Li, Wei, Wang, Hu, Li and Guan16]. Achieving high absorption levels is feasible by crafting metamaterials on cost-effective printed circuit boards, even with their slender design, thus attaining nearly flawless absorptive properties [Reference Lim, Lee and Lim17, Reference Khuyen, Tung, Yoo, Kim, Kim, Chen, Lam and Lee18]. These metamaterials are constructed around arrays of resonators, with their absorptive attributes influenced by frequency, resulting in a relatively narrow bandwidth. While its limited bandwidth serves well in sensor applications, broader bandwidth is necessary for the majority of use cases. As a result, numerous techniques have been suggested to expand the bandwidth of metamaterial absorbers. Furthermore, the absorptive characteristics of these absorbers are influenced by polarization and incident angles. Although achieving polarization insensitivity can be accomplished through adept unit cell design, ensuring angle insensitivity in metamaterial absorbers remains a challenging task. Consequently, various endeavors have been undertaken to achieve absorbers that are insensitive to incident angles [Reference Chen, Li, Cao, Gao and Guo19, Reference Wen, Huang, Guo, Yang, Han and Zhang20].
Various applications necessitate distinct design specifications, encompassing performance in single, dual, and multiple frequency bands. Bhattacharyya et al. introduced a dual-layer, dual-band metamaterial absorber employing concentric CRR structures, achieving bandwidths of 1.24 and 1.92 GHz in the C and X bands. However, it is important to note that this design is multilayered [Reference Bhattacharyya, Ghosh, Chaurasiya and Srivastava21]. Guo et al. proposed a confined gap surface plasmon absorber configuration equipped with a reflective mirror, demonstrating polarization-independent attributes across the terahertz spectrum. Nevertheless, it should be highlighted that this structure is complex and multilayered in design [Reference Guo, Yang, Shen, Zhou, Gao and Guo22]. Bhattacharyya et al. introduced a metamaterial absorber design utilizing electric field-driven LC resonators. This structure exhibits a bandwidth of 0.42 GHz, spanning from 5.04 to 5.28 GHz. Notably, the design showcases polarization insensitivity for incident angles up to 30∘; however, it is important to note that the range of angles for which absorption is effective is relatively limited [Reference Bhattacharyya, Ghosh and Srivastava23]. Ghosh et al. showcased a metamaterial absorber driven by an electric field, employing an LC configuration featuring a swastika-like structure. This design demonstrates a limited bandwidth of 0.33 GHz (10.22–10.55 GHz), while maintaining absorption rates above 85%. However, it is crucial to acknowledge that the size of the structure is substantial [Reference Ghosh, Bhattacharyya and Srivastava24]. Uddin et al. engineered a periodic dual-resonance metamaterial absorber employing an octagonal ring, cross-wires, and a cut-off circle shaped structure. This design covers a frequency range spanning from 9 to 18 GHz, achieving 70% absorption even for oblique incidence angles [Reference Uddin, Ullah and Islam25]. Soheilifar et al. put forth a metamaterial absorber design encompassing a bandwidth spanning from 5.796 to 20.732 GHz, and accommodating a 45∘ angle of incidence for both transverse electric (TE) and transverse magnetic (TM) polarizations. It should be noted, however, that this structure involves multiple layers with considerable thickness [Reference Soheilifar and Sadeghzadeh26]. Wen et al. presented a multi-layer configuration featuring two metallic patches operating across four frequencies within the range of 8–16 GHz. Nevertheless, it is pertinent to mention that the angle of incidence is limited to 45∘ for both TE and TM polarizations [Reference Wen, Huang, Guo, Yang, Han and Zhang27]. Notably, the design’s bandwidth is restricted, and the structure comprises multiple layers. In light of these existing gaps, a novel design is proposed to address these limitations.
In the proposed paper, a single layer metamaterial absorber structure for a wide frequency band is presented. The structure consists of a combination of S- and partial M-shaped resonance structures. In the structure, the incorporation of a square-toothed circular resonator closes the outer circle. The square tooth acts like a stub to enhance the bandwidth. To achieve the maximum bandwidth, the parameters are optimized to the best possible values. The simulation results are analyzed, and parametric analysis is carried out to understand the mechanism of the designed structure. In addition, the proposed structure has a good amount of absorption, thin configuration, and compact size.
Unit cell design
A unit cell planar geometry is designed on an FR4 substrate, as shown in Fig. 1. The top resonance structure consists of a SM-shaped square-tooth circular resonator on the substrate. The design parameters are initially chosen sensibly to achieve a broadband absorber. The design process of a unit cell consists of four steps, as shown in Fig. 1(a). Initially, the resonance structure takes the form of an S-shaped design represented as stage 1. In the second stage a partial M shaped structure which acts like a split ring resonator is taken. The first and second structures are combined in a third step, resulting in a SM-shaped structure. Initially, the bandwidth is less, but to obtain maximum bandwidth, the S-shaped structure is extended to form a complete circle. Stubs, which looks like square tooth are further added to the extended structure in order to increase bandwidth. Finally, a unit cell metamaterial absorber is realized, as shown in Fig. 1(b). To prevent electromagnetic waves from being transmitted, the bottom layer is covered with a metallic layer. The above geometric parameters are optimized using Ansys HFSS software and are shown in Table 1. In order to maximize cost-effective design an FR4 substrate is selected with the thickness of 3.2 mm, loss tangent as 0.02, and dielectric constant of 4.4. The top and bottom metallic layers on FR4 substrate are of thickness 0.035 mm and conductivity of 5.8 × 107 S/m.
Geometry of designed unit cell: (a) all stages and (b) detail dimension.
Optimized parameters of the metamaterial absorber
To check the S-parameter simulation results for the unit cell geometry the boundary conditions are applied along X and Y directions and Floquet ports are considered infinite slabs along the Z direction.
The mathematical expression for absorption in terms of the frequency is defined as 
$ A(\omega )= 1 - \left| {S_{11} (\omega )} \right|^2 - \left| {S_{21} (\omega )} \right|^2 $ [Reference Landy, Sajuyigbe, Mock, Smith and Padilla28] where 
$S_{11}(\omega)$ and 
$S_{21}(\omega)$ are the reflection coefficient and transmission coefficient, respectively. For near unity absorption it is essential to minimize transmission coefficient S21 and reflection coefficient S11 concurrently. To make this possible, the absorber must have resonating structures. By using a metallic ground plane, the transmission values are reduced to zero in the proposed metamaterial absorber. Thus, the absorption is calculated using only the reflection coefficient. It is feasible to simplify the absorption by 
$A(\omega ) = 1 - \left| {S_{11} (\omega)} \right|^2$. Now, to realize unit absorption, S11 must be reduced, which is realized by using SM shaped with square tooth circular resonator. For perfect absorption of EM waves, the structure needs to have occurrence of electrical and magnetic resonances simultaneously.
Results and discussion
The absorptivity results of the four stages are shown in Fig. 2. According to the results, it can be observed that at the 4th stage, absorptivity has a wide band absorption compared to the other stages. The S-parameter results for the proposed unit cell structure for both TE and TM polarizations for normal incidences are shown in Fig. 3. From figure, the reflection coefficient is below −10 dB at 13.60–16.14 GHz with more than 96% absorptivity. These findings demonstrate the effectiveness of the proposed unit cell structure in achieving high absorption rates within the specified frequency range.
A simulation of absorption for all stages of unit cell geometry.
The simulation results for the unit cell geometry in terms of reflection coefficient and absorption are presented: (a) TE polarization and (b) TM polarization.
Unit cell parameter retrieval
For the unit cell geometry, the metamaterial parameters are extracted using modified Nicholson–Ross–Weir technique [Reference de Araújo, Siqueira, Kemptner, Weber, Junqueira and Mosso29]. The resonance frequency from 13.60 to 16.14 GHz is analyzed to obtain the unit cell electromagnetic parameters. It is observed that the real part of the permittivity is negative from 13.7 to 16.14 GHz. The imaginary part is near zero value except below 13.7 GHz as shown in Fig. 4(b). Similarly, from Fig. 4(a). The real part of the permeability is negative from 13.7 to 16.14 GHz and the imaginary part is near 0. From 13.60 to 16.14 GHz, both permittivity and permeability are negative resulting in a double negative metamaterial absorber. Over the entire frequency range from 13.60 to 16.14 GHz, the refractive index becomes negative as shown in Fig. 4(c). A negative refractive index confirms that the proposed metamaterials behave in a left-handed manner. From Fig. 4(a, b), the real part of the permeability and permittivity results demonstrates occurrence of electric and magnetic resonances.
The real and imaginary values of permeability, permittivity, reflective index, and impedance plots for unit cell geometry.
Unit cell parametric analysis
This section illustrates how a unit cell structure can be analyzed based on the design parameters. Based on the proposed unit cell structure, performance and characteristics are analyzed for different substrate heights (h) and resonator widths (w1 and w2). The dimensions of the outer ring width is w1, and the inner ring width is w2. In order to evaluate the unit cell’s behavior accurately, the parametric results are shown Figs. 5 and 6(a, b). The substrate thickness (h) varies from 0.8 to 4.8 mm, and the absorptivity is represented in Fig. 5. At a substrate thickness of 3.2 mm, the absorptivity is maximum over a wide bandwidth, indicating destructive interference of multiple reactions that causes near-unit absorption. The unit cell behavior for the varying widths of the rings w1 and w2 is represented in Fig. 6(a, b), respectively. The width w1 is varied from 0.13 to 0.16 mm, and it is observed that the optimum value for maximum absorption is found to be 0.15 mm. The width w2 varied from 0.05 to 0.35 mm, and it is observed that the absorptivity is better when w2 is 0.25 mm. By analyzing the unit cell, we will gain a better understanding of its function, be able to design, and optimize similar structures in the future.
Parametric analysis results for different substrate thicknesses (h) values.
Parametric analysis results for different parameters: (a) w1 and (b) w2.
Bandwidth enhancement
However, in order to achieve the maximum bandwidth, an S-shaped structure is extended until it becomes a complete circle. In order to further enhance the bandwidth, stubs look like as square tooth are added to the extended S-shaped structure. A square tooth is a branch or offshoot that is connected to a main transmission line, which effectively enhances the bandwidth, as shown in Fig. 2. Furthermore, the full width at half maximum (FWHM) bandwidth is calculated from the absorptivity results from Fig. 3. The computed frequency range value is from 13.2 to 16.8 GHz, which is 3.6 GHz FWHM bandwidth achieved.
Oblique incidence angles
In this section, the analysis of the proposed metamaterial absorber response for incident TE and TM waves at different incident angles is presented. It is of utmost importance that the absorptivity of the structure be less affected by the oblique incidence angles (θ). The incident angle is varied from 0∘ to 60∘ in steps of 15∘, and the corresponding absorptivity is measured for both TE and TM polarizations as shown in Fig. 7. Results showed that the absorptivity for both polarizations is stable. The absorptivity of 92% is achieved for the TE and TM polarizations when the incident angle is close to 60∘. Furthermore, it is observed that the absorptivity for the TE polarization is slightly lower than that of the TM polarization. The unit cell has rotational mirror symmetry; therefore, the simulated absorptive performance under oblique incidence is identical up to 60∘ for both polarizations. These results indicate that the absorptivity of the metamaterial is independent of the incident angle and polarization of the incident wave.
A simulation of absorptivity results for oblique incidence angles: (a) TE polarization and (b) TM polarization.
Moreover, to comprehend the characteristics of electromagnetic waves in various polarizations, such as co-polarization (Ryy) and cross-polarization (Rxy), the simulated reflection coefficients of Ryy and Rxy are represented in Fig. 8. The results demonstrate that the proposed design functions as an electromagnetic wave absorber.
Simulated co- and cross-reflection coefficients for y-polarized incident waves.
Electric field distribution and surface current distribution
To understand the physical mechanism of absorption, the electric field and surface current distributions are shown in Figs. 9 and 10 at frequencies of 13.89 and 15.21 GHz, respectively. The frequencies with maximum reflection are selected. At the absorption frequency of 13.89 GHz, the maximum electric field intensity is present on the unit cell geometry except for diagonal lines l 1 and some parts of the partial M-shaped design which indicate the occurrence of electric resonances. Similarly, at the absorption peak of 15.21 GHz, the maximum electric field intensity is present except for some portion of the S-shaped structure, and some part of l 1 shows occurrences of electric resonances. Figure 9(a, b) indicates the occurrence of electric fields at all the high absorption peaks. Further, the overlapping of the electrical resonances results in wide-band absorption.
The electric field distribution of the unit cell geometry: (a) at 13.89 GHz and (b) at 15.21 GHz.
The surface current distribution of the unit cell geometry: (a) at 13.89 GHz and (b) at 15.21 GHz.
The surface current density plot is shown in Fig. 10 at the highest absorption peaks. The surface current density for the proposed structure at the top and bottom is shown in Fig. 10(a, b) for the absorption peak at 13.89 GHz. Similarly, for the absorption peak at 15.21 GHz, the top and bottom current densities are illustrated in Fig. 10(c, d). From Fig. 10(a–d), for both absorption peaks, there are parallel and antiparallel currents from the top and bottom surfaces, which results in strong magnetic resonances in the unit cell structure. Therefore, from Figs. 9 and 10, there is a strong presence of electric and magnetic resonances for maximum absorption peaks, which causes broadband absorption.
Experimental setup and measurement
In order to experimentally verify the real-time performance of the metamaterial absorber, a prototype unit cell and array of unit cells are fabricated and tested, as shown in Figs. 11(a) and 12. The measurements are carried out in two stages. Initially, a unit cell with dimensions of 11 mm × 11 mm × 3.2 mm is tested with the help of a coaxial waveguide. Then, an array of unit cells with dimensions of 275 mm × 275 mm × 3.2 mm is placed in the anechoic chamber as shown in Fig. 11(b). In the measurement process, devices such as a vector network analyzer (VNA) up to 40 GHz and a standard horn antenna are used. The measurements are performed in an anechoic chamber. The reflectivity of the sample is measured under normal incidence angles. From Fig. 13, it is shown that the simulation and measurement results are in good agreement with the absorption of more than 92% in the frequency range from 13.60 to 16.14 GHz. The results of the simulation showed a strong agreement with the measured results, which confirms that the dispersion-engineered design strategy is successful in achieving wideband and wide-angle absorption for both TE and TM polarizations.
A measurement of electric permittivity and magnetic permeability provides valuable insight into materials electrical and magnetic properties as shown in Fig. 14. The proposed structure exhibits a strong correspondence between simulated and measured values.
(a) Fabrication of an array of unit cell geometry and (b) measurement setup.
Fabrication of unit cell geometry.
Simulations and measurements of the proposed unit cell structure: (a) TE polarization and (b) TM polarization.
Measured results of: (a) relative permittivity and (b) relative permeability.
The measurements of oblique incidents for the proposed design, considering both TE and TM polarizations, are carried out within an anechoic chamber. The angle of incidence is adjusted in increments of 15∘, ranging from 0∘ to 60∘, while measuring the corresponding absorptivity for both TE and TM polarizations, as illustrated in Fig. 15. The results indicated that the absorptivity remains consistent for both polarizations as shown in Fig. 16. Absorptivity higher than 85% is achieved for both TE and TM polarizations when the incident angle approaches 60∘.
Experimental setup for oblique incidence angles.
The measurements of absorption under oblique incidence for both polarizations: (a) TE polarization and (b) TM polarization.
The comparison between simulated and measured absorptivity is conducted for incident angles of 0∘, 30∘, and 60∘ in Fig. 17(a) for TE polarization and in Fig. 17(b) for TM polarization. The simulated and measured results exhibit similarities across all cases.
The comparison between simulation and measurement results of absorption under oblique incidence for both polarizations: (a) TE polarization and (b) TM polarization.
The proposed metamaterial absorber characteristics are compared with the published literature characteristics, as shown in Table 2. This comparison revealed that our design strategy was more effective in terms of bandwidth, unit cell size, substrate layers, polarization insensitivity.
Table of comparisons with published literature
Conclusion
This work presents a microwave metamaterial absorber with wide band, wide angle, and polarization insensitivity. A detailed analysis of the absorber’s performance confirmed near unity absorption for both TE and TM polarizations at normal and oblique incidence angles from 13.60 to 16.14 GHz. As a result of these findings, microwave engineering will be advanced, and absorbers will get a whole new edge. The physical mechanism of the proposed metamaterial absorbers is also studied with the help of surface current and electric field distributions. A determination of permittivity and permeability confirms the metamaterial properties of the presented structure. In the end, the present state of the art is compared with those previously published, and it is concluded that the presented one had a high frequency with a wide bandwidth. As a result, metamaterial absorbers offer interesting applications in solar cells, detection, and imaging.
Competing interests
None declared.
Ramesh Amugothu received his B.Tech degree in Electronics and Communication Engineering from Jawaharlal Nehru Technological University in Hyderabad, India, in 2013, and an M.Tech degree in the department of electronics and communication engineering from the National Institute of Technology Surathkal, India, in 2016. Currently, he is pursuing his Ph.D. degree in the department of electronics and communication engineering at the National Institute of Technology, Warangal, India. He has over 3 year’s research/academic experience. He is an IEEE student member, voice chair for IEEE-MTT and IEEE-APS at NIT Warangal, India.
Vakula Damera received a bachelor’s degree in electronics and communication engineering from Nagarjuna University, Andhra Pradesh, India, and a master’s degree from the Birla Institute of Technology, Mesra, India. With a focus on microwave specialization in 1992 and 1994, respectively, and a Ph.D. degree in Fault Diagnostics of Antenna Arrays from the National Institute of Technology, Warangal, India, in 2010. She is a professor at the National Institute of Technology, Warangal. She has authored 77 papers for international conferences and journals. Her areas of interest include phase array antennas, ultra-wideband antennas, multiband antennas, fault diagnostics, neural networks, and metamaterials. She has over 30 years research/academic experience in the areas of RF and microwave systems/components and has executed over 10 projects sponsored by DST/AICTE/MHRD or other sponsored R&D project.
