1 Introduction

Optical metamaterials have potential in photonics and can be engineered to have desired electromagnetic properties. Optical metamaterials have led to increased research in electromagnetic absorbers due to their significant importance (Feng et al. 2020). Research on electromagnetic absorbers has increased due to their importance in solar energy harvesting (Liu et al. 2021), photovoltaic devices (Cui et al. 2016), and sensing (Beruete and Jáuregui-López 2020). There are two types of absorbers: resonant absorbers, which absorb specific frequencies, and broadband absorbers, which absorb a wide range of frequencies (Zhou et al. 2020). Different types of metamaterial geometries have been analyzed, including the double split-ring resonator, U-shaped SRR, chiral metamaterial (Tian et al. 2017) and multi-layer structure (Zheng et al. 2024a). Various types of electromagnetic absorbers have been developed for different frequency ranges, such as microwave (Liu et al. 2018), terahertz (Wang et al. 2022), infrared (Bağmancı et al. 2017), and visible frequencies (Hakim et al. 2022). Different structures and materials, including carbon nanotubes dispersed in polymers (Kang et al. 2019), graphene-based applications (Li et al. 2024a; Zheng et al. 2024b, 2024c), hash-shaped geometries, dual-band designs, and gold layers with dielectric spacers, have been investigated to achieve high absorption in specific frequency ranges. These absorbers show polarization insensitivity and wide-angle absorption capabilities (Zhang et al. 2016). Gold nanoparticles with a gold reflector and a dielectric spacer also result in high absorption in the visible spectrum, with polarization insensitivity at certain incidence angles (Yan et al. 2014). Different nanostructured materials have been utilized for industrial heater applications (Ali et al. 2024; Agravat et al. 2024a, 2024b). A metal-dielectric-metal structure has been created using a Cu/Si3N4/Cu stack on a silicon substrate. This structure can absorb almost all of the visible light. It has been found that this structure can achieve an average absorbance of over 80% in the visible range of 400–700 nm (Zhu and Jay Guo 2012). Another type of absorber called a terahertz metamaterial absorber, has been developed using four metallic gold rings. This absorber can absorb light regardless of its polarization. The absorption peaks of this absorber are due to the resonance state of the individual rings, and adding another metallic ring can produce even more absorption peaks (Wang et al. 2015). Researchers have also used a genetic algorithm to create an optical metamaterial with a wide range of absorption in the mid-infrared wavelength range (Bossard et al. 2014). This metamaterial is also polarization-insensitive. Plasmonic nanoantenna patches made of ZnS and gold have been placed over a thick gold layer to create an efficient and wide-band plasmonic absorber in the infrared spectrum (Xu et al. 2021). A research group has demonstrated that including multiple sublattices in a metamaterial perfect absorber can enhance absorption peaks in the mid-infrared range (Hou et al. 2021). Another absorber has been built for the visible spectrum using four split-ring resonators. This absorber can achieve high absorption for both TE and TM polarizations due to the coupling effect between gold and GaAs (Cheng et al. 2023). Finally, a silica-chromium-silica layer has been used to create an absorber structure without patterning the metamaterial. This structure can absorb light in the visible and near-infrared ranges with wavelengths of 0.4–1.4 µm (METAL, L.O.R. 2018). In a study (Jiang et al. 2018), a tunable terahertz absorber called bulk-Dirac-Semimetal (BDS) is introduced. By applying a biasing potential, the absorption properties of the BDS layer can be adjusted. A new absorber structure, consisting of split circular resonators with metallic split rings and graphene stacks in SiO2, has been developed. This structure offers a tunable absorption coefficient exceeding 0.9 within the frequency range of 2.58—3.56 THz (Dong et al. 2017). Plasmonic graphene-based absorbers with metallic cross structures provide absorption peaks using graphene (Xiong et al. 2015). A structure with graphene/MgF2 stacks on gold film shows two absorption peaks and a nanosecond photothermal effect (Su et al. 2015). A tunable absorber is designed using a random hill climbing algorithm to achieve a wide bandwidth of absorption (Torabi et al. 2017). Researchers have developed a broadband metasurface solar absorber that operates in both the infrared and visible ranges of the solar spectrum (Liang et al. 2023; Li et al. 2024b). Using an evolutionary algorithm, they optimized the unit cell area to enhance absorption bandwidth (Heidari and Sedighy 2018). The absorber, made of a cross-shaped metasurface with gold nanorods, achieves multiple absorption resonances across the entire solar spectrum (Khan et al. 2018). A broadband terahertz absorber has been developed using eight gold nano-resonators arranged in a symmetrical pattern. This absorber is capable of absorbing a wide range of frequencies, from near-infrared to visible light (Azad et al. 2016). The authors suggest a new architecture that utilizes a multifunctional metamaterial absorber to absorb longwave IR energy (8–12 μm) directly in a thin-film lithium niobate layer. This absorber also serves as the contacts for the two-terminal detector. The device achieves a narrowband absorption (560 nm FWHM at 10.73 μm) with high efficiency (86%) (Suen et al. 2017). The authors have proposed a new type of absorber that can perform multiple functions. This absorber is integrated with a detector that can detect both mid-wave infrared (MWIR) and long-wave infrared (LWIR) wavelengths. The detector is made using a very thin InAs/GaSb Type-II superlattice (T2SL) interband cascade detector (Montoya et al. 2017). The research shows that these multifunctional metamaterials can effectively detect specific wavelengths in the infrared spectrum. This can be useful for improving infrared imaging in various applications.

In this research, we have presented the design of a nano-metamaterial-based wideband solar absorber using gold and nickel as resonators, and it was investigated in terms of reflectance, absorptance, and various properties. The suggested construction was examined by concurrently altering materials and various geometrical factors. The design of ONMMA has an absorption rate of over 90% from 593.84–829.8 THz, with an average absorption rate of 93.891%. This covers more than 50% of the visible range and a small portion of the ultraviolet range. Additionally, the ONMMA has an absorption rate of over 75% from 226.64–853.04 THz, with an average absorption rate of 88.945%. This covers the entire visible spectrum, with a small portion in the infrared and ultraviolet regions. The operational bandwidth of the design is 200–920 THz, with an average absorption rate of 86.424%. The ONMMA achieves a maximum absorption rate of 99.866% at 705.44 THz.

2 Design and modelling

The suggested design of a metamaterial-based wideband solar exploiter is depicted in Fig. 1. Where Fig. 1a gives a three-dimensional schematic using materials, Fig. 1b displays a front view, and Fig. 1c shows the side view using parameters of the design. The structure includes an octagonal elliptical shape of nickel inside a square box shape of nickel. A circular gold ring is located above the octagonal elliptical nickel shape. Also, a square shape of gold is located on the nickel at the center as resonators and a gold ground plane is separated by a Quartz (Fused) substrate. The specifications of substrate material (Quartz) are tanδ = 0.0004, ε = 3.75, thermal conductivity = 5 [W/K/m], Rho = 2200 [kg/m3], heat capacity 0.7 [KJ/K/Kg], thermal expan. 0.5 × 10–6 /K and µ = 1. Quartz can withstand very high temperatures with a melting point of about 1,710 °C (3,110°F). It has low thermal expansion, maintaining its structural integrity under thermal stress. Its low thermal expansion and high thermal conductivity also enable it to resist thermal shock, allowing it to endure rapid temperature changes without cracking or breaking. Due to its thermal stability, quartz is commonly used in applications like furnace linings, high-temperature windows, laboratory crucibles, and semiconductor manufacturing. Gold has an Electric conductivity of 4.561 × 107 [S/m], Thermal conductivity = 314 [W/K/m], Rho = 19,320 [kg/m3], Heat capacity of 0.13 [KJ/K/Kg], Thermal expan. 14 × 10–6 /K and µ = 1. Nickel has electric conductivity 144 × 107 [S/m], thermal conductivity = 91 [W/K/m], Rho = 8900 [kg/m3], heat capacity 0.45 [KJ/K/Kg], thermal expan. 13.1 × 10–6 /K and µ = 600. The radius of gold resonators is considered ‘r’, the radius of octagonal elliptical nickel resonators is ‘ron’, the height of gold ring resonators is ‘hr’, the thickness of square shape gold ‘tsg’ the thickness of nickel ‘tn’, the thickness of the substrate as ‘ts’, the thickness of the ground plane as ‘tg’, and the length and width of the substrate and ground plane as ‘w’, the length and width of square shape the gold plate ‘wrg’, the width of plus shape nickel resonator ‘wpr’ the width of square shape nickel resonator ‘wsr’ that is the overall width of the geometry. The structural parameters for proposed unit cell construction are shown in Table 1.

Fig.1
figure 1

a The geometry of the proposed unit cell, b front view, and c side view

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The proposed structure is analyzed using Computer Simulation Technology (CST). Positioned in the x–y plane, it is subjected to a transverse electric field directed from + z to -z. The boundary conditions are configured with unit cells in the x–y plane, Et = 0 at Zmin, and Zmax is set to open (add space). A mesh, which divides the structure into small elements, is generated to create a discretized model. CST provides an adaptive mesh automatically for accurate results, although the mesh settings can be manually adjusted for more precise control.

The relation between absorption (A), reflectance (R), and transmittance (T) is given as,

$${\text{A}} = {1}{-}{\text{R}} - {\text{T}}$$

Where the reflection coefficient (S11) and transmission coefficient (S21),

$${\text{R}}\, = \left| {{\text{S11}}} \right|{\text{ and T}}\, = \left| {{\text{S21}}} \right|$$

The gold material used in the design has a skin depth for light ranging from 5.55 nm to 2.59 nm, which is smaller than the thickness of the material. Consequently, the transmittance is zero (Abohmra et al. 2020).

$${\text{A}}\, = \,{1}{-}{\text{R}}$$
(1)

Electron Beam Lithography (EBL) as a possible manufacturing method. EBL uses a focused electron beam to create specific patterns on a substrate coated with resist.

Table 1 Structural parameters for proposed unit cell construction
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3 Results and discussion

This section discusses the simulated results and behaviors of ONMMA. It starts by discussing the absorption characteristics in Sect. 3.1. Then, it describes how the polarization insensitivity angles (0°, 90°, and 180°) and incident angles (0°, 15°, 30°, 45°, and 60°) affect ONMMA in Sect. 3.2. Section 3.3 illustrates the different geometric parametric analyses and material characteristics of absorption. Additionally, Sect. 3.4 discusses the E-field, H-field, and surface current distributions, as well as the power loss distribution, which is responsible for the absorption mechanism.

3.1 Absorption characteristics of the proposed ONMMA

The absorption characteristics of the proposed ONMMA were analyzed using equation (1). The absorption exceeded 75% in the frequency range of 226.64–853.04 THz, covering a small portion of inferred light wave frequencies, full visible frequency ranges, and a small section of ultraviolet frequencies. In the range of 593.84–829.28 THz, absorption was over 90%, spanning more than 50% of visible frequencies and a small ultraviolet range. Overall, the proposed ONMMA achieved 86.424% absorption in the sunlight range of 200–920 THz, making it an ultra-wideband absorber. Figure 2 shows the absorption and reflection of the proposed ONMMA. The two peak absorptions are 99.866% and 96.19% at frequencies 705.44 THz and 814.88 THz.

Fig. 2
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The absorption and reflection rates of the proposed structure

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3.2 Polarization insensitivity and incident angle stability

The study examined how the absorber's effectiveness is affected by different angles at which electromagnetic (EM) waves hit it. The angles at which the waves hit and refract have a significant impact on the amount of reflection that occurs. Figure 3a, b illustrates the polarization angle (phi) and the oblique incident angle (theta) of the EM wave hitting the absorber. The EM wave travels towards the negative z-axis. The red circle represents the area where the incident angle theta can range from 0 to 180 degrees, and the green circle represents the area where the angle phi can range from 0 to 360 degrees, encompassing the electric and magnetic field vectors of the EM wave.

Fig. 3
figure 3

a Incident of EM wave on ONPMA b Indication of Phi and Theta angle of incident EM wave on ONPMA, c Incident angle, d Polarization insensitivity

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The absorption characteristics of the design were analyzed at different polarization angles (φ), showing that the ONPMA performed well even at angles up to 180°. The research on ONPMA architecture for solar cell implementation focuses on complying with the design framework for capturing different polarizations of EM radiation from the sun. Designing an effective solar cell is challenging as it requires containing arbitrary polarizations of EM radiation. Numerical analysis showed that the proposed ONPMA had maximum absorption of 99.866%, 99.849%, and 99.952% with a total average absorption of 86.424%, 86.413%, and 86.415% in the range 200–920 THz for polarisation angles of 00, 900, and 1800 respectively, making it a promising candidate for solar energy collection. Figure 3c and d show that as the angle of incidence increases, there is a decrease in average absorption and a shift towards higher frequencies. Higher incidence angles reduce the coupling impact and the wave-confining ability of the dielectric layer. Specular reflection was used to determine absorption, which revealed that most reflected energy was concentrated in a certain direction. Based on the numerical analysis, the highest peaks are 99.866%, 96.199%, 99.502%, 98.350%, and 80.680%, at a frequency of 705.44THz, 706.88 THz, 683.84 THz, 891.20 THz and 782.48 THz; Also, a total average absorption in the range 200–920 THz is 86.424%, 85.199%, 86.547%, 81.950% and 66.930% for incident angles of 0°, 15°, 30°, 45°, and 60° respectively. The numerical analysis identified the highest absorption peaks at various incident angles.

3.3 Parametric analysis

This section examines the results of the parametric analysis. It investigates how the performance of the metamaterial is affected by the type of substrates used, the influence of different conducting materials on scattering parameters, variations in structural dimensions, and the impact of different thicknesses of shapes. The following subsection concentrates on studying the distribution of surface current, electric field, magnetic field, and power distributions.

3.3.1 Dependence on geometric parameters

This section analyzes the results of the parametric analysis. It investigates how the performance of the absorber is affected by the variations in geometric parameters of the ground, substrate, and conducting materials. The influence of variations in structural dimensions, shapes, and the impact of different material thicknesses changes the absorption characteristics, which are shown in Fig. 4. The absorption data with variations in geometric parameters is shown in Table 2.

Fig. 4
figure 4

Different absorption characteristics of a changes in dimensions of substrate and ground; b various substrate thicknesses; c different elliptical shapes; and d several thicknesses of nickel conductor

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Table 2 Comparison table for dependence on geometric parameters
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Table 2 shows the maximum peak absorption to be 99.866%, the maximum average absorption to be 86.424%, and the maximum bandwidth to be 626.40 THz with absorption above 75%. Additionally, at a dimension of 200 \(\times\) 200 um2, the absorption is above 90% at 235.44 THz. The best performance is achieved with a substrate thickness of 60 nm. The absorption characteristics also depend on the conducting elliptical radius, with the best performance observed at r1/r2 = 125 nm/ 125 nm. Similarly, the maximum average and peak absorption alter with changing conductive nickel thickness, and the best performance is obtained at a thickness of 20 nm.

3.3.2 Dependence on materials

This study examines how the absorber's performance is impacted by changes in the materials used for the ground, substrate, and conducting patch. The absorption characteristics are influenced by the different properties of these materials, as depicted in Fig. 5. Table 3 presents the absorption data for various material variations.

Fig. 5
figure 5

Different absorption characteristics of a changes in conducting patch materials; b various substrate materials; c different ground materials

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Table 3 Comparison table for variation of material on absorption characteristics
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Different metamaterials have been found to alter absorption characteristics, as shown in Table 3. When using different conducting materials, the highest average absorption, maximum peak, and width of absorption above 75% and 90% are changes with using materials. The best absorption characteristics were observed with gold rings and octagonal nickel as the conductive materials. On the other hand, when using various substrate materials, the highest peak, average absorption, and width are achieved with quartz as the substrate. As for the ground material, copper and silver yield the highest peak absorption but show overall absorptions are less. However, overall, the best performance is obtained when using quartz as the substrate, nickel, and gold as the conducting patch, and gold as the ground material. With these materials, the proposed design achieves a peak absorption of 99.866%, absorption above 75% in the total range of 626.40 THz, absorption above 90% in the total range of 235.44 THz, and a total average absorption of 86.424% in the ranges 200–920 THz.

3.4 Mechanisms of absorption

This section analyzed the properties of absorption of the proposed ONMMA. In the numerical analysis, the finite integration technique (FIT) method-based CST Electromagnetic (EM) simulator is used to numerically study a specific structure. The boundary conditions are set up with a unit cell boundary condition in the x and y directions, and an open boundary condition in the z-direction. The electromagnetic wave propagates along the z-axis, with the electric field parallel to the x-axis and the magnetic field parallel to the y-axis.

3.4.1 Analysis of surface current, electric field, and magnetic field distribution

An analysis was conducted to understand how absorption works by examining the surface current and electric field at two specific resonance frequencies: 705.44 THz and 814.88 THz. These frequencies were chosen because they represent the points where absorption is at its highest level. When absorption is perfect, the absorbers' electric and magnetic responses match those of the incoming wave, resulting in resonance frequencies. Figure 6 illustrates that the absorber causes a significant concentration of circulating current along the edge of the nickel resonators. Further investigation reveals the presence of parallel and anti-parallel surface currents traveling across the nickel slabs, which generate an electric resonance in the absorber. Additionally, the flowing current creates a magnetic resonance.

Fig. 6
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Surface current distribution at a 705.44 THz, b 814.88 THz

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Another method of comprehending the absorption process involves analyzing the distribution of the electric field and magnetic field at resonant frequencies shown in Fig. 7 and Fig. 8 respectively. Figure 7 demonstrates that the electric field is primarily concentrated along the edges of the nickel slabs. This behavior resembles that of electric dipoles, which are accountable for electrical resonance. Additionally, the strong electric field, resembling a dipole, generates surface charges that oscillate in conjunction with the electric field, resulting in magnetic resonance.

Fig. 7
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E-field distribution at a 705.44 THz, b 814.88 THz

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Fig. 8
figure 8

H-field distribution at a 705.44 THz, b 814.88 THz

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3.4.2 Analysis of power loss distribution

The study also analyzed power loss distributions at two resonant frequencies, 705.44 THz and 814.88 THz, to gain a better understanding of how absorption happens in the dielectric and metallic layers. Figure 9 demonstrates that the resonators have a significant impact on wideband absorption, even though quartz has a low loss tangent of 0.0004. This is because the metallic layer tends to have higher losses than the dielectric in the infrared frequency range, making it more responsible for wideband absorption.

Fig. 9
figure 9

Power loss distribution at a 705.44 THz and b 814.88 THz

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The suggested absorber is being compared to absorbers from previous studies that have similar properties, such as ultra-wideband absorption and functioning in the infrared, visible, and ultraviolet frequency ranges. The data in Table 4 shows that the suggested absorber has a significantly average absorption, peak absorption and compact dimension across a wider frequency range. With these qualities, the suggested absorber has the potential to be used in infrared detection, solar energy harvesting, and multicolor imaging applications.

Table 4 Comparison of proposed ONMMA with relevant works
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4 Conclusion

This article suggests using a small concentric cylindrical gold ring on an elliptical nickel conductor, along with a square sheet of gold placed in the center of a plus-shaped nickel structure, to create an ultra-wideband absorber. This device is used for harvesting solar energy and multicolor imaging in the infrared, visible, and ultraviolet frequency ranges of the solar spectrum, which is between 200 and 920 THz. The size of the device is 200 × 200 × 190 nm3 and it consists of four layers (Au-Qz-Ni-Au). The designed device has a high absorption rate, with absorption above 90% in a range of 235.44 THz bandwidth and above 75% in a range of 626.40 THz bandwidth. The maximum absorption rate is 99.866% at a frequency of 705.44 THz, and the average absorption rate in the entire range of 200–920 THz is 86.424%. The article also analyzes the properties of the device, such as the magnetic field, electric field, surface current distribution, and power loss distribution, to understand how it absorbs solar energy. Finally, a comparison with other similar devices is presented, which demonstrates that the proposed device has better characteristics in terms of size, absorption rate, and peak absorption. Therefore, the proposed device has great potential for applications in solar energy harvesting, infrared detector, and multicolor imaging applications.