Dual‐Band Terahertz Metamaterial Absorber Based on LC Resonance and Dipolar Response and Its Applications

This study presents a new dual‐band terahertz absorber (DBTA) with ease of production consisting of a metallic base plane of a certain thickness, a dielectric layer on this plane, and a hexagonal metallic metasurface structure. The proposed absorber exhibits absorption band peaks above 99% at two distinct frequencies (7.51 and 8.08 THz). The absorption origin is explained as a dual‐band response using the LC resonance and dipolar response. In this way, the presented absorber facilitates production by improving absorption responses with a much simpler structure, unlike studies with complex geometries. The proposed dual‐band absorber results in sensitivity to the polarization of the incident light. Thus, it also makes the proposed structure very helpful for manipulating wave polarization and detecting waves with particular polarization. The hexagonal structure of the absorber is scaled to millimeter dimensions, and its transformation into another dual‐band absorber that can also operate in microwave frequency regions. Similarly, the hexagonal structure is transformed into a circular structure with the same geometric dimensions, and a different dual‐band absorber is obtained in the terahertz (THz) region. Moreover, the proposed concept can be extended for various applications such as bolometric sensing, thermal imaging, energy harvesting, sensing, and selective thermal emitters.


Introduction
Metamaterials with extraordinary electromagnetic (EM) properties, which are not found in nature but may be created intentionally, are determined more by the size and geometry of their resonance structures than by their chemical composition.Applications of negative refractive index, [1] invisibility/concealment, [2] lensing, [3] and extensive amplitude modulation with vigorous polarization cycling [4] have been investigated and studied by DOI: 10.1002/adts.202300918appropriately designing metamaterial structures.As a result of this and similar research, filters, modulators, switches, etc., based on metamaterials have been developed.[7] In applications including bolometric detectors, selective thermal emitters, thermal imaging, and energy harvesting, nearly complete absorption of incoming waves in specified frequency ranges is crucial in numerous manner.However, metallic metamaterials' absorption loss frequently can cause a decrease in their resonance performance.Therefore, various approaches (such as the use of low-loss materials, optimization of the absorber structure design, and the use of gain materials) have been recommended in the literature [8][9][10][11][12] to reduce the absorption losses of metamaterials.However, the absorption losses of the metamaterial may be helpful for an artificially obtained light absorber.In this way, the absorption losses are increased significantly and can give excellent absorption results by adequately designing the resonance structure.[24][25][26] The first of these approaches is to create a unit cell structure by superimposing several coplanar subunit resonators with different geometric dimensions.The other is to employ multiple layers that are arranged vertically.However, these approaches have problems such as larger unit cell size and technical difficulties in production, especially at higher frequencies such as terahertz, infrared, and visible regions.Therefore, reducing stacked layers and unit size or simplifying complex structures is necessary.In summary, it can be said that there is an urgent need to design new metamaterials that can operate at higher frequencies, are easier to produce, and more applicable.
THz radiations have advantages such as sensitivity to many nonconducting materials, spectroscopic signatures of organic materials, and nonionizing properties that are difficult to detect at frequencies other than THz.As chemical and biological agents become increasingly sophisticated, practical tools are needed to detect and/or identify threats such as explosives made from plastic and fertilizer.Therefore, using THz radiation between 0.5 and 10 THz is one of the solution approaches to spectroscopically sense such materials utilizing characteristic transmission/reflection spectra. [27]For example, the literature states thatTNT was detected with absorption peaks at center frequencies of 5.6, 8.2, 9.1, and 9.9 THz.In contrast, ammonium nitrate (NH 4 NO 3 ) has been reported to be detected at resonance frequencies of 4 and 7 THz. [28]Considering these frequencies, the frequency region selected in this study can be used in the detecting explosive substances and their derivatives.At THz frequencies, absorber structures offer several benefits, including physical customization, multi-band absorption peaks, and flexibility.It is possible to adjust absorption peaks by modifying the metamaterial's structure. [29]This study shows that the presented absorber can be transformed into an absorber that can be operated not only in the THz region but also in the GHz region as a result of mechanical adjustments.
Herein, we present a dual-band metamaterial absorber (DBMA) with the metasurface structure obtained by removing a square structure from the middle-upper part of the hexagonal structure.Two absorption peaks above 99% were obtained at 7.51 (f 1 ) and 8.08 THz (f 2 ) frequencies.The absorption origin of the proposed DBMA structures was explained with the help of electric field, magnetic field, and surface current distributions.The lossy or lossless status of the substrate materials was examined, and it was understood that the metasurface on the upper part of the DBMA structure caused the absorption.The polarization dependence of the proposed DBMA structure was investigated, and it was concluded that it is sensitive to the polarization of the incident light.Thus, the structure will help control the polarization of light and detect EM waves with the determined polarization.The proposed structure was investigated with metals with different electrical conductivities.The effect of undoped metals with different electrical conductivities on absorption was investigated.It was understood that the hexagonal DBMA structure, which is the main subject of this study, achieved dual-band absorption in the THz range when converted to circular form.In addition, after the dimensions of the hexagonal DBMA were scaled to mm dimensions, it was observed that it exhibited the feature of being a dual-band absorber in the microwave bands.

Design of Proposed Structure and Simulation Medium
The DBMA structure obtained as a result of a square structure removed from the upper-middle part of the hexagonal structure is shown in Figure 1a.In Figure 1b, the front view of the structure is shown together with the design parameters, while in Figure 1d, the side view is shown together with the design parameters.
Additionally, Table 1 defines the design parameters that give the best dual-band absorption results as micrometers.DBMA Smooth meshing with an equilibrate ratio is selected as 2, including mesh optimization, and considering material properties for refinement.In the model preparation settings menu, 1 × 10 −6 is selected as the "trying to force coincidences inside" option, and a self-intersection check is applied.The suggested absorber's structure has been optimized by adaptive tetrahedral mesh refinement, employing a frequency domain solver with a threshold value of 0.01 for S-parameter convergence.The simulations have employed periodic boundary conditions driving floquet port excitation because the periodic application of unit cell boundary conditions offers the benefit of enabling a quick and precise simulation of the absorber surface.In the simulations, the unit cell is illuminated at normal incidence by a plane electromagnetic wave with the electric field (E-field) parallel to the x-axis.Perfectly matched layers are applied along the z-direction, and periodic boundary conditions are applied in the x-and y-directions.
(Figure 1c).Metamaterial surface absorption of EM waves occurs according to the principle of impedance matching.When EM waves reach the metamaterial absorber surface, some of the waves will be reflected while the other part will be transmitted.Therefore, it is clear that the reflection and transmission coefficients must be as low as possible to ensure maximum absorption.To achieve good absorption results, the metal array's surface impedance must match the free space wave impedance.With a matching impedance between the air and the metamaterial absorber, the calculation of the absorption rate of the metamaterial is given by the following formula [30 ] : A(ɷ), R(ɷ), and T(ɷ) represent absorption, reflection, and transmission, respectively.R(ɷ) and T(ɷ) are determined from the frequency-dependent scattering parameters S 11 (ɷ) and S 21 (ɷ), respectively.Simultaneous reflection and transmission coefficients can maximize the maximum absorption rate.The metallic surface on the substrate is thick enough to prevent the transmission of the incoming wave, that is, T(ɷ) = zero, and the ab- sorption property of the metamaterial absorber mainly depends on the reflection rate.Under these conditions, perfect absorption is achieved, with the R (reflectance) close to zero.In this way, the absorption formula can be expressed as follows, depending only on reflection, independent of the transmission parameter:   have a normalized impedance of approximately unity value (1).It means that the resonance is occurred because of impedance matching (Z 0 = 1).Absorption spectra were performed in lossy and loss-free properties for two different substrates, Arlon AD 350 and Polyimide (Figure 3a).Two distinct absorption peaks above 99% were obtained for each examination, located at frequencies of 7.51 (f 1 ) and 8.08 THz (f 2 ).The fact that the resonance peaks are at the same frequency values makes no difference whether the substrate materials are lossy or loss-free.From the absorption graph of Figure 3a, it can be seen that lossy and lossless dielectric substrates did not cause any change in the resonance frequencies.Therefore, the energy absorption is attributed solely to the DBMA metal structure.During simulations on this work, Arlon AD 350 substrate is preferred.

Results and Discussion
From Figure 3a, at a normal oblique angle of incidence, the quality factor [31] (Q = f/FWHM) was calculated using absorption bandwidths (as full width at half maximum, FWHM) and resonance frequency values.The absorption bandwidths based  on f 1 and f 2 conditions are ≈0.06 and 0.07 THz, respectively.In contrast, these absorption peaks' quality factors (Q) are approximately calculated as 139 for the f 1 condition and 109 for the f 2 condition.These values demonstrate the superb dual-band absorber with remarkable frequency selectivity because of its narrow absorption bandwidth.The LC resonance and the dipolar response of the hexagonal metallic structure to one another are attributed to the absorption seen in these two resonance peaks.In order to understand such a double-band absorption mechanism, the electric and magnetic field distributions are explained in detail (Figure 5).The simulations (Figure 3b) are extended to understand absorption at four orthogonal polarizations (0, 30, 60, and 90deg.) of the incoming light.Thus, the polarization dependence of the proposed DBMA is investigated, concluding that it is susceptible to the polarization of the incoming light.The resonance frequency of the proposed absorber can be adjusted simply by tuning the polarization angle of the incoming light.Thanks to this feature, the proposed structure helps control the polarization of light and detect EM waves with specified polarization. [32]esides the simulations abovementioned, the relationship between the absorption and different types of metallic conductivities is examined.Namely, the dependence of the different types of metallic structures with the different electrical conductivities on the absorption performances are investigated for Gold ( Au = 4.561e + 7 S m −1 ), Chromium ( Cr = 8e + 6 S m −1 ), Silver ( Ag = 6.301e + 7 S m −1 ), Copper ( Cu = 5.8e + 7 S m −1 ), and Nichrome ( NiCr = 6.301e + 7 S m −1 ).From Figure 4, these conductivities do not significantly affect the absorption performances of the proposed DBMA, including the resonance frequencies, absorbency, and quality factor.It has also been observed that metamaterial absorber design based on metallic structures created from doped metal materials such as Nichrome (NiCr), 80%Ni + 20%Cr, distorts the natural appearance of absorption.The results show that using undoped metal structures for the design in this study is an advantage.
We present the simulated absolute electric field, |E|, the electric field in z-direction, E z , the absolute magnetic field, |H|, and surface current distributions corresponding to the two absorp- tion resonance frequencies in order to understand the physical mechanism/origin of the proposed DBMA.
Based on this, we defined the lower-frequency resonance peak as the f 1 circumstance and the higher-frequency resonance peak as the f 2 circumstance.In the f 1 circumstance, the absorption origin of the proposed DBMA structure is due to LC resonance, while the absorption mechanism of the proposed absorber is due to the dipolar response in the f 2 circumstance.It is helpful to remember that the f 1 and f 2 resonance frequency values are 7.51 and 8.08 THz, respectively.The findings for f 1 circumstance: In Figure 5a 1 , while the amplitude of the absolute electric field of DBMA is focused on the middle parts of the outer edges in the lower region of the structure, it is focused toward the middle axis of the side edges in the upper part and is also focused on other surfaces except the corners of the arms.The situation at the edges indicates that the charges along the electric field (xaxis) are focused at the edges.In Figure 5a 3 , looking at the electric field distribution in the z-direction, it is seen that the charges are focused at the corners of the arms of the absorber structure.In contrast, while they are focused at the edges at low intensity in the lower region of the structure.The findings for f 2 circumstance: In Figure 5a 2 , While the charges were focused on the arms of the absorber structure and at the bottom of the gap, focusing along the baseline was observed in the lower part of the absorber structure.In addition, some charges were accumulated at the right and left corner ends of the hexagonal absorber structure with lower density.For Figure 5a 4 , in the z-direction electric field distribution examination, while the charges accumulated in the arms and at the bottom of the gap, their intensity decreased in the lower region of the absorber structure and focused along the baseline.
From Figure 5a 3 and a 4 , the accumulation of opposite charges on the upper and lower surfaces of the structure indicates that the electric dipole response is stimulated.The electric dipole effect indicates that anti-parallel surface currents occur in the upper and lower layers of the DBMA structure.This causes a solid magnetic resonance (Figure 5b).Figures 5a 5 ,a 6 show the absolute magnetic field distributions.From Figures 5a 1 ,a 5 , the induced surface currents show that the metallic DBMA structure is subject to a loop current.This situation arises from the LC resonance of the structure in the f 1 circumstance.Again, from Figure 5a 4 , the fact that surface currents occur in the lower and upper regions indicates that the resonance structure arises from the dipolar effect for the f 2 circumstance.The impact of specific geometric parameters on absorption performance can be clearly understood once the physical absorption origin of the DBMA has been explained.The f 1 and f 2 circumstances are caused by the LC resonance and the absorber structure's dipolar response, as was previously discussed.In other words, the resonance frequencies depending on the geometric parameters depend on the effective inductance of the structure or the effective length of the loop current in the DBMA structure in the f 1 circumstance.[35] The alteration of resonance frequencies in the f 2 circumstance is associated with the fundamental length of the DBMA structure.Therefore, when other geometric parameters are kept at constant values, the change of the gap only affects the frequency of the f 1 circumstance.In contrast the frequency change of the f 2 circumstance should be neglected.
As shown in Figure 6a, there is LC resonance in the f 1 circumstance.As the a = b dimensions increased equally, the opposite directional surface currents at the base of the DBMA structure (along the electric field) tended to cancel each other.In contrast the field strength increased at the side edges.However, an increase in the intensity of the currents was observed throughout the a = b square structure (Figure 7).This situation is attributed to the decreased in the effective length of the resulting vector of surface currents loop current.For this reason, it is explained that the resonance frequencies due to a = b shift to higher frequencies.In the f 2 circumstance, there is almost no change in resonance frequencies.
From Figure 6b, increasing DBMA structure's dimensions affects the currents's effective length for the f 1 circumstance.However, it is necessary to take into account that there are surface currents in opposite directions along the bottom.Therefore, in the f 1 circumstance, the resonance frequencies are attributed to the effective length of the loop current as the R dimension changes increase, and the resonance frequencies shift to higher frequencies.No surface current distribution was observed along the base of the DBMA structure for the f 2 circumstance (Figure 5b).Therefore, increasing R will not affect any current along the base.The increase in the current intensity at the side edges can be explained by the increase in the effective length of the surface currents.For this reason, resonance frequencies tended to shift to lower frequencies.

Applications of Proposed DBMA Structure
At this stage, we present absorbers in two new forms to present the important features of our hexagonal structured dual-band terahertz metamaterial absorber approach in terms of application.The first is to present a new absorber that can achieve absorption in the THz range with the contribution of LC resonance and dipolar response by transforming the hexagonal absorber structure into a circular structure.The second is to present a feasible absorber in the GHz frequency range by changing to the geometry parameters of our designed hexagonal absorber structure.The dual-band absorption capabilities and absorption mechanisms for these two forms have the same absorption mechanisms (overlapping of LC resonance and dipolar response) as the actual DBMA absorber we presented above.For the first form, the geometry of DBMA is converted into a circular plate, removing  located ≈7.67 (f 1 ) and 8.07 THz (f 2 ) with absorption coefficients of 96.00% and 97.00%, respectively.The proposed hexagonal structured DBMA was implemented in the second form at lower frequencies (in the GHz range) by altering the absorber dimensions.We briefly give a design as an application in the microwave range.Similar to the structure design in Figure 1, it was simulated with the same substrate (Arlon AD 350, lossy) and metal material.The proposed structure is shown in Figure 8c, and the optimal geometric parameters of the structure are given as follows: a = b = 6 mm, d = 0.1 mm, h = 1.6 mm, P = Px = Py = 100 mm, R = 15 mm, and t = is 0.1 mm. Figure 8d shows the calculated absorption spectra of the proposed absorber.As shown in Figure 8d, it is obvious that the absorber has two distinct absorption bands (located at frequencies of 8.97 (f 1 ) and 9.34 GHz (f 2 ), respectively), with peaks of 98.84% and 95.09%.
According to the distributions of the electric field (|E| and electric field along z-direction (Ez)) of the circular absorber (Figure 9a-d), the double-band occurs.The circular structured absorber results from the LC resonance's superposition and the circular absorber's dipolar response.Thus, the circular structure absorber is suitable as a new dual-band terahertz metamaterial absorber.
To better understand the origin of the proposed hexagonalstructured GHz-order operated absorber, we present the calculated electric field and the electric field along the z-direction, corresponding to the two absorption maxima in Figure 10a-d.The electric field distributions appear to be similar to the case of the terahertz hexagonal-shaped DBMA structure.Therefore, it is concluded that f 1 and f 2 circumstances are suitable for designing a dual-band microwave absorber, where the proposed new hexagonal structure has LC resonance and dipolar response.In addition, due to the asymmetric structure, its polarization-sensitive absorption feature is valid for circular and new-type hexagonalshaped structures.
Finally, we examined the dependence of the absorption of the proposed hexagonal DBMA structure, which is the main subject of this study, based on the change of geometry parameters: a, b spacing, and length R. As shown in Figure 11a, it is obvious that for the proposed DBMA absorber, the resonance frequency of the f 1 circumstance gradually increases with the increase of the gap, while the frequency variation of the f 2 circumstance has a neglected change.Figure 11b shows the effect of length R on the resonance frequencies and absorption coefficients of the proposed DBMA absorber.It has been observed that the f 1 circumstance resonance frequencies gradually increase with the increase of the R length.In contrast, the f 2 circumstance resonance frequencies gradually decrease with the increase of the R length.Based on this, it was found that the proposed DBMA hexagonal structured absorber has geometric dependence.Therefore, it provides significant freedom to change or shift the frequencies of the absorber using different geometric parameters.Especially for the variation of a and b spacing (see Figure 11c), it is found that the Q value of the LC resonance and the Q value of the dipolar resonance gradually decrease with the increase of the spacing.Moreover, for the variation of the length R (see Figure 11d), the theoretical results show that the Q value of the LC resonance and the Q value of the dipolar resonance gradually decrease with the increase of the length R.These results show that we can use a different geometry to enable tuning of the quality factor, Q.A comparison table with research studies selected from the literature in terms of structural strategy, operated frequency, band type, number of sub-resonators, absorption percentage, and production difficulty is given in Table 2. Based on the comparisons, the presented work can be converted into two different metamaterial absorbers in different frequency regions of GHz and THz with easier production and changes in geometric parameters.Additionally, the number of sub-resonators is minimal compared to its counterparts.

Conclusion
We present a dual-band metamaterial absorber with a metasurface structure obtained by removing a square structure from the middle-upper part of the hexagonal structure.Theoretical results show that two absorption peaks above 99% are obtained at frequencies of 7.51 (f 1 ) and 8.08 THz (f 2 ).Whether the substrate materials were lossy or lossless did not cause a change in the frequency values of the resonance peaks.This situation (that the use of lossy and lossless dielectric substrates does not cause any change in the resonance frequencies) is attributed to the fact that energy absorption originates only from the DBMA metasurface.It shows that the proposed DBMA is sensitive to the polarization of incident light.From this perspective, it is concluded that DBMA can help to control the polarization of light and detect EM waves with specific polarization(s).The proposed structure has been studied for metals with different electrical conductivities.DBMA does not affect absorption performances, including resonance frequencies, absorbance, and quality factors.It has also been observed that the metamaterial absorber design, which is based on metallic structures created from doped metal materials such as Nichrome (NiCr), 80%Ni+20%Cr, disrupts the natural appearance of the absorption.This result shows that using pure metal structures in the proposed design has advantages.The contribution of the LC resonance and dipolar response explains the absorption origin of the proposed DBMA structures.Our proposed DBMA approach is presented in two new forms for applications (circular structure with micrometer dimensions and hexagonal structure with mm dimensions).It was concluded that transforming the hexagonal absorber into a circular structure can provide absorption at different resonance peaks.An absorber at low frequencies (GHz) can be achieved by using a new metasurface with the same geometric shape and different design parameters in mm dimensions.Another critical point is that these designs overcome difficulties in terms of production.

Figure 1 .
Figure 1.a) Unit cell array, b) Unit cell with design parameters, c) Simulation medium, and d) Side view of the structure with the design parameters.

Figure 2 .
Figure 2. a) Simulated S-parameters and calculated absorption for TE mode under normal oblique incidence angle and b) Normalized input impedance.

3. 1 .
Outcomes of Proposed Structure CST Microwave Studio performed simulations to analyze the scattering parameters (S 11 and S 21 ) and calculate the absorption by the DBMA.The obtained results are shown in Figure 2a.The normalized input impedance of the proposed DBMA is calculated and plotted in Figure 2b to explain the resonance mechanism.The first and second resonance peaks at 7.52and 8.08 THz

Figure 3 .
Figure 3. Absorption spectra of the proposed DBMA a) on different loss conditions (lossy and loss-free) of the substrate and b) on four orthogonal polarizations of the normal oblique incidence.

Figure 4 .
Figure 4.The absorption of the proposed DBMA based on different electrical conductivity ().

Figure 5 .
Figure 5. a) The simulated absolute electric field, electric field in z-direction, and absolute magnetic field and b) the surface current distributions at the two absorption resonance frequencies.

Figure 6 .
Figure 6.Parametrical investigation based on a) the gap dimensions and b) the length of DBMA structure.

Figure 9 .
Figure 9. Electric field distributions of the circular DBMA for two resonance modes.

Figure 10 .
Figure 10.Electric field distributions of hexagonal-shaped microwave DBMA for two resonance modes.

Figure 11 .
Figure 11.The absorption on a) different gap spacings (a = b) of the proposed hexagonal structured DBMA and b) the length (R) change of the hexagonal structured DBMA absorber.Dependence of Q values and dipolar response of LC resonance on c) different gap spacings of the proposed hexagonal structured DBMA absorber and d) the length change of the hexagonal DBMA absorber.

Table 1 .
Design parameters of the best performing dual-band metamaterial absorber.

Table 2 .
Comparison table based on various performance metrics.