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Abstract
In this paper, a conformal optical transparent metamaterial absorber (COTMA) is proposed based on the circuit analog optimization method (CAOM), which can effectively enhance the optimization speed in the metamaterial absorber structure design by quantifying the equivalent circuit parameters. The operating frequency band can be customized at any band through CAOM, such as microwave, terahertz, and near-infrared frequencies. Here, a five-square-patch structure absorber with transparency and flexible properties is achieved. The simulated and measured incident electromagnetic (EM) wave absorptions of COTMA can reach above 90% in 15.77 - 38.69 GHz band. Meanwhile, COTMA exhibits excellent conformal EM absorption, a thinner substrate (0.078 wavelength at 15.77 GHz), lower structure complexity and polarization independence, and it can also be adapted to the EM absorption of different curved screens. This design is expected to have potential applications for wearable electronics, curved surface screens and OLED displays.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials have attracted much attention as artificially designed materials. Its unique electromagnetic characteristics, especially its two-dimensional perfect electromagnetic absorption performance, are still not readily available in nature [1–5]. Metal-dielectric-metal based structures have been widely employed for metamaterial absorbers (MMAs) [6,7]. In 2008, Landy et al. reported a perfect MMA, which achieved nearly 100% effective absorptivity at 11.5 GHz [8]. Multifarious structures of MMAs were designed in the microwave, terahertz, and optical regimes thereafter [9–14]. With the development of stealth technology, designing radar absorbing materials to meet the high-performance requirements of “light, wide and strong” has become a research focus [15–17]. Various methods have been proposed to achieve this goal in researching metamaterial absorbers. First, from the perspective of lightness, most absorbers are now made of epoxy resin sheets [18–21]. Second, for broadband and high absorptivity, most metamaterial absorbers select multilayer structure superimposition for wideband absorption. Another method is the coplanar unit cell design of absorbers, which can also obtain the same performance [22–25].
However, these metamaterial absorbers generally have thick layers with oversized unit cells, and they perform poorly in conformal degree and optical transparency. Because of these physical characteristics of constituent materials, the non-conformal MMAs usually have shortages in offering enough flexibility to the low-profile conformal applications. On the other hand, there is a huge shortage in optical transparent metamaterial absorbers (OTMA) used in visible screens and wearable electronics. Compared with non-transparent metamaterial absorbers, OTMAs have adjusted the surface resistance to expand the absorption and the operation band. For example, Jang et al. employed aluminum wire grids to construct transparent MMAs for broadband and higher absorptivity performance, and the optical transmittance was over 62% [26]. Shen et al. reported an absorber made of indium tin oxide (ITO), polymethylmethacrylate (PMMA) and water to achieve an adjustable and higher absorptivity performance [27]. Although many OTMAs have been presented, they are thick, heavy and non-conformal, largely limiting their effectiveness [28–33]. Meanwhile, their design methods are as same as non-transparent MMAs, which consume plenty of time to optimize the structure parameters. Li et al. proposed a semiempirical optimization method based on equivalent circuit to design OTMA, but the double-resonance-layer increased the difficulty of optimizing the structure parameters. The thickness of OTMA is so large that the absorber cannot achieve the purpose of conformal [34]. Jiang et al. employed coupled hexagonal combined elements and equivalent circuit model to get the ultra-wideband absorption, but this design needs plenty of time to optimize coupled structure [35]. Therefore, the retrenchment of optimization time and medium thickness in the design progress of OTMA with conformal performance are of great significance for both physics and other application research on absorption-dominated electromagnetic wave shielding curved windows.
In this paper, a circuit analog optimization method (CAOM) based on a square patch structure is proposed to simplify the design method of the conformal optical transparent metamaterial absorber (COTMA). The CAOM can obtain an optimization scope of square patch structure parameters by obtaining equivalent circuit parameters of COTMA. In this method, the desired COTMA can be simply designed by selecting the target frequency and dielectric material. Compared to the other design methods of MMA, it exhibits a higher optimization speed and adjustability in the structure design of MMA. We designed one conformal optical transparent metamaterial absorber to demonstrate the effectiveness and customization of this method. The measured EM absorption of COTMA exceeds 90% from 15.77 GHz to 38.69 GHz band, which covers the operation range of the 5G millimeter wave band. In addition, the proposed COTMA exhibits excellent conformal EM absorption, small relative thickness, and polarization independence. This design would have potential applications for wearable electronics, curved surface screens and OLED displays.
2. Design of the COTMA through the circuit analog optimization method
The circuit analog optimization method (CAOM) is composed of four steps. First, the materials and structure can be analysed through CST microwave studio frequency domain solver, and the effective structure parameters impacting the COTMA absorption are obtained. Then, the COTMA’s equivalent circuit model is established by the determined structure and the transmission line theory. In addition, the determined equivalent circuit relevant parameters can be calculated by the materials, structure, and desired frequency. Finally, based on the relevant equivalent circuit parameters, the COTMA unit cell size can be confirmed by optimizing the effective structure parameters.
2.1 Parameter analysis of structure and materials
The designed COTMA, which consists of ITO, PET and PDMS with excellent conformal degree and optical transparency, is shown in Fig. 1. Due to the excellent surface resistance characteristics, ITO is used as the metallic structure and ground. PET and PDMS materials are cascaded as dielectric materials with relative permittivity of 3.2(tanδ=0.003) and 2.35(tanδ=0.06), respectively. The square patch is employed as the COTMA surface resonant structure since its equivalent circuit can be directly constructed. To analyse the mechanism of the square patch structure absorption under normal incidence and calculate the effective structure parameters in the equivalent circuit, we investigate square structures with different quantities and configurations. Figures 2(a)–2(i) illustrate the electric fields (E-field), the surface current distributions, and the surface power loss of the square patches at corresponding resonant frequencies. Figures 2(j)–2(k) demonstrate the incident EM energy absorption and reflection coefficient of different quantity and configuration square structures.
Fig. 1. Single unit size diagram: (a) Schematics of the designed absorber: the lengths are marked with the letters a, b and p. For the electromagnetic incident direction, φ is the polarization angle in the magnetic direction and θ is the incident angle in the electric direction. (b) The Sandwich Structure of COTMA.
Fig. 2. E-field distribution, surface current, surface power loss, reflection coefficient and absorption: (a)-(c) surface E-field distributions, (d)-(f) surface current distributions, (g)-(i) surface power loss distributions (j) reflection coefficient of different quantities and configuration squares, and (k) absorption of different quantities and configuration squares.
There exists distance among each unit’s single square, which results in the accumulation of charges. The induced max E-field occurs on the upper and lower patch edges. The distance of each unit’s single square can be defined as an equivalent capacitance, as shown in Fig. 2(a). In addition, the surface current around a single square resists the surface current that the external E-field promotes. It can be defined as an equivalent inductance. As shown in Fig. 2(d), for the single square patch, the surface current of the conductive surface structure is produced because of the directional movement of the carriers under the action of the external E-field promotion. However, the absorption of a single square is inefficiency because the surface equivalent resistance of a single square does not match well with the free-space characteristic impedance, as shown in Figs. 2(g), 2(j) and 2(k).
For a perfect matching between the surface resistance and the free space characteristic impedance, the double squares structure is proposed. The electric field distribution, surface current and surface power loss are shown in Figs. 2(b), 2(e) and 2(h). The surface current and induced E-field of double squares are much more intense than those of a single square. In addition, the equivalent inductance of the double squares structure can be easily adjusted because the surface current is mainly influenced by the edge of the double squares. The equivalent capacitance is still mainly introduced by the induced E-field on the upper and lower ends of the squares. Meanwhile, as the area of the double squares increases, the effect area of surface resistance also enlarges. The junction of the double squares induces the accumulation of charges, which vastly enhances the resistance loss and the absorption of metamaterials, as shown in Figs. 2(h), 2(j) and 2(k).
Therefore, the five squares structure is selected as the resonant structure of COTMA. The electric field distribution, current and power loss of the five-square structure are shown in Figs. 2(c), 2(f) and 2(i). Since the five-square structure has four junctions, the surface resistance will be easily matched with the free-space characteristic impedance, and the absorption of COTMA can be significantly increased, as described in Figs. 2(j) and 2(k). As shown in Fig. 2(c), 2(f) and 2(i), based on the above method analysing the single and double squares, the equivalent capacitance and the equivalent inductance of the five squares structure can be adjusted by the length b and the length a, respectively. The effective resistance area can also be estimated.
2.2 Equivalent circuit-relevant parameter analysis of COTMA
The equivalent circuit relevant parameter analysis mainly consisted of three steps. First, the relation between the metamaterial absorber and the equivalent circuit transmission line is constructed. The absorption of COTMA is mainly influenced by transmission and reflection according to electromagnetic field theory. The absorption could be expressed as:
Here, $R(\omega )$ is the reflectance and $T(\omega )$ is the transmittance. In order to eliminate the influence of polarization in absorption, the cross-polarization component is added to the calculation of the absorption. In Eq. (1), ${s_{11}}$ is the summation of the co-polarized and cross-polarized reflection coefficient, and ${s_{21}}$ is the summation of the co-polarized and cross-polarized transmission coefficient. Due to the existence of the ground, the transmission of COTMA becomes zero. The absorption of COTMA is only influenced by the $R(\omega )$. The $R(\omega )$ and $A(\omega )$ could be expressed as:
Here, $Z_{in}$ is the input impedance of the COTMA, where $Z_{0} = 377\Omega $ is the free space characteristic impedance, and $\theta $ is the incident angle of the electromagnetic wave. As Eq. (3) expresses, the absorption is mainly influenced by the input impedance of the equivalent circuit and the incident angle of the electromagnetic wave.
Next, as shown in Fig. 3, the equivalent circuit of the COTMA is illustrated as a one-port network based on the transmission line theory. The patterned ITO film on the top surface is equivalent to the series inductance L, capacitance C and resistance R. The intermediate dielectric layer can be treated as a transmission line with characteristic impedance $Z1$ and electrical length $d1$. The ground is modeled as the equivalent resistance $Rg$. The equivalent circuit parameters would be extracted by analysing the equivalent COTMA circuit.
The input impedance $Za$ can be expressed as:
Here, the characteristic impedance of the intermediate dielectric layer is $Z_{1} = \frac{{Z_{0}}}{{\sqrt {\varepsilon_{r}(PDMS)} }}$, and the input impedance $Z_{b}$ can be calculated as:
where $\beta_{1} = \frac{{2\pi f\sqrt {\varepsilon_{r}(PDMS)} }}{c}$ is the propagation constant of the incident electromagnetic wave, f is the frequency of incident electromagnetic waves, and c is the speed of light. In addition, the thickness $d_{2}$ of material PET is so small that it can be negligible. Since there is no transmission, the equivalent resistance $R_{g}$ is zero. The input impedance $Z_{b}$ can be simplified as:In addition, the impedance of the surface ITO pattern could be written as:
Hence, the overall input impedance $Z_{in}$ of the COTMA could be calculated as:
The overall input impedance $Z_{in}$ needs to be equal to the free space characteristic impedance $Z_{0}$ so that the absorption of COTMA will be equal to 1. When $Z_{in} = Z_{0} = 377\Omega $, we can obtain R and $L$ values as follows:
From Eq. (9) and Eq. (10), it can be summarized that the equivalent resistance R, the equivalent inductance L and the equivalent capacitance C of COTMA are mainly dependent on the relative permittivity $\varepsilon_{r}$ of PDMS, thickness $d_{1}$ of PDMS and the operating frequency. They can be considered equivalent circuit parameters. Meanwhile, the equivalent inductance L is affected by the equivalent capacitance C.
2.3 Optimization of the effective structure parameters
Based on the above analysis of COTMA, the equivalent resistance R of COTMA plays an important role in consuming the EM energy, and the equivalent inductance L and the equivalent capacitance C mainly affect the operating frequency. Therefore, before optimizing the effective structure parameters, it is necessary to determine the equivalent resistance R, equivalent inductance L and equivalent capacitance C. The frequency response curve of the equivalent resistance R can be calculated by Eq. (9). Then, the value of the equivalent inductance L and the equivalent capacitance C can be obtained through the two frequencies, which have equal resistance in the frequency response curve of the equivalent resistance R.
The desired operating frequency range is designed from 15 GHz to 40 GHz. The PDMS thickness $d_{1}$ can be determined by the frequency response curve of equivalent resistance R. Figure 4(a) shows the frequency response curves of equivalent resistance R with different thicknesses $d_{1}$, and the maximum value of equivalent resistance R is equal to the free space characteristic impedance of 377 Ω. Meanwhile, it can be observed that there exist two perfect absorption frequencies with the same equivalent resistance less than 377 Ω. The absorption curves with different thicknesses $d_{1}$ are shown in Fig. 4(b). Theoretically, when the input impedance $Z_{in}$ of COTMA matches the free-space impedance, the absorption of the two peaks can reach 1. To verify the effect of different $d_{1}$ on absorption, we provided a preliminary value for the relevant structural parameters. Here, lengths a and b are selected as 1.2 mm and 1 mm, respectively. And the square resistance of ITO is 6 Ω. The absorption with different thicknesses of PDMS is simulated. As keeping the other relevant parameters unchanged, two absorption peaks can be adjusted by selecting proper $d_{1}$, as shown in Fig. 4(b). The frequency response curve of equivalent resistance R with a thickness of 1.4 mm satisfies the center frequency of the purpose operating frequency range.
Next, the value of the equivalent inductance $L$ and the equivalent capacitance C can be determined by finding the appropriate R. Here, based on the purpose operating frequency range, two absorption peaks that exactly match the free space characteristic impedance at 18.317 GHz and 35.364 GHz are selected because they are close to 15 GHz and 40 GHz, respectively. The corresponding equivalent resistance R is 197.88 Ω, as shown in Fig. 5(a). From Eq. (10), the intersections of the calculated L-C curves are $L$= 1.758 nH and $C$= 0.022 pF, as given in Fig. 5(b). Under this value of node, the equivalent inductance L and the equivalent capacitance C could have the absorption peaks of COTMA locked at 18.317 GHz and 35.364 GHz, respectively. According to the parameter analysis of the structure and materials, the value of equivalent capacitance is mainly determined by the length a, length b and length p, as shown in Fig. 6. The value of the equivalent capacitance C can be approximately composed of a certain number of $C_{1}$ and $C_{2}$ in parallel. $C_{1}$ and $C_{2}$ are the gap capacitors between cells. To better understand the physical meaning of the equivalent capacitance and inductance values, electrostatic principles can be exploited. The equivalent capacitance C can be approximated as:
Fig. 5. Frequency response curves of COTMA in the 15 GHz−40 GHz band: (a) equivalent resistance R, (b) the equivalent inductance L versus the equivalent capacitance C and (c) compared absorptions. Frequency response curves of COTMA in 3 GHz-8 GHz: (d) equivalent resistance R, (e) the equivalent inductance L versus the equivalent capacitance C, and (f) compared absorptions.
Here, $\varepsilon_{0}$ and $\varepsilon_{r}$ are the vacuum permittivity and the relative permittivity of air, respectively. $d_{ITO}$ is the thickness of the material ITO. $n_{1}$ and $n_{2}$ are constants. Hence, the value of the equivalent capacitance C is proportional to the value of a and inversely proportional to the values of b and p.
The equivalent inductance L can be approximated as [36]:
Here, $n_{3}$ is a constant. In this case, the value of inductance is quite small because the plate is pretty large and corresponds to an increase in the wire radius. The value of the equivalent inductance L is proportional to the value of a and inversely proportional to the value of b. The equivalent inductance and the equivalent capacitance can achieve $L$ = 1.758 nH and $C$ = 0.022 pF by adjusting the length a, the length b and the length p, respectively. To ensure that the full wave simulation matched the equivalent circuit simulation, we call CST Microwave Studio from MATLAB to modify the configuration of the square patch. Then the effective structure parameters can be determined by the optimization above, as shown in Table 1. Next, we determined the surface resistance of ITO through simulation analysis. From the comparison between absorption curves with different square resistances and equivalent resistances in Fig. 7, we could see that with increasing resistance, the absorption in the operating band increased, but the absorption at the peak point deteriorated. Therefore, the equivalent resistance R of COTMA could not be excessively raised since impedance mismatch would occur in this condition. The square resistance of ITO can be converted to equivalent resistance R through the effective resistance area. The relation between them can be obtained from the formula below:
where $R_{ITO}$ is the square resistance of ITO, $Aunit$ is the area of the unit cell and $Aer$ is the effective resistance area. Combining the analysis of the above area of the resistance loss and the formula, the effective resistance area can be estimated, as the resistance loss is mainly concentrated in the middle square. Finally, all steps of designing COTMA by CAOM are accomplished. As shown in Fig. 5(c), compared the calculated absorption based on the equivalent circuit by MATLAB with the simulated result by CST Microwave Studio, they matched well.Fig. 7. Simulated absorption with different (a) ITO square resistances and (b) equivalent resistances
Table 1. Optimal parameters of the final structure.
In order to further demonstrate the effectiveness and customization of CAOM, another model low-frequency COTMA from 3 GHz to 9 GHz is designed. Similar to the high-frequency COTMA, the thickness of PDMS can be calculated as 7.2 mm by analysing the frequency response curve of equivalent resistance R with different PDMS thicknesses. Based on the desired operating frequency range, two absorption peaks that exactly match the free-space characteristic impedance occur at 3.686 GHz and 7.801 GHz, and the corresponding equivalent resistance R is 165.871 Ω, as shown in Fig. 5(d). Referring to the L-C curves in Fig. 5(e), the corresponding equivalent inductance and the equivalent capacitance are $L$ = 7.801 nH and $C$= 0.121 pF. The final effective structure parameter values of low-frequency COTMA are also shown in Table 1. The simulation absorption curves are shown in Fig. 5(f), where the equivalent-circuit calculation and the full-wave simulation are consistent. Therefore, the above results of the two COTMA models indicate that the proposed CAOM is effective and feasible for various operating absorbers and reduces the parameter optimization process.
3. Results and discussions
As Fig. 8(a) shows, the absorption exceeds 90% under the frequency band from 15.77 GHz to 38.69 GHz, which accords with the purpose operating frequency range. By observing the ${s_{11}}$ curve of COTMA, it can be seen that two absorption peaks are settled on 18.3 GHz and 35.3 GHz, respectively. And the broadband absorption of COTMA is achieved by the combination of these two absorption peaks and the surface resistance of ITO. The result that the transmission coefficient ${s_{21}}$ of COTMA is lower than −60 dB indicated that there is nearly no EM wave through the COTMA.
Fig. 8. (a) Simulated S parameters and absorption of the absorber at 0–50 GHz. (b) The absorptions of COTMA are wrapped in cylinders of different radii. (c) and (d) Simulated absorption energy distribution of TFMA with different φ and θ.
Due to the PDMS and ITO properties, the proposed COTMA is flexible. As shown in Fig. 8(b), when wrapped on cylinders with different radii (15 mm, 30 mm and 45 mm), the absorption values are still over 90% in the operating frequency range, meaning that the absorber has excellent conformal absorbing performance. Moreover, the angles of polarization and incident impact the COTMA absorption performance. The absorption energy distribution of COTMA with different $\varphi $ is shown in Fig. 8(c). The absorption of COTMA remains almost the same from 15.77 GHz to 38.69 GHz. The results convincingly demonstrate that COTMA is insensitive to the polarization angle. Figure 8(d) shows the distribution of COTMA absorption energy at different EM wave incidence angles. It can be observed that as the incident angle increases, the absorption of COTMA will gradually decrease by 21.73 GHz to 34.24 GHz range. From 15.77 GHz to 21.73 GHz and 34.24 GHz to 38.69 GHz, the absorption of COTMA is stable at the two absorption peaks, as it would not be influenced by the incident angle $\theta $. Therefore, COTMA has the characteristics of wide-angle absorption at two absorption peaks.
The absorption principle of COTMA is analysed, and the power loss in different layers and normalized impedance are simulated in Fig. 9. The normalized impedance of the absorber needs to be matched with the free-space characteristic impedance. The real part of the normalized impedance represents the resistance, and the imaginary part means the reactance of the absorber. Meanwhile, when the real part of the normalized impedance is close to or less than 1 and the imaginary part of the normalized impedance is close to 0 or more than 0, the absorber will operate. As shown in Fig. 9(a), the real part of COTMA’s normalized impedance is nearly 1, and the imaginary part of COTMA’s normalized impedance is nearly 0 at the two absorption peaks. In addition, the real part of COTMA’s normalized impedance between the two absorption peaks is close to 1, and the imaginary part of COTMA’s normalized impedance is close to 0, which means COTMA tends to match with the free-space characteristic impedance during the operating frequency. The COTMA can obtain 90% absorption within the operating frequency range. Moreover, the power loss in different layers of COTMA is simulated to analyse the absorption, as shown in Fig. 9(b). The result shows that the power loss is mainly assembled in the ITO structure layer, and it is considerably small and negligible in the dielectric materials.
4. Experimental measurement
We performed the measurement by the bow-frame method, which consists of two pairs of standard broadband horn antennas at different frequency and a vector network analyser (Agilent N5224A). The photo and block diagram of measurement system were shown in Fig. 10(a) and Fig. 10(b). As the measurement frequency bands of antennas are 2–18 GHz and 18–40 GHz, the actual measurement parameters of COTMA are measured at 2–40 GHz. The measurement result is shown in Fig. 10(c), and the simulated and measured results are almost consistent. The slight discrepancy may come from the fabrication tolerance and the PDMS property deviation. The optical transparency of COTMA is shown in Fig. 10(d), and the measured transparency by a photometer is approximately 75%. The fabricated sample is also shown in Fig. 10(d), and the different substrate layers are bonded together through plasma surface treatment and bonding technology, and the COTMA sample is bendable and could be conformal on any object surface.
Fig. 10. (a)The photo of bow-frame method measurement system. (b)The block diagram of measurement system. (c) Measured absorptivity of the fabricated sample. (d) Measured average optical transmittance of fabricated sample.
To show the advantages of the proposed absorber, Table 2 compares the relative bandwidth, structure complexity, optical transparency and other properties with those of other metamaterial absorbers. With almost the same optical transparency, the proposed COTMA has a thinner substrate thickness, lower structural complexity and higher flexibility.
Table 2. Comparison of present absorber.
5. Conclusion
In summary, we report a circuit analog optimization method to design a conformal optical transparent metamaterial absorber. This method can extract equivalent circuit parameters of the absorber and enhance the optimization speed in the structural design of the metamaterial absorber. To verify the feasibility and customization of this method, one conformal optical transparent metamaterial absorber is designed, and the results of the full wave simulation and circuit simulation match well. The measured results indicate that the absorption of COTMA could exceed 90% from 15.77 GHz to 38.69 GHz. The designed metamaterial absorber has a smaller relative thickness, lower structural complexity and polarization independence. With excellent optical and conformal characteristics, COTMA can be perfectly matched with LCD screens and windows that need EM stealth and shielding. Based on this method, the absorption of MMA can be uniform flat under target frequency range by adjusting the calculated equivalent resistance. Meanwhile, COTMA can employ the new conformal transparent materials to increase its transparency. The design methodology can be readily applied to any other metamaterial absorber where transparent and flexible design is required. Therefore, it can be widely used in transparent EM stealth defense systems and wearable electronics applications.
Funding
National Program on Key Basic Research Project (173 Program) (Grant No. 2019-JCJQ-349); National Key Research and Development Program of China (Grant No. 2018YFF0212103); National Natural Science Foundation of China (Grant No. 61527805); 111 Project (Grant No. B14010); International Cooperation Research Base Foundation of Beijing Institute of Technology (Grant No. BITBLR2020014).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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