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Abstract
In this work, we demonstrate a flexible frequency-selective rasorber (FSR) with great angular stability and conformal superiority using metal-graphene hybrid metamaterial. The metamaterial is fabricated by filling the designed metal patterns with graphene-based ink. It can replace the traditional resistors to introduce loss for the absorption purpose. Therefore, the FSR does not need any lumped components soldered onto its surface, enabling a high flexibility and conformal capability. The metal-graphene FSR is fabricated and measured on flexible substrates that have a 60° angular stability and a 128° conformal angle. The simulations and experiments confirmed that the proposed metal-graphene FSR exhibits excellent angular stability and considerable flexibility, making it ideal for stealth systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Frequency selective surface (FSS) is a periodic structure with spatial filtering characteristics that enables electromagnetic waves to be transmitted or reflected in specific frequency bands [1,2]. Since the bandpass FSS can transmit electromagnetic waves in the pass-band and reflect out-of-band waves, it is widely used in radar cross section (RCS) reduction. But this approach is only applicable to monostatic situations. To avoid out-of-band reflected waves from being detected by the multi-station radars, the ideal way is to mitigate the reflection of out-of-band electromagnetic waves using absorbers [3,4]. In this context, in addition to the above absorbers developed in microwave band, advances on broadband absorbers in the ultraviolet regime [5,6] and in the infrared regime [7] have been made. In order to achieve pass-band transmission and out-of-band absorption, frequency selective rasorbers (FSRs) have been proposed and attracted extensive attention [8]. To date, the research of FSRs can be grouped into two categories: two-dimensional (2-D) FSRs [9–12] and three-dimensional (3-D) FSRs [13–16]. Due to the inability of 3-D structures to be flexible and conformal, this work focuses exclusively on 2-D structures. In recent years, 2-D FSRs have made numerous advancements in terms of insertion loss reduction [17], working bandwidth expansion [18], combined with antenna [19], and functional reconfiguration [20,21]. However, due to the limitations of printed circuit board (PCB) processing technology and low angle stability, high-performance flexible FSRs have not been widely studied.
Graphene is a new type of two-dimensional material that exhibits exceptional optical transparency, flexibility and high electron mobility [22–24]. Once it was discovered, it attracted widespread attention. At present, graphene-based metamaterial devices have been widely used in absorbers [25,26], polarization converters [27], sensors [28] and so on. They primarily use monolayer graphene [29], graphene-based sandwich structure (GSS) [30], graphene nanoplates [31] and multilayer graphene film with high conductivity [32]. Compared with a pure graphene-based metamaterial, the metal-graphene hybrid metamaterial has a more flexible design method and can achieve more diversified functions. However, it is very challenging to develop metal-graphene hybrid metamaterial using monolayer graphene and GSS. Additionally, the reported works on the metal-graphene hybrid metamaterial [33–36] are theoretical analyses and simulations with no experimental validation. As a result, research into the design, fabrication, and validation of metal-graphene hybrid metamaterials is critical.
Reference [37] uses chemical vapor deposition (CVD) graphene to realize a flexible FSR design for the first time. Subsequently, in Ref. [38], the design of a conformal FSR is realized by using a standard printed circuit board (PCB) process. However, the angle stability of these two designs is only 45°, limiting the conformal angle. In addition, the preparation of CVD graphene is complicated and costly, and the conventional PCB process requires many soldering processes. Both are time-consuming to process and prepare.
In this work, we propose a flexible FSR based on metal-graphene hybrid metamaterial. The metal-graphene hybrid metamaterial is realized by transferring the prepared graphene ink to the PCB board through a screen-printing technology. It can replace the lumped resistors, making it suitable for flexible applications. Moreover, the fabrication of the metamaterial is lower cost compared with CVD graphene or GSS, and it can be flexibly combined with metal to improve the performance of the device. The metal-graphene based FSR can achieve a high angle stability of 60° and a large conformal angle of 128°. The experimental results are in good agreement with the simulation results, indicating that our design is feasible.
2. Rasorber design and graphene preparation
2.1 Structural design
Typically, the 2-D FSR consists of a lossy layer, a supporting substrate, and a bandpass FSS. At the passband frequency, the incident wave can pass through with little loss, while frequencies outside the passband are absorbed, only a few electromagnetic waves were reflected, as illustrated in Fig. 1(a). The S21 and S11 were simulated with TE and TM polarizations as the incident angle increased from 0° to 60°, as shown in Fig. 1(b)-(e). The S21 results indicate that the passband is located at 8.3 GHz with a small insertion loss of 0.29 dB, and there are transmission zeros on both sides of the passband. Meanwhlie, S11 is less than -10dB on both sides of the passband, which can have a good absorption effect in these frequency bands. The maximum absorption rate is over 97% ($A = 1 - {|{{S_{11}}} |^2} = {|{{S_{21}}} |^2}$). It can be seen that the designed FSR has a high angle stability of 0° - 60° under both TE and TM polarizations.
Fig. 1. (a) The schematic diagram of FSR with metal-graphene hybrid metamaterial; (b) Variation of S21 with incident angle under TE polarization; (c) Variation of S21 with incident angle under TM polarization; (d) Variation of S11 with incident angle under TE polarization; (e) Variation of S11 with incident angle under TM polarization.
Figure 2(a) shows the flexible FSR structure based on metal-graphene hybrid metamaterial is shown in Fig. 2(a). A PDMS substrate with ${\varepsilon _r} = 2.7$ and $h = 4mm$ is selected as the supporting substrate. Since the metal cannot be processed directly on PDMS, polyimide (PI) substrates with ${\varepsilon _r} = 3.5$ and $h = 0.05mm$ are added on the upper and lower sides of the PDMS. The lossy layer is shown in the bottom right corner of Fig. 2(a). The cross-shaped unit is simple in structure and good in angular stability. Therefore, the metal part of the lossy layer adopts an approximately cross-shaped structure and the graphene resistive film with a sheet resistance of 200 Ohm/sq is located in the center of the unit. The bandpass FSS layer is composed of a square ring patch and a Minkowski fractal square ring patch, as shown in the bottom left corner of Fig. 2(a). The conformal schematic diagram is shown in Fig. 2(b), and the FSR array is conformed to a cylindrical surface, the conformal angle is $\beta$.
Fig. 2. (a) The structure of the proposed FSR; (b) Conformal structure diagram; (c) The surface current distributions of FSR. The geometric dimensions are: p = 8, a = 1.5, d1 = 7.8, h = 4(unit: mm).
The commercial software High Frequency Structure Simulator (HFSS) is used to analyze the structure. The Floquet port and periodical boundary conditions are set to model and simulate the proposed FSR. Among them, the graphene film is modeled as a zero thickness square surface with a sheet resistance of 200 Ohm/sq. The surface conductivity of graphene can be obtained from the Kubo's formula [39]
Then, we investigated the surface current distributions at the 5.5 GHz (in low frequency absorption band), 8.3 GHz (in passband) and 11 GHz (in high frequency absorption band), as shown in Fig. 2(c). At 8.3 GHz, a parallel resonance occurs at the end of the metal branch, and almost no current flows through the graphene resistive film, which implements the passband. At 5.5GHz and 11GHz, the current flows from one end of the unit to the other end, and it has loss through the graphene resistive film, which achieves the absorption band. Therefore, the FSR can achieve a low insertion loss passband in the middle of the two absorption bands.
The oblique incidence performance of FSR with different conformal angles under TM polarization is also analyzed, with Fig. 3 depicting the results. From Fig. 3(a)-(d), when the conformal angle is 64°, there is an angular stability of 40°. As the conformal angle increases, its angular stability decreases continuously. When the conformal angle is 128°, there is only 20° of angular stability. The results for TE polarization are similar to those for TM polarization, so they are not described in detail in this paper.
Fig. 3. S-parameters of FSR at different conformal angles as a function of incident angle under TM polarization. (a) The S11 with a conformal angle of 64°; (b) The S21 with a conformal angle of 64°; (c) The S11 with a conformal angle of 128°; (d) The S21 with a conformal angle of 128°.
2.2 Theoretical analysis
The corresponding equivalent circuit [17] is shown in Fig. 4(a). If the parallel circuits L2C2 and L3C3 resonate at frequency fp simultaneously, it is possible to realize a low insertion loss passband at fp. In the absorption band fa, the bandpass FSS can be regarded as a metal floor, so the parallel L2C2 circuit can be regarded as a limited inductance (fa < fp) or capacitance (fa > fp), forming a new series RLC circuit with the original RL1C1. In this case, the equivalent circuit of FSR is shown in Fig. 4(b).
Fig. 4. (a) The equivalent circuit of 2-D FSR. (b) The equivalent circuit for the absorption frequency band.
In Fig. 4(b), YA is the admittance of the series RLC circuit, and Yd is the input admittance of the short-circuit transmission line. YA and Yd can be respectively expressed as
Among them, $\omega$ is the operating frequency, ${\varepsilon _r}$ is the relative permittivity of the substrate, ${k_0}$ is the free space propagation constant, and d is the thickness of the substrate.
The reflection coefficient of the circuit shown in Fig. 4(b) can be expressed as
Among them, Y0 is the characteristic admittance of free space and Yin is the input admittance of the circuit.
In order to minimize the reflection, it is necessary to make Yin equal to Y0, which means,
In most FSR designs, this impedance matching condition shown in Eqs. (6) and (7) can be satisfied at normal incidence. However, when the incident angle changes, YA, Yd, and Y0 all inevitably change. Therefore, selecting structures and substrates that minimize the variation of YA and Yd at oblique incidence is vital for the design of FSR with high angular stability. The change of impedance matching caused by oblique incidence is analyzed below.
Since broadband absorber generally introduces resistive elements, R primarily manifests as ohmic loss, regarded as constant when obliquely incident. The change of LC is related to the structure of FSS. For a patch array, the capacitance is angular dependent for TE polarization [43] (decreases as the incident angle increases), while the cross array capacitance is almost angle-independent [44]. Since we adopt the cross array, The change of YA at oblique incidence is limited.
The expression of Yd at oblique incidence is
The designed passband of the FSR is around 8GHz, therefore, under the condition of different dielectric constant ${\varepsilon _r}$ and dielectric thickness d, the variation of Yd with the incident angle at 8GHz is analyzed.
When f = 8GHz, d = 4mm, the magnitude of ${Y_d}$ changing with $\theta$ under different ${\varepsilon _r}$ is shown in Fig. 5(a) and (b). It can be seen from Fig. 5(a) that under TE polarization, with the increase of the incident angle, the change of ${Y_d}$ is not significant, and the same is true for different ${\varepsilon _r}$. However, as shown in Fig. 5(b), when ${\varepsilon _r}$ is close to 1, ${Y_d}$ under TM polarization increases sharply with the increased incident angle. Fortunately, as ${\varepsilon _r}$ increases to 3, ${Y_d}$ changes smoothly with the increase of $\theta$. It is worth noting that, the increase of ${\varepsilon _r}$ from 3 to 10 does not significantly improve the stability of the ${Y_d}$. Therefore, the choice of ${\varepsilon _r}$=2.7 is suitable for the oblique incidence.
Fig. 5. The variation of ${Y_d}$ with $\theta$ under different ${\varepsilon _r}$. (a) TE polarization. (b) TM polarization. The variation of ${Y_d}$ with θ under different d. (c) TE polarization. (d) TM polarization.
Meanwhile, when f = 8GHz, ${\varepsilon _r}$=3, the magnitude of ${Y_d}$ varying with $\theta$ under different d are calculated, as shown in Fig. 5(c) and (d). Under TE and TM polarization, when d is small, ${Y_d}$ hardly changes with the increase of the incident angle. As d increases, the change of ${Y_d}$ with the incident angle is increasingly prominent. Therefore, a substrate with relative permittivity of 2.7 and thickness of 4.1mm is selected so that the changes of Yd tends to be consistent under TE and TM polarization.
The free space admittance Y0 at oblique incidence is
Thus, with the increase of $\theta$, Y0 exhibits opposite variation trend under TE and TM polarization. It is almost impossible for YA to realize the admittance matching under TE and TM polarization simultaneously when the incident angle increases. Therefore, as the angle increases, impedance mismatch is inevitable.
2.3 Preparation of graphene ink
In this work, graphene ink is used to realize a metal-graphene hybrid metamaterial. The preparation and characteristics of this graphene ink are introduced below.
The graphene ink is composed of graphene flakes, carbon black, solvents, related binders, and dispersants. Table 1 provides the detailed ingredients and dosage. The ingredients according to Table 1 were added and mixed, as shown in Fig. 6(a). To make carbon black (CB) and graphene flakes uniformly dispersed, they were mixed and ultrasonically dispersed in a planetary mixer/deaerator (MAZERUSTAR KK300SSE) and an ultrasonic cleaner. The resulting ink was then printed on the substrate and cured at a high temperature. If the obtained ink met the sheet resistance requirement, it would be printed on the prepared PCB pattern. Figure 6(b) shows the printed graphene film. This material has superior flexibility from the graphene film in the bending state compared with the lumped elements.
Fig. 6. (a) Schematic diagram of graphene ink preparation; (b) The printed graphene film in the flat and bending state; (c) The SEM image of the prepared graphene film; (d) The measurement results of the sheet resistance of the graphene film.
Table 1. Ingredients in Graphene Ink
Figure 6(c) depicts the graphene ink’s scanning electron microscopy (SEM) image. The carbon black particles and graphene nanoflakes are uniformly distributed without agglomeration. Since the sheet resistance of the prepared graphene film is 200 Ohm/sq, the conductivity is poor, so the overall image is dark. The upper left, upper right, lower left, lower right, and middle parts of the resistive film were labelled as 1-5, and the sheet resistance was measured. Figure 6(d) presents the results, which were 198.4 Ohm/sq, 194.7 Ohm/sq, 196.5 Ohm/sq, 206.3 Ohm/sq, 196.5Ohm/sq, respectively, with an average value of 198.48 Ohm/sq. These indicated that the sheet resistance of the ink met the requirements of 200 Ohm/sq, with a very even distribution.
3. Measurement setup and results
The prepared ink is printed on the PCB through the screen template, as shown in Fig. 7(a) and the details presented in Fig. 7 (b), the black part in the picture is the graphene resistive film. Figure 7(c) depicts the sample in the conformal state, exhibiting good flexibility. The processed sample array has 25×25 units. As shown in Fig. 7(d), we measured the FSR sample in an anechoic chamber using a pair of horn antennas operating from 2 GHz to 18 GHz. The two horns are connected to a vector network analyzer (Anritsu MS46322A).
Fig. 7. (a) The sample array; (b) The sample details; (c) The sample in the conformal state; (d) The measurement environment.
For the conformal test, we prepared foam cylinders with radii of 180/107/90mm, respectively. If the sample conformed to the foam cylinder, the corresponding conformal angles of 64°, 107° and 128° can be achieved. First, the test of S11 is performed. The flexible metal is fixed to the cylindrical foam, and the S11 at this time is mostly reflection and calibrated to zero. The sample then is fixed to the cylindrical foam, and S11 results under conformal angles are tested. The test of S21 is a little different. The foam cylinder is placed between the two antennas, and the S21 is almost transmission and calibrated at this time. The sample is then fixed to the cylindrical foam, and S21 results under conformal angles are also tested. In this way, the scattering problem caused by conformality can be effectively removed [45].
The simulation and measurement results under TM polarization for flat and conformal FSRs are shown in Fig. 8(a)-(d). They can achieve a large conformal angle of 128° under TM polarization. For conformal cases, the structures under TE polarization and TM polarization are no longer entirely consistent, so the S-parameters are slightly different, but a large conformal angle of 128° can still be achieved. First, the FSR in the flat state is also tested. It can be seen that the passband is at 8.3 GHz with the insertion loss of 0.93dB. The low frequency absorption band is 5.2-5.89GHz, and the high frequency absorption band is 9.9-12.2GHz. Then the conformal FSR is tested, and the conformal angle remains consistent with the simulation. The measured results are in good agreement with the simulation results, which shows that the FSR has good conformal application potential.
Fig. 8. (a) The simulated S11 results in flat and conformal states; (b) The simulated S21 results in flat and conformal states; (c) The measured S11 measurement results in flat and conformal states; (d) The measured S21 results in flat and conformal states.
Table 2 lists the comparison between the proposed FSR and the recently reported FSRs. It can be concluded that the proposed FSR has a smaller thickness and period unit size, and at the same time achieves an excellent angle stability of 60°. In the fabrication process, this work uses the graphene resistive film, which not only avoids the welding process, but also facilitates the flexibility of the FSR. Meanwhile, compared with CVD graphene, graphene films are cheaper and easier to be combined with metal. As a flexible FSR, this work has the largest conformal angle at present.
Table 2. Comparison of Proposed FSR with Other FSRs
4. Conclusions
In this work, a flexible FSR based on metal-graphene hybrid metamaterial is presented. It has a good angle stability until 60° and a large conformal angle of 128°. The variation of the impedance matching condition at oblique incidence is analyzed by using an equivalent circuit method, and the key parameters are well selected to improve the FSR’s angle stability. The FSR using metal-graphene hybrid metamaterial not only avoids the welding process, but also facilitates the flexibility. The process and transfer methods of graphene resistive film with particular sheet resistance are described in detail. Flat and conformal FSRs are measured, and the measured results are in good agreement with the simulation results. The high-performance low-cost flexible FSR has the potential applications in the conformal stealth platforms.
Funding
National Natural Science Foundation of China (61771360, 62071357, 62171348, U19A2055); China Postdoctoral Science Foundation (2020M673342); Fundamental Research Funds for the Central Universities (XJS200217); Key Industry Innovation Chain of Shaanxi ( 2018ZDCXL-GY-08-03-01).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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