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Abstract
We introduce a metasurface to modify the reflection phase for multispectral microwave absorbers. General quantitive design criteria are proposed by carrying out field analysis, so that design of multispectral microwave absorber can be effectively realized. Optimal design process is discussed to develop an understanding of the absorbing mechanism. Experiment results show that the absorber having only 0.015 times the wavelength at the center frequency can simultaneously achieve high absorption in the microwave, visible light and near-infrared light bands. Multispectral absorption comes with added features of flexibility, ultrathin thickness and a light weight that make it a powerful candidate in advanced stealth application.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the modern military field, the new generation of reconnaissance methods drives the development of defense materials. In many cases, radar detection, optical telescope and infrared detection are carried out to find out the trace of stealth targets. Absorbers that can operate specifically in microwave range [1–8], infrared range [9–11] or visible-light range [12–14] have been widely researched. Various emerging materials have been studied for broadband microwave or light absorption. However, traditional absorbers that work in only a single range cannot satisfy the stealth necessity when all detection methods are applied simultaneously.
Compatible multispectral absorbers are urgently needed, but only a few researches [10,15–18] have been reported for absorbers with such capabilities. Yang et al [10] found that BaTiO3/polyaniline and BaFe12O19/polyaniline composites can have high absorption in both infrared and microwave band. Similarly, microwave absorber composed of SrTiO3/BaFe12O19/polyaniline developed by Hosseini et al [15] shows absorbing property in 10-40 μm and 8-12 GHz range. However, limited by the intrinsic electromagnetic property, addition of absorption capability in other spectra is difficult to achieve just by material itself. Metamaterial, composed of subwavelength artificial patterns has been researched for microwave absorber [3,4,6] that provides new thoughts on designing compatible multispectral absorbers. Shi et al. [18] reported a metamaterial microwave absorber (MMA) with low-infrared-emissivity polyurethane/aluminum composite coating as stealth material against both radar and infrared detections.
The metamaterial absorber is advantageous for being able to realize multiple functions by proper design [18–21]. For example, optically transparent microwave absorber can be realized by introducing transparent dielectrics such as water and transparent metasurface [19,20,22–24]. In order to absorb the microwave, visible and near-infrared energy simultaneously, emerging black phosphorus [25,26], carbon nanotube [13,14], 2D material such as graphene [27,28] and MoS2 [29] and artificial optical metasurface can be used at the surface. These surface coating can have ideal absorption in visible light band [13,14], infrared band [25] or terahertz band [25,28,29]. As a more convenient approach, contact ultra-black conductive film (UCF) can be utilized to compose the metamaterial microwave absorber. However, most MMAs are structured by a metal ground, dielectric layer and lossy metasurface from the bottom to top [3–8]. MMAs of this configuration are undesirable for total visible light absorption due to the area uncovered by UCF. More importantly, lack of the design criteria and methods for compatible multispectral absorbers still need further investigation.
In this work, we carried out theoretical field analysis and proposed general design criteria for compatible multispectral absorbers. Guided by the theory, a flexible ultra-thin multispectral absorber that can work in microwave, infrared and visible light ranges simultaneously was designed and experimentally researched. The optimal design process and absorbing mechanism were discussed in detail. Meanwhile, both simulated and measured results were compared to support the design criteria.
2. Theory and design
2.1 Field analysis and design criteria
Here, the proposed structure consists of a metal ground at the bottom, a lossless metasurface in the middle, an intact UCF on the top and supporting dielectric substrates as shown in Fig. 1(a). In this configuration, the lossless metasurface serves as a phase modulator, while the top resistive sheet dissipates not only microwaves but also visible and near-infrared light.
Fig. 1 (a) Schematic of proposed configuration of MMAs in field analysis. (b) Required reflection phase range.
Design criteria are investigated by performing field analysis to pave a path to the easy design of congeneric MMAs. When the electromagnetic wave irradiates the metamaterial absorber, it will be reflected or absorbed by UCF, as shown in Fig. 1. We set the xoy plane on the metasurface and z-axis normal to it. The E-fields of the incident wave (w0), the secondary radiation of UCF (w1) and the secondary radiation of metasurface (w2) can be expressed as E0, E1 and E2, respectively.
where k = 2π/λ is the wave number, and ex is the unit vector along positive x-axis.Due to the metal ground, all electromagnetic energy will be reflected at bottom. In case of continuous illumination, the amplitude of reflection at the metasurface is unity. Let’s define φ0 the total reflection phase of the whole structure below the metasurface (including the metasurface, bottom dielectric and metal ground). Then, we have,
Combine Eqs. (1)–(4), E2 can be expressed as,According to electromagnetic field theory [30], the boundary condition and relation between electric and magnetic components are
where ez is the unit vector along positive z-axis; d+ and d- represent the positions just lying on the top and bottom sides of the plane z = d; and ω is the angular frequency. Then we have,where J(d) is the induced surface current density on the UCF, and is the characteristic admittance of the free space. Using the Ohms’ law, there’s a certain relationship between J(d) and the total electric field at the plane z = d,where σs is the surface conductivity of the resistive sheet. Putting (1), (2), (5) and (8) into (9), we have,Let normalized impedance ηr = σ0/σs, and coefficient q1 = A1/A0, we can obtain
On the one hand, the amount of energy flow that the absorber receives is,On the other hand, according to Joule’s law, the energy dissipation by the absorber is,Then, the expression of absorptance is,Since the value of thickness d is small, the value of kd approaches zero and absorptance can hardly be affected. Therefore, we have,Perfect absorption condition learned from Eqs. (15) and (16) is obtained when relative sheet resistance ηr is 1 and the reflection phase φ0 is 0, as shown in Fig. 1(b). In case of the impedance ηr a constant as 1, the requirement of above 90% absorption is |φ0| ≤ 67.4°.
2.2 Optimal design and discussion
Here, the criteria, ηr = 1 and |φ0| ≤ 67.4°, are applied to design multispectral absorbers. A design is first proposed as shown in Fig. 2(a). In order to minimize the total thickness of the absorber, d is set as zero, which means covering an intact UCF on the metasurface without space.
Fig. 2 (a) Proposed structure multispectral absorber with the simplest metasurface. (b) Center frequency f0 (where φ0 equals 0) versus patch gap of the metasurface under different thickness h.
In the simulations, polyimide (εr = 3.5) was selected as the dielectric substrate. The period p is 3 mm, and the patch gap s and substrate thickness h are adjustable. Learned from Fig. 2(b), the decrease in thickness results in a smaller dimension of gap. It is demonstrated that the extremely narrow gap, which corresponds to a large equivalent capacitance between two metal patches, is needed to satisfy the impedance matching condition if the MMA is ultrathin.
However, limited by the minimum machining precision (0.001 inch), all the ultrathin absorbers with the dimensions in Fig. 2(b) are impractical because of the extremely narrow gaps. Hence, another structure consisting of double layer square metasurfaces is proposed in Figs. 3(a) and 3(b). The two metasurfaces are identical in size with a staggered arrangement. Equivalent capacitance is enhanced by two staggered metasurfaces, and absorption that center frequency f0 locates at 10 GHz is realized with parameters p = 3 mm, a = 2.8 mm, hgap = 0.05 mm, h1 = 0.15 mm and h2 = 0.2 mm.
Fig. 3 Optimized structure of compatible multispectral absorber: (a) structure and (b) periodic unit. (c) Relationship between the reflection phase and thickness h2. (d) The optimum surface resistance versus different h2 for above 90% absorption. (e) Relationship between surface resistance and thickness h2 when f0 = 10 GHz. (f) Absorption performance versus different h1. (g) Calculated equivalent permittivity and permeability of the proposed structure. (h) Absorption performance of the structure with and without UCF.
The reflection phase of the metamaterial surface is studied first. It’s indicated in Fig. 3(c) that the bandwidth range of |φ0| ≤ 67.4° is h2 independent when the total metamaterial is ultrathin. Theoretically, a metamaterial absorber can be constructed to cover a 377 Ω UCF on the metasurface. But in fact, coupling exists between the metasurface and the UCF, leading to non-uniform surface current distribution on the UCF, as shown in Figs. 4(a)-4(e). It was found that the thinner the thickness h2, more serious the nonuniformity. In this case, the optimum sheet resistance deviates from the theoretical value (ηr = 1) and the deviation is positively correlated to the strength of coupling, as shown in Fig. 3(d). As h2 increases, the coupling between the metasurface and the UCF weakens, and the optimum surface resistivity approaches the theoretical value. The resistance range where absorption is better than 90% is calculated and shown by the “blue” zone. The absorption performance of the structure with various values of h2 is simulated and plotted in Fig. 3(e). Comparing Figs. 3(c) and 3(e), f0 and bandwidth of the metasurface are found in complete agreement with the phase conditions.
Fig. 4 (a-e) Surface current distribution on the resistive sheet in the condition of different h2. (f) Surface loss distribution on top UCF. (g) Vector current distribution on top UCF, two metasurfaces and ground sheet.
Theoretically, the upper limit of the absorption bandwidth is closely related to the thickness of the absorber, as seen in the Rozanov limitation [31].
where Δλ = (λmax-λmin) is the absorption bandwidth, ρ0 is the voltage reflection coefficient, and d is the thickness of the absorber.According to Rozanov limitation, the absorption bandwidth of an absorber is in direct proportion to its thickness. Thus, to increase the bandwidth, the thickness should be increased. As for present structure, absorption bandwidth is related to the reflection angle of metasurface, the effective means to increase the bandwidth is to increase h1. It is verified by simulation as shown in Fig. 3(f).
In order to reveal the absorbing mechanism, surface current distribution and surface loss distribution of proposed structure were investigated in Figs. 4(b), 4(f) and 4(g). When the absorber is illuminated by external microwaves, carriers in the UCF will directionally move along with the E-field of external waves. In this manner, surface current is induce in UCF. As discussed above, owing to the coupling between the metasurface and the UCF when h2 is 0.2 mm, more surface current will concentrated at the central belt that is perpendicular to external E-field. According to Joule’s law, the microwave energy will be dissipated by the conductive film and converted into heat. The more intensive the surface current is, the higher the energy loss is, as shown in Fig. 4(f). We can learn from Fig. 4(g) that the current on UCF and ground sheet is anti-parallel to the current on metasurface, which demonstrates the existence of magnetic resonance.
Furthermore, we calculated the equivalent electromagnetic parameters of the structure [32], as shown in Fig. 3(f). It obviously shows that leaps appear in both real part of permittivity and permeability at around 10 GHz, namely the center absorbing frequency. The peak values of imaginary part of permittivity and permeability are also located around the center frequency. Besides, as shown in Fig. 3(g), nearly 70% absorption is retrogressed after removing the top UCF. The rest 40% absorption is contributed by the dielectric loss of PI substrate. Thus, we consider that both electrical and magnetic resonances contribute to the absorption, and the energy is mainly dissipated at the lossy UCF.
3. Experiment results and discussion
3.1 Experimental detail
The carbon-filled conductive Polyethylene films (CCPFs) were fabricated by a tape casting process. Commercial conductive carbon black powder with purity higher than 99.9% (Alfa Aesar) and low-density (0.9215-0.9255 g/ml) PE (Sigma-Aldrich) were used as the raw material. Major steps involved in the process are introduced as follows. The granular PE was completely melted at about 120 °C first. A ratio of 33 wt. % conductive carbon black powder was uniformly blended into the plastic melt by stirring. Then the mixture was transferred into a tape cast machine, where the height of the scraper was set as 0.04 mm to control the thickness of the film. After cooling down, the film was dried in vacuum at 40 °C for 4 hours. Finally the film was cut into a size of 180 × 180 mm2 for later use.
The metasurface was realized by the flexible circuit printing technology. 0.0175-mm thick copper foil was stuck to 0.025-mm polyimide film first. Then the designed periodic square patches were etched by the circuit printer. At last, CCPF, dielectric slabs and metasurfaces were glued together sequentially by PI adhesive. The thickness of the PI film is only 0.013 mm, which does not influence the absorption performance.
Morphologies of CCPF were observed in field emission scanning electron microscopy (FESEM, SU8220, Hitachi, Japan). Optical absorption was characterized by ultraviolet-visible-near-infrared (UV-Vis-NIR) spectrophotometer (Agilent Cary 5000, Agilent, USA) in a wavelength range from 220 nm to 2500 nm. Surface resistance were tested by four point probe instrument (CRESBOX, Napson, UK). Porosity and pore size distribution were measured by automatic mercury porosimeter (AutoPoreIV 9510, Micromeritics, USA).
Microwave performance was measured by the arch test method. In the measurement, Double-ridged broadband horn antennas (BBHA 9120 D, schwarzbeck Mess-Elektronik OHG, Germany) and Vector Network Analyzer (ZVB 20, Rohde & Schwarz, Germany) were used. Before testing the sample, an aluminate plate with the same size was tested before as calibration. Normal incidence and oblique incidence at 15°, 30°, 45° and 60° under both TE and TM mode were measured. Each test condition was measured three times for veracity of the results.
3.2 Results and discussion
As shown in Figs. 5(a) and 5(b), the size of the as-fabricated compatible multispectral absorber is 180 × 180 × 0.45 mm3, and other dimension parameters are p = 3 mm, a = 2.8 mm, hgap = 0.05 mm, h1 = 0.15 mm and h2 = 0.2 mm. Carbon-filled conductive Polyethylene film (CCPF) was used as UCF. According to Fig. 3(d), required surface resistance of the CCPF is 800 Ω when h2 equals 0.2 mm. In the experiment, the thickness of the film is controlled by adjusting the height of scraper. Here we compared the surface resistance of CCPFs with different thickness values, as shown in Table. 1. It can be observed that with the decrease of thickness, the surface resistance of CCPF increases. The measured surface resistance of the CCPF used in the absorber is 806 Ω. The absorber is flexible and can be bent freely.
Fig. 5 (a) Top view of the fabricated metasurface. (b) Side view of the absorber. The thickness of the sample is measured as 0.45 mm. (c) Measured absorption and reflection phase φ0 of the absorber. (d-e) Measured absorption under different incident angles (θ) for (d) TE and (e) TM polarization. (f) Optical absorption of the absorber. (g-h) SEM morphologies of CCPF. (i) Pore size distribution in CCPF.
Table 1. Surface resistance of CCPFs with different thickness values
Microwave performance was measured by the arch test system, as shown in Fig. 5(c). Both reflection phase φ0 and reflection loss were taken into consideration. Seen from Fig. 5(c), a perfect absorption is achieved at 9.98 GHz where the corresponding φ0 is zero. Meanwhile, above 90% absorption is realized in the range of 9.69 GHz to 10.22 GHz, and φ0 at two critical frequencies are 67.4° and −67.4°, respectively. The experimental results agree well with theoretical and simulation results in Figs. 1(b) and 3(d). In Figs. 5(d) and 5(e), the absorption remains unchanged under normal incidence for either TE or TM mode, suggesting the absorber is polarization insensitive. However, as expected, the absorption is incident angle (θ) dependent. With the increasing of θ, center frequency shifts to higher band, accompanied by a little attenuation in absorption intensity. On the one hand, according to [33], the equivalent normalized impedance of UCF are ηrTE = ηrcosθ and ηrTM = ηr /cosθ for TE and TM polarization respectively under oblique incidence, where θ is the incident angle. On the other hand, full wave simulation software is applied here to obtain the φθTE and φθTM, as shown in Figs. 6(a) and 6(b), where φθTE and φθTM are the reflection phase of the metasurface for TE and TM polarization, respectively.
Fig. 6 The calculated reflection phase of metasurface for (a) TE and (b) TM polarization under different oblique angle. (c) Theoretical and measured absorptance under oblique incidence.
As improvement, Eq. (16) in cases of oblique TE and TM polarization can be expressed as
For the perfect absorber in this work, ηr equals to one. Then we have, It can be learnt that Eqs. (20) and Eq. (21) can reach their maximum values when φθTE = 0 and φθTM = 0, respectively. Therefore, the relationship between absorptance and incident angle θ is,Based on Eq. (22), the theoretical and measured absorption results under oblique incidence for both TE and TM polarizations are in high agreement, as displayed in Fig. 6(c).We have to emphasize that the thickness of the absorber is only 0.015 times the wavelength at f0, demonstrating an ultra-thin feature compared with the results in literature. Generally, full width at half maximum absorption (FWHM) is used to evaluate the performance of ultra-thin absorbers [5–8]. Table 2 unveils a comparison of the ultra-thin absorbers working near 10 GHz. It reveals that the present work can maintain good FWHM in a very thin thickness, outperforming the reported works in terms of thickness. Although [6] and [8] possess higher FWHMs compared to the proposed structure, but with thicker dimensions.
Table 2. Comparison of the ultra-thin absorbers working near 10 GHz
According to Figs. 5(b) and 5(c), the surface of the absorber is ultra-black. Almost no reflection of visible light can be observed by naked eyes. The visible light absorption depends on the optical absorption of the CCPF. It’s shown in Fig. 5(f) that 96% absorption can be achieved in the visible light and near-infrared bands. The best absorption can reach up as high as 97%. Except for two drops caused by the instrument, the spectrum is steady in the whole range from 300 to 2400 nm.
Three-dimensional porous structures with 2~5-μm size, can be clearly observed in the CCPF from Fig. 5(g). After further magnification, tinier pores, sized from 50 nm to 1 μm, can be observed in Fig. 5(h). Agreeing with the SEM results, the mercury intrusion measurement reveals that the porosity of the CCPF is 6.83%, and the pore size distribution is shown in Fig. 5(i). The size of small pores in the film are in nano-scale below 100 nm, while the larger pores are around 4.3 μm. These pores are connected in 3D networks and uniformly distributed in the film. The large pores are in size of subwavelength of in visible light band while the small ones are in size of subwavelength of near-infrared band. Therefore, they can act as equivalent ‘black cavities’ interacting with the visible and near-infrared light [13]. Due to the porosity, the light can go to the inner areas of CCPF and be scattered repeatedly in the pores with similar size. Little light will be reflected back. Finally, light is dissipated by the carbon powder, leading to ultra-black behavior. In addition, the CCPF is a composite material composed of polymer and conductive carbon black. Conductive carbon black is amorphous [34], which is prone to form random multi-pore structures, and possesses high specific surface area, seen in Figs. 5(g) and 5(h). Besides, CCPF is a kind of material with a certain resistivity that helps absorb the electromagnetic energy. Therefore, in visible range, the electromagnetic waves incident to those random multi-pore structures come across multiple scattering and multiple internal reflection, and are finally absorbed by the film due to its leakage-conductance effect between conductive particles.
4. Conclusions
In summary, we proposed general design criteria of compatible multispectral absorber by field analysis: relative sheet resistance ηr is 1 and the reflection phase of the metasurface φ0 is 0. For better than 90% absorption, φ0 should be |φ0| ≤ 67.4° when ηr = 1. The derived relations are equivalent expressions to support the impedance matching principle. The criteria and the method are of high effectiveness and reliability to guide the rapid design of multispectral microwave absorbers. We discussed the absorption mechanism and optimal design process in detail. Small thickness of the top dielectric layer leads to coupling effect and deviation of surface resistance. Required surface resistance is quantitatively studied. Experimental results show that the absorber can simultaneously have high absorption in the microwave, visible light and near-infrared light bands. The thickness of absorber is only 0.015 times the wavelength at center frequency. Multispectral absorption, flexibility, ultrathin and lightweight features of the absorber make it promising in future application.
Funding
National Natural Science Foundation of China (NSFC) Grant 51907185.
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