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Abstract
Perfect absorbers are highly desired in many engineering and military applications, including radar cross section (RCS) reduction, cloaking devices, and sensor detectors. However, most types of present absorbers can only absorb space propagation waves, but absorption for surface waves has not been researched intensively. Surface waves are easily excited on the interfaces between metal and dielectrics for electronic devices, which decreases their working performances due to the electromagnetic disturbances. Thus, it is of great significance to design appropriate absorbers to dissipate undesirable surface waves. Here, we propose the concept of a surface wave absorber, analyze its working principle, and prove its good performances experimentally. To demonstrate our concept, we design and fabricate a realistic surface wave absorber that is fixed on a metal surface. Experiments are performed to verify its electromagnetic characteristics. The results show that our designed meta-absorber can achieve an excellent surface wave absorption within a wide frequency window (5.8–11.2 GHz) and exhibit a very high efficiency over than 90%, but only with the thickness of 1 mm (0.028 λ). Our device can help to solve the issues of absorption at large angles, and it can find wide applications in large antenna array design and other communication systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic (EM) stealth technology has gradually become an important means in modern military science and technology. Absorbers have been demonstrated as an effective method to achieve EM stealth. However, traditional absorbers are usually constituted of natural material, such as wedge absorbers [1–2] and ferrite [3], and they still suffer from bulky forms, narrow bandwidth, and sensitivity to the working environment. These disadvantages limit their potential integration applications. Metamaterials and metasurfaces have received great interest due to their abilities to manipulate the wavefronts of transmitted and reflected EM wave [4–35]. They have become a hot research topic with their remarkable achievements, including invisibility cloaks [4,5], super lenses [6,8], planar holograms [9,10] and perfect absorbers [21–34]. Since 2008, Metamaterial/metasurface absorbers have attracted strong attention [21], due to their outstanding performance. Recently, a series of methods has been used to improve the performances of the metamaterial/metasurface absorbers, such as adopting multiple point resonance structures or load lumped elements to expand the bandwidth [22–25], introducing an improved meta-atom to make the absorber have great polarization-insensitive and incident angle insensitive characteristics [26–28], using complex three-dimensional structures, such as a Huygens structure or a zigzag-shaped structure, to improve absorption efficiency [29–30], and many meta-absorbers have multifunctional or tunable ability [31–34].
However, current absorbers provide excellent performances for the space wave at normal incidence or small incident angles, but they are immune to the surface wave. For most electronic devices with metal surfaces, surface wave is easily excited under the illumination of a large oblique incidence angle EM signals [36–38]. Because traditional meta-absorbers are always matched with the free space wave, they can absorb an incident space wave without reflection. For a surface wave, since its eigenmode is fundamentally different from the propagation space wave, the mismatch effect is induced for traditional meta-absorbers, and resulting in the significant degradation of absorption performances. Due to the unique properties of the surface wave, there are two key issues in the design of corresponding absorbers. The first point is to achieve the match of the wave vector, ensuring that the excited surface wave travel is stable without decoupling and scattering. The second key point is to achieve the impedance match with the surface wave, guaranteeing high absorption efficiency for the surface waves.
In this paper, we propose an ultra-thin and broadband meta-absorber, consisting of an array of microstructures to solve the key issues. The meta-atom can tune the wave vector by optimizing the structural size, and can also control the impedance by tuning the square impedance of indium tin oxide (ITO). As a result, the designed meta-absorber can absorb the surface wave efficiently. Moreover, the meta-absorber can work well (efficiency better than 90%) within a wide frequency band (5.8–11.2 GHz), but only with the thickness of 1 mm (0.028 λ). The experimental results demonstrate the feasibility of our design. Before this work, we have taken a similar approach to realize a broadband absorber for the surface wave under spoof surface plasmon polariton (SSPP) mode [39]. In this work, we adopted the same principle to achieve a realistic absorber for the surface waves which are excited on the metal. This kind of surface wave absorber can have greater practical significance and application value. Our study provides an effective design method for high-efficiency surface wave absorbers at other extended frequency regions, and it paves the way for an alternative approach to solve the problem of electromagnetic compatibility.
2. Design of the surface wave meta-absorber
Working principle and meta-atom design of the surface wave meta-absorber. We first discuss the absorption mechanism of the surface wave absorbers. As schematically shown in Fig. 1(a), when the space propagation wave strikes the metal with large oblique angles (here, the angle with the vertical direction is set to 88.5°), the surface wave is excited on the interface. The excited surface wave is not stable, and it can decouple or reradiate to free space, especially via transmission to the structure edge. The decoupling effects greatly affect the working performances and increase the RCS of the target device. Therefore, our goal is to avoid the decoupling effects introduced by the surface wave. The two key factors of achieving the wave vector matching and the impedance matching conditions [40–43] are obligatory to reach this end. The former achieves the transmission of the surface wave without scattering, while the latter achieves the absorption of the surface wave and ensures a high absorption efficiency, as seen in Fig. 1(b). For the case of the vector being matched while the resistance of the absorber is set as 0, the surface wave transmits along the absorber, as shown in Fig. 1(c). For the case with impedance matching while the vector is mismatched, the decouple effect appears obviously and thus decreases the absorption efficiency, as shown in Fig. 1(d). For the case with vector matching while the impedance is mismatched, shown in Fig. 1(e), the surface wave is not absorbed efficiently. A high-performance absorption of the surface wave is achieved when both conditions are satisfied, as seen in Fig. 1(f).
Fig. 1. Structural components and working principles of the proposed surface meta-absorber. a) A beam of a plane wave shining on a metal plate in parallel excites a surface wave at the interface between metal and air. The surface wave generates strong scattering for the space. b) When the proposed surface wave absorber is added at the edge of the metal, the surface wave can be absorbed, and the scattering of the metal can be ultimately reduced. c) The magnetic field amplitude for the case wave vector is matched. d) The magnetic field amplitude for the case wave vector is mismatched. e) The magnetic field amplitude for the case wave vector is matched but the impedance is mismatched. f) The magnetic field amplitude for the case wave vector and the impedance are matched.
Excitation of the surface wave. To demonstrate our concept, we adopt a wedge-shaped metal structure with a small tilt angle to excite the surface wave. The wedge-shaped metal structure has a size of L×W = 220 mm×240 mm, and the thickness increases gradually from 0.5 mm to h = 11 mm with a tilt angle of 3°, as shown in Fig. 2(a). When an X-polarized incident wave shines on the wedge-shaped metal structure, the surface wave is obviously excited at the edge of the structure within a wide frequency interval. The magnetic field in the Z direction distributions (Hz) is shown in Figs. 2(b)–(d). When the excited surface wave interacts with the device edge, a wave vector mismatch appears, and the excited surface wave decouples to the free space or reflects in reverse and thus induces strong scattering. Based on the excited surface wave, the real part of the Hz at the edge of the metal structure can be quantitatively retrieved to obtain the its wavelength, as shown in Figs. 2(f)–(h). The wave vector of the surface wave at different frequencies can be calculated based on formula (1), and the dispersion relationship between k and the frequency is plotted in Fig. 2(e). Based on the relationship, it is possible to design a realistic structure to achieve the wave vector match with the excited surface wave.
Control of wave vector with a realistic meta-structure. To match the mode profiles with the surface wave coupler, we choose a dual-layered H-shaped structure as the absorber meta-atom. The physics can be understood easily from the effective medium. Such a structure is equivalent to a magnetic material with effective permeability μ that is placed on a metal ground. The excited anti-parallel electric currents between the two metallic layers can support the propagation of the surface wave when μ is controlled effectively. As schematically shown in the inset of Fig. 3(a), the meta-structure is composed of two layers, which are attached on an F4B substrate and separated by a layer of Polyethylene Terephthalate (PET). With the microstructure in hand, we next show how to tune the wave vector exactly. Here, a three-step wave vector tuning method is derived for a convenient meta-absorb design. For the first step, a coarse control over the wave vector is performed by changing the parameter, where “a” represents the periodicity in the X direction. Figure 3(a) plots the effect of the parameter “a” on the dispersion relationship. The other parameters are fixed to ensure a fair comparison. It can be clearly seen that the dispersion changes greatly at a lower frequency and undergoes a continuous shift as the parameter “a” increases from 5 mm to 7 mm. For the second step, the fine control over the wave vector is achieved by adjusting the arm length “l1” of the lower H-shaped structure. Figure 3(b) depicts the dispersion relationship of the meta-structure as “l1” increases from 5 mm to 7 mm in steps of 1 mm. In this process, the residual geometrical parameters of the H-shaped resonator are kept constant. As can be seen, the wave vector constant at a lower frequency can be stable and unaffected. At the higher frequency, however, the dispersion curve changes significantly. In the last step, the precise control over the dispersion relationship is achieved by tuning the parameter “l2”. The wave vector changes slightly as “l2” increases from 3 mm to 5 mm, as seen in Fig. 3(c).Fig. 2. The wave vector calculating process of the surface wave. (a) The schematic of the simulated model. The Z direction magnetic field (Hz) of the surface wave at (b) 7 GHz, (c) 9 GHz, and (d) 11 GHz. The real parts of the curves of the Hz at (f) 7 GHz, (g) 9 GHz, and (h) 11 GHz on the “L” edge of the metal. (e) The curve of the dispersion relationship between k and the frequency.
Fig. 3. The design process of the meta-atom for the X-polarized incident wave with the FDTD simulation. Schematic diagram of the design of the meta-atom that contains two H-shaped patches and a F4B substrate. The lengths of the two H-shaped units, “l1” and “l2,” and the width of the F4B substrate “a” are three parameters that we can change to adjust the wave vector of the meta-atom. The curves of the wave vector influenced by changing (a) the width “a” of the F4B, (b) the length of the lower H-shaped structure, (c) the length of the upper H-shaped structure, (d) The magnetic field for the Z direction (Hz) distribution when the matching condition is met, (e) The final matching result of the absorber and the surface wave, (f) Curves of the absorption efficiency as ITO resistance changes (g) The magnetic field for the Z direction (Hz) distribution when the resistance of the absorber that is set as 10 Ω/square, (h) The Hz distribution when the resistance of the absorber that is set as 100 Ω/square, and (i) The Hz distribution when the resistance of the absorber that is set as 50 Ω/square.
To summarize, the flexible three-step wave vector control method provides a comprehensive guideline for the exact design of the meta-structure. As a result, the carefully optimized dispersion coincides well with the extracted case from the wedge-shaped structure, as seen in Fig. 3(e), which can ensure that the surface wave propagates without scattering, as shown in Fig. 3(d).
Control of impedance of the surface wave using the meta-structure. Here, because it is difficult to directly determine the impedance of the surface wave exactly, we optimize the resistance of the meta-structure to obtain the best absorption performance. Noting that the dual-layered H-shaped resonator is composed of ITO, we can easily control its resistance in the experiment. When the resistance R changes from 10 Ω/square to 100 Ω/square, different absorption phenomena can be observed with the simulated amplitude of the magnetic field, as shown in Figs. 3(g)–(i). There is no energy scattering in these cases since the wave vector is matched well, but the slope of the amplitude attenuation rate is different, as seen in Fig. 3(f). As demonstrated, when the resistance of the ITO layers is about 50 Ω/square, the amplitude of the magnetic field exhibits the largest attenuation, and the meta-absorber achieves the maximum absorption rate.
FDTD simulation of the meta-absorber. In order to demonstrate the surface wave absorption effect of our meta-absorber, the wedge-shaped metal structure and the surface wave absorber are combined and simulated with CST Microwave Studio. The real part of the magnetic field in the Z direction (Hz) of the metal-only structure and the metal with the meta-absorber structure can be calculated at three representative frequencies, as shown in Figs. 4(a)–(c) and Figs. 4(d)–(f). It is obvious that the reflected surface wave is significantly depressed when the meta-absorber is worn. The slight scattering in Figs. 4(d)–(f) is caused by the mismatch at the edge of the structure and the air, which can be alleviated by extending the structure size. To quantitatively evaluate the absorption effect, we extract the Hz for both conditions. As depicted in Figs. 4(g)–(i), the real part of the Hz is reduced significantly when the meta-absorber is added at the edge of metal, which shows the high absorption of our device for the surface wave. When the surface wave barely touches the absorber, it may reserve some energy. However, when the surface wave travels some distance along the absorber, a higher absorption can be achieved.
Fig. 4. Absorption effects displayed by the magnetic field result diagrams. The Hz diagram of the metal without the absorber model at (a) 7 GHz, (b) 9 GHz, and (c) 11 GHz. The Hz diagram of the metal with the absorber model at (d) 7 GHz, (e) 9 GHz, and (f) 11 GHz. The real parts of the curves of Hz for the model with and without an absorber at (g) 7 GHz, (h) 9 GHz, and (i) 11 GHz.
3. Experimental results and discussions
In order to verify the characteristics of the proposed surface wave absorber, we fabricate an absorber sample (with a size of 51 mm × 220 mm) that consists of a periodic array with 6 × 35 meta-atoms, as shown in Fig. 5(a). In the fabrication process, the 3D printing technique is used to produce a piece of wedge-shaped metal, which has the same size as the simulation piece. For the absorber, we first coat the ITO on the surface of the Polyethylene Terephthalate (PET) with magnetron sputtering technology, and then we etch the designed H-shaped structure with photolithography technology. Next, we fix the PET with ITO on the F4B layer to make a complete surface wave absorber. Finally, we attach the surface wave absorber to the edge of the metal structure to experiment with their absorption performance.
Fig. 5. Fabricated sample and its measured performances. (a) The photographs of the fabricated sample and the far field test. (b) Comparison of the absorption rate for the test results and the simulation results. The far-field scattering pattern of the metal sample with and without an absorber tested at (c) 7 GHz, (d) 9 GHz, and (e) 11 GHz.
In our experiment, two broadband horn antennas are used to act as the transmitter and the receiver, respectively. Both antennas are connected to a vector analyzer (Anritsu MS4644A) to record the electric information, with the experimental setup shown in the Fig. 5(a). The horn antenna can emit a plane wave within our working frequency interval of 5 GHz to 12 GHz. Additionally, the irradiation direction of the incident plane wave is set to 88.5° in relation to the horizontal plane of the metal. The scattering signal can be captured by our automatically controlled rotation platform system with a step of 1°. Figures 5(c)–(e) plots the far-field scattering diagrams at three representative frequencies (7 GHz, 9 GHz, and 11 GHz) with and without surface wave absorbers. This indicates that compared with the only-metal structure, the proposed meta-absorber can decrease at least 10 dB in the direction of the incident wave. Moreover, we perform the FDTD simulation of the far-field patterns at different frequencies, which agrees well with the measured cases. To directly describe the absorption of our meta-absorber, we define the absorption efficiency as the reduction of the RCS in the incident direction. Figure 5(b) shows the absorption efficiency with the step of 0.1 GHz. It should be noted that in the range of 5.8–11.2 GHz, our device can have a high absorption (above 90%), and the measured results have good agreement with the simulated results.
4. Conclusion
In summary, we propose a ultra-thin, broadband and high-efficiency surface wave absorber based on the theories of wave vector matching and impedance matching. With the three-step wave vector tuning method described in this paper, the wave vector matching between the meta-absorber and the surface wave can be realized to ensure high efficiency for the surface wave energy entering the absorber. Additionally, the maximum absorption rate can be achieved by properly choosing the square resistance of ITO to satisfy the impedance matching condition. The simulated and experimental results indicate that the absorber can effectively absorb the surface wave in the range of 5.8–11.2 GHz with an absorption rate better than 90%. Furthermore, our device only has a thickness of 0.028$\lambda $, which can conform to various shapes of metal electronic devices. In addition to verifying the feasibility of the surface wave absorption mechanism, our work also helps to solve the issues of absorption at large incident angles, and it can be used to find applications in large antenna array design and other military stealth systems.
Funding
Postdoctoral Innovation Talents Support Program of China under Grant No. BX20190293 (20190293); Key Projects of Aviation Foundation (201918037002); National Natural Science Foundation of China (61701572, 61871394, 61901512).
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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