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Abstract
Metasurfaces, usually composed of 2D arrays of sub-wavelength metallic patterns (also called meta-atoms), have provided unprecedented freedoms for manipulating electromagnetic (EM) waves. In practice, meta-atoms are usually patterned on a certain substrate, so the EM properties of substrates directly affect the performances of metasurfaces. Therefore, it is desirable that the substrates can also be engineered with a high degree of freedom (DOF) so as to augment the functions of the metasurfaces. With this in mind, in this paper, we propose a method of designing functional metasurfaces by engineering the EM properties of substrates. By embedding frequency selective surface (FSS) within dielectric substrates, the electrical thickness of the substrates can be tailored according to the specific operating frequencies. In this way, functions of the metasurfaces can be augmented, either by better performances or by additional functions. As an example, we designed a multi-functional metasurface and applied it to a low-RCS reflector antenna. A circular patch was inserted into the dielectric substrate beneath the meta-atom. Due to the band-stop property of the metallic patch, two polarization conversion (PC) bands, together with a polarization-keeping band in between them, were created. Using this meta-atom, the metasurface is further designed, which can simultaneously achieve in-band focusing and out-of-band PC. A prototype was fabricated and measured. Both the simulated and measured results verified the good performance. Empowered by the metasurface, the reflector antenna achieved high radiation gain in band and significant RCS reduction out of band. This work provides a facile method of designing multi-functional metasurfaces and can be readily extended to terahertz, optical and other frequency regimes.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As one of the most important member of the artificial materials family, electromagnetic metamaterial has undergone an unprecedented development since its birth [1–4]. Unlike traditional materials, which consist of molecules or atoms, the metamaterial is composed of sub-wavelength scaled meta-atom. Thus, the metamaterial's property can be freely engineered by designing the meta-atom and hardly or even cannot be obtained in nature material [5–9]. As a result, metamaterials have shown unparalleled advantages in manipulating electromagnetic waves. Metasurface, as a two-dimension metamaterial, is the extension and development of metamaterial. One of the milestones in metasurafce study is the work done by Nanfang Yu et al. in 2011 [10]. They put forward the generalized laws of reflection and refraction. Based on the theory, the door is open for metasurface manipulation phase, polarization state, and scattering of electromagnetic wave.
However, in recent years, single functional metasurface has been challenging to meet the electromagnetic materials’ development needs. Therefore, it is imperative to study multifunctional metasurface. So far, the multifunction is mainly reflected in the function changes with the polarization state of frequency. In 2018, Boyu Sima et al. proposed the concept of frequency-selective coding of meta-mirrors and fabricated a metasurface to combine the diffusion like scattering and specular reflection together in a frequency-selective manner [11]. Yongqiang Pang et al. proposed a novel metasurface with a transmission window within the wide RCS reduction band via combining the FSS and anisotropic structure [12]. Wenlong Guo et al. proposed and designed a multi-functional meta-device to realize isotropic focusing and anisotropic beam deflection in the X and Ku band, respectively [13]. Tong Cai et al. design a helicity-dependent Pancharatnam-Berry(PB) phase bi-functional metasurface, which realizes different functions with different polarization waves [14]. The dual-band RCS reduction band metasurface is designed by loading resistor or phase cancellation [15,16]. In addition to understanding the advantages of the multifunctional metasurface, we should also see some challenges ahead on the road of the development [17–20]. For instance: how to extend the different function bandwidth; how to avoid the crosstalk between the different bands; how to adjust the phase of different polarization wave or frequency band independently; how to extend the function at a low frequency while ensuring the function at high-frequency band [21–23].
In this paper, we focus the metasurface design on the longitudinal thickness of the meta-atom rather than the flat pattern and design multi-functional (in-band focusing and out-of-band RCS reduction) metasurfaces via engineering the substrates. We analyzed the function acquirement and proposed the excellent PC dispersion(in-band co-polarized reflection and out-of-band cross-polarized reflection) to design the functional metasurface. For this, the circular patch, a typical band-stop frequency selective surface(FSS), is inserted into the dielectric substrate beneath the PC meta-atom. The idea comes about mainly because the performance of the meta-atom depends heavily on its effective thickness. Under the circular patch's band-stop property, the efficient thicknesses of the dielectric substrate under the PC meta-atom can be engineered and are different at lower and higher frequencies. By such a design, the meta-atom realizes high-efficiency PC in the low and high-frequency bands, and its co-polarized reflection is lower than −25 dB. The frequency window between the two PC bands is left intentionally to manipulating co-polarized waves. Moreover, the cross-polarized reflection at the frequency window is lower than −30 dB. In this case, the different bands’ reflection phase can be engineered independently via manipulating the co- and cross-polarized wave. The proposed multi-functional metasurface can realize in-band focusing and out-of-band RCS reduction simultaneously based on such a design. Both simulation and experiment demonstrate the accuracy of the proposed design. One of its potential applications is to be employed as the reflector to form a reflector antenna. We design a patch antenna as the feed source of the metasurface. The simulated and measured results verify that the designed metasurface reflector antenna can not only ensure the radiation performance but also realize significant RCS reduction at the outer band.
2. Design
2.1 Design method and scheme
The means of phase regulation include PB phase, resonant phase and so on. In 2014, the researchers developed the PB phase concept and studied its relationship to the angle of rotation meta-atom. When the meta-atom is rotated by α around its center, the phase difference will be 2α [24].
To further analyze the characteristic of PB phase, the dipole model is employed to decipher [25]. Consider the electric dipole momentum induced by a beam of electromagnetic waves normally incident on the dipole. And the electric dipole momentum can be expressed as [24,25]:
The resonance phase describes the discontinuity produced by the emitted electromagnetic wave when the metamaterial interacts with the electromagnetic wave. It can be explained and analyzed by the spring-oscillator model [26]. The oscillator is subjected to periodic external force F. The kinetic equation is [27]:
where the ω is the resonant frequency of the oscillator, γ is the spring damping, $F = f\cos (\varpi t)$. We can obtain the oscillator amplitude c as follows [28]:The Phase change of amplitude $\varphi \textrm{ = }{\tan ^{ - 1}}\left( {\frac{{\varpi \gamma }}{{\varpi_0^2 - {\varpi^2}}}} \right)$, by regulating the ω 0, the maximum phase change of 180° can be obtained. That is to say, the resonance frequency of the meta-atom can be changed by changing the geometric size, and then the resonance phase can be obtained and the resonant phase of a single-cell system can only cover 180°. In the metasurface design, phase coverage of 360° is usually achieved by combining PB phases or using complex structural designs with multiphase coupling.
In this paper, aiming at the requirement of low RCS performance of reflector antenna, a multifunction metasurface with out-of-band scattering and in-band focusing is proposed. This metasurface implementation's key lies in the independent design of the reflection phase and amplitude in different frequency bands. According to the above theoretical analysis of phase adjustment, to achieve such multifunction, the meta-atom of metasurface should have the polarization conversion characteristics as shown in Fig. 1(a).
Fig. 1. (a) Schematic of the ideal co- and cross- polarized reflection of the metasurface. (b) The schematic of the proposed metasurface with multi-function.
Specifically, there are two cross-polarization reflection bands in the low and high frequency band, and in the frequency window between them, there is a co-polarization band intentionally left. Then the PB phase and the resonant phase are employed to manipulate the co- and cross-polarized wave. When rotating the meta-atom, there will be a phase difference in the out-of-bands, and the in-band will be no phase difference. Moreover, when changes the meta-atom parameters, the phase difference can be introduced in the in-band. Under such circumstances, the reflection phase of different bands can be independently adjusted to achieve a multi-functional metasurface shown in Fig. 1(b).
2.2 Meta-atom design and analysis
In our previous work, the biarc structure has great polarization conversion performance [27]. So, it is employed to act as the PC meta-atom in this paper. As illustrated in Fig. 2(a), the metal pattern is etched on the FR4 (ɛr=4.3, the loss tangent of 0.025), and the patterned dielectric slab pasted on polymethacrylimide (PMI) foams with ɛr=1.1. To verify its polarization conversion, the reflection of the meta-atom under linear incident electromagnetic wave is simulated by CST Microwave Studio. The polarization conversion performance is closely related to the meta-atom thickness, that is to say, even for the same meta-atom, different thickness will correspond to different conversion efficiency and band. Figure 2(b) shows the variation of the meta-atom reflection with the foam thickness d. When d = 5 mm, the meta-atom has a great PC performance at high frequencies (9–13.5 GHz) and then increases d to 9 mm. At this point, the PC efficiency of high frequencies is significantly reduced. When d=13 mm, it can be seen that the PC efficiency improves at low frequencies (3–6 GHz).
We can see that with the d increases, the operation band shift to low frequency. By regulation d, an efficient cross-polarized reflection band can be achieved at low or high frequencies. Inspired by the influence of the dielectric substrate thickness on operation frequency band, the PC characteristic proposed in Fig. 1(a) can be obtained via regulating the thickness. And how can we realize untrammeled regulation? The FSS gives an alternative.
The FSS structure can realize pass band in low frequency while stop band in high frequency. From an intuitive perspective, the efficient thickness can be manipulated if the FSS structure is employed. Based on such an idea, a circular patch is inserted into the PMI foam beneath the PC meta-atom, and the meta-atom is designed and shown in Fig. 3(a) and (c) is the perspective and top view of the meta-atom. The top layer is a biarc structure, while the bottom layer is the circular patch structure, a typical FSS structure. They are etched on the F4B (ɛ r=2.65, the loss tangent of 0.001). The patterned slabs are pasted on polymethacrylimide (PMI) foams with ɛ r=1.1. Other geometrical parameters are: a=18.0 mm, w 1=0.2 mm, w 2=1.0 mm, d 1=1.0 mm, df 1=5.5 mm, d 2=0.3 mm, df 2=5.0 mm, α=66.0°, r=7.0 mm. The reflection (ryx, rxx, rxy and ryy) is shown in Fig. 3(b), in which ryx (rxx) represents the cross- (co-) polarization reflectivity under x polarized wave while rxy(ryy) is the cross- (co-) polarization reflectivity under y polarized waves. Encouragingly, we can see the design can realize high efficiency PC in two bands. One band is 2.7–5.8 GHz, the other is 9.2–14.5 GHz. The co-polarized reflection is even lower than −20 dB. Besides, between the two cross-polarization reflection frequency bands, there is a co-polarization reflection window left intentionally. In the co-polarization band, the cross-polarization reflection is even lower than −20 dB, too.
Fig. 3. (a) The perspective view of the meta-atom. (b) The co- and cross- polarized reflection of the meta-atom. (c) The diagram of the meta-atom.
For the sake of description, the three frequency bands (the low frequency PC band, the middle band and high frequency PC band) are named as I, II and III, respectively. To better understand the formation of the two cross-polarized reflection bands and the intermediate co-polarized reflection band. We choose 4.3 GHz and 11.6 GHz to represent the band I and III, respectively. The power flow at the 4.3 GHz and 11.6 GHz are calculated and shown in Fig. 4. The power flow is clearly that the EMW in 4.3 GHz is reflected by the bottom metal backboard. And that means the effective thicknesses of dielectric substrate is the whole thickness. While at 11.6 GHz, the EMW is reflected by the FSS structure and can′t reach the metal backboard. Fis. 4(c) shows the S parameters of the single FSS. It can be seen that it acts as transmitted and reflected performance at low and high frequencies respectively, which is mutually verified with the energy flow diagram.
Fig. 4. The power flow under x-polarized incident wave. (a) 4.3 GHz. (b) 11.6 GHz. (c) The S parameter of the FSS.
So, as for the high frequency, the efficient thickness has been reduced by the FSS structure. It is demonstrated that the efficient thickness of the meta-atom can be adjusted by employing an FSS structure. Furthermore, that is the reason that the two PC bands emerge.
3. Function design
The meta-atom designed in the above section is the basis for multifunctional metasurface. We expect to regulate scattering to reduce RCS at band I and III, and get a focusing performance in band II at the same time. According to the P-B phase theory analyzing in part 2.1, if we rotate the biarc structure with 90°. There will be a 180° phase difference for cross-polarized wave, while for the co-polarized wave, there will be no phase difference. Figure 5(a) and (b) shows the phase and reflection change of the reflected wave before and after rotating meta-atom. It is demonstrated that the 180° phase difference can be obtained in the two bands, while the reflection amplitude will be invariant. As for the co-polarization reflection band, the reflection phase can be regulated by changing the radius of circular patch. Figure 5(c) and (d) show the reflection phase with different radius. We can see that the phase difference is generated by changing the circular patch's radius in 6.5GHz-8.0 GHz. Although the cross-polarized wave also has a phase difference, its amplitude is very low in band II. In particular, the two ways of regulation reflection phase in different frequency bands don't conflict with each other. Thus, we can see that the meta-atom can perfectly meet the design requirements.
Fig. 5. (a) and (b) The phase and reflection amplitude of the cross- and co- polarized reflected wave while rotating the meta-atom, respectively. (c) and (d) The phase and reflection amplitude of the co- and cross- polarized reflected while change the radius of the circular patch, respectively.
In the paraboloid case, the reflected wave can be focused because all waves travel the same distance to the focus. However, for the planar metasurface, the propagation path length of reflected waves will be different. So, to achieve focusing, the metasurface should compensate the phase difference resulting from the different paths. To this end, each element's reflected phase that makes up the metasurface can be freely designed. The required phase contribution of each element can be calculated from the formula:
The metasurface consists of m×n meta-atoms. P is the meta-atom periodicity. F represents the focus length. φ(0,0) is the reflected phase of the center element. Figure 6 is the calculated phase profile required for focus. The whole metasurface consists of 13×13 meta-atoms. We can get the required phase by adjusting the diagram of circular patches and arrange them according to the phase profile, as shown in Fig. 6(a).
Then, we consider arranging the top layer meta-atom to manipulate the scattering of the metasurface. In the published literature, researchers have done much meaningful work on reducing RCS. One of the most significant researches is to propose the checkboard structure. Its operation mechanism is based on the cancellation effect of both contributions. If the scattered field of the two meta-atoms has the same amplitude and the 180° phase difference, the total scattering field will be cancelled in the normal direction and redirected towards the four principal quadrants. Thus, if the upper and lower meta-atoms can adjust the phase independently, the biarc structure and the circular patch are manipulated, according to the required phase of their phase profile shown in Fig. 6. To further verify the performance of focus and scattering design. The electric field component and 3-D far-field scattering pattern are numerically simulated and shown in Fig. 7, respectively. It can be seen that at 4.5 and 12.5 GHz, the beam is divided into four beams, which deviate from the normal direction, resulting in a lower RCS in the normal direction. The Fig. 7(c) depicts the RCS compared with the metal with same area, which indicated the RCS reduction performance in the low and high frequency bands.
Fig. 7. The electric field component at 4.5 GHz, 7.3 GHz and 12.5 GHz, respectively. (b) The far Field patern at 4.5 GHz, 7.3 GHz and 12.5 GHz, respectively. (c) The RCS comparison of the metasurface and metal with the same size.
Then, to verify the design, we fabricate a prototype shown in Fig. 8(a) with an area of 234 mm×234 mm. For the convenience of testing, the simulated and measured specular reflection are depicted in Fig. 8(b). We can see that the measured results basically verify the correctness of the design. In band I (2.7–5.8 GHz) and III (8.1–14.2GHZ), the specular reflection is lower than −10 dB, consistent with the RCS simulation. In band II, the metasurface can focus the electric field, which causes the specular reflection is lower than 0 dB. It should also be noted that there is some discrepancy between the measured and simulated result. Through further simulation analysis, we think that it is resulting from the spacing between layers. Regardless of the discrepancy, the proposed metasurface has the potential to be applied to the reflector antenna system.
Fig. 8. (a) The prototype and experiment picture. (b) The simulated and measured specular reflection of the metasurface.
4. Application value
One of the applications of the proposed multi-functional metasurface is applied to the planar reflector antenna. It comes from the traditional parabolic reflector antenna. If a feed source is put on the focus point, the spherical wave from the feed will impinge the metasurface and is reflected as a plane wave. The designed multifunctional metasurface not only guarantees the radiation performance, but also introduces out of band low RCS characteristics.
For this, we first design and fabricate a patch antenna as the feed source. Its central frequency f = 7.3 GHz. The metal patch is etched on the F4B (ɛ r=2.65, the loss tangent of 0.01). The geometrical parameters are: p=25.0 mm, L=11.4 mm, d=2.0 mm. The radiation performance shown in Fig. 9(c) and (d) demonstrated that the patch antenna is competent as a feed source. Then, the patch antenna is placed at the focal point of the planar metasurface. Figure 10(a) depicted the measured picture. The feed source is located in the metasurface focus point, and they all both on the turntable. The receiving antenna is located in a far-field position and remains inactive to receive electromagnetic waves reflected from the metasurface. The proposed planar metasurface reflector antenna can not only guarantee the gain, but also realize great RCS reduction performance out of the operation band. To further verify the reflector antenna design.
Fig. 9. (a) The illustration of the feed source. (b) The S11 and efficiency of the patch antenna. The radiation pattern (c) 7.3 and (d)7.5 GHz.
Fig. 10. (a) the measured picture. (b) and (c) The simulated and measured radiation pattern at 7.3 GHz and 7.5 GHz, respectively
Figure 10(b) and (c) show the simulated and measured radiation pattern at 7.3 GHz and 7.5 GHz. We can see that the simulation results are in good agreement with the measured results. The measured gain is slightly lower than the simulated, and the side lobe is slightly higher. The case mainly due to the focus phase deviation. Moreover, the cross-polarization level is lower than −10 dB.
5. Conclusion
In summary, we propose and verify the method of designing multi-functional metasurface by engineering the substrate thickness of meta-atoms. To engineer the thickness, a FSS is inserted into the dielectric substrate under beneath the PC meta-atom. Via the band-stop characteristic of the FSS, the efficient thickness of the PC meta-atom can vary with frequency, which leads two PC bands with very high efficiency. In between the two PC bands, a band without PC is left intentionally for manipulating co-polarized waves. Under such conditions, we can manipulate both co- and cross-polarized waves. Then, the reflected phase of co- and cross-polarized waves can be regulated via PB phase and resonant phase so that the metausrface realizes in-band focusing and out-of-band RCS reduction simultaneously. Both the full-wave simulation and measure on the fabricated prototype verify the performance of the multifunctional metasurface. For such a metasurface combining the scattering and focus, we believe that it not only provides a new design idea for the multifunctional metasurface, but also has great application value in many aspects, such as the application of the reflector antenna to achieve radiation gain, with significant RCS reduction out of band. To prove its potential application value, we design and fabricate a planar reflector antenna with the multifunctional metasurface. Both the simulated and measured results demonstrate that the designed planar reflector antenna not only has satisfactory radiation performance, but also realize the efficient RCS reduction. More importantly, the method engineering the substrates thickness of the metasurface gives high degree of freedom to design the multi-functional metasurface.
Funding
National Key Research and Development Program of China (SQ2017YFA0700201); National Natural Science Foundation of China (61671466, 61671467, 61971435).
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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