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Abstract
In this work, we propose a method of suppressing the side-lobe level for transmitted waves based on foldable spoof surface plasmon polariton (SSPP). To this end, an SSPP structure is designed and folded with different angles to manipulate the amplitudes of co-polarization transmission coefficients, while the phases remain unchanged. In order to obtain the corresponding relationship between the transmission amplitudes and the folded angles, a nonlinear fitting was performed to get the mapping. After this, SSPP structures are arrayed according to the corresponding amplitudes of the discrete Taylor-distribution, so as to suppress the side-lobe level. To verify this idea, a transmissive metamaterial with wideband side-lobe level suppression (SLLS) was designed, fabricated and measured. The results demonstrated that the metamaterial has a good SLLS performance for transmitted waves, with approximately -20 dB SLL in a wide frequency region. This work provides an effective alternative to achieving SLLS and may find applications in antennas, radomes and stealth techniques, etc.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past few decades, the emergence of metamaterials has made it possible to manipulate electromagnetic (EM) waves flexibly [1–4]. Due to its unique and excellent physical properties, such as negative index of refraction, near-zero index of refraction, and extremely strong chirality, metamaterials have attracted more attention [5,6].
In practice, the arbitrary manipulation of EM wave depends on not only the spatial phase, polarization state, but also amplitude. However, most of these studies focused on the transmission phase and polarization state [7–10]. Some studies on the amplitude manipulation have been proposed, but very few of them on amplitude being manipulated independently. Thus, the modulation of amplitude independently is difficult to achieve while keeping the phase unchanged [11]. It is believed that some novel devices may be designed if the amplitude could be manipulated at will, such as SLLS, beam forming, radomes and so on [12–15]. High SLL is a problem to be solved in the radar cross section (RCS) reduction, signal transmission and radar acquisition [16,17]. An antenna array with high directivity and low SLL that can enhance the reliability and validity of communication system is also greatly desired [18]. Reference [19] introduced a novel method of reducing side-lobe level of surface mounted printed leaky-wave antenna. It is worth mentioning that A wide-angle scanning circularly polarized leaky-wave antenna with suppressed side-lobe levels is proposed in Ref. [20], which can be a good candidate for future radar and wireless communication systems.
Initially, SPP was primarily investigated in the field of optics, resulting in a discipline called plasmas. In fact, the excellent sub-wavelength properties of SPP have attracted scientists in other fields such as microwaves, which has led to the study of SPP-like modes excited on structured metallic surfaces or metamaterials at microwave frequencies [21–23]. However, surface waves exhibit very weak confinement at terahertz and EM fields mostly reside in dielectric region because the metal can be treated as a perfect electric conductor (PEC), into which the EM fields cannot penetrate [24]. But it can be supported by the plasmonic metamaterials named as spoof surface plasmon polaritons (SSPP), which are usually achieved at terahertz and microwave frequencies by decorating periodic arrays of sub-wavelength slots, holes or blocks on the metal surface [25]. Owing to its distinctive properties of strong field confinement and enhancement, SSPP metamaterials promise useful applications in miniaturized devices, low-cross-talk waveguides, miniaturized sensors, and so on [26–28].
Therefore, the strong field confinement and enhancement properties of SSPP can be utilized to achieve independent modulation of amplitude. Here, a metamaterial based on the foldable SSPP structure with adjustable amplitude but unchanged phase is proposed to suppress SLL. In the case of keeping the phase constant, it is very difficult to obtain the adjustable amplitude through the energy loss. For a given SSPP structure, folding a certain angle along its longitudinal symmetry axis can realize the adjustment of transmission amplitude while keeping the transmission phase unchanged, which realized the independent adjustment of the amplitude and then greatly improved design freedom. To this end, an SSPP structure is designed and folded into different angles to manipulate the amplitudes of the co-polarization transmission coefficients, while the phases remain unchanged. Then, we simulated the transmission amplitude from to 0° to 150° and made a nonlinear fitting. In this way, we can easily obtain the transmission amplitude we want. As an example, a transmission metamaterial composed of 16×12 units was designed and fabricated to suppress side-lobes, according to the amplitude arrangement of discrete Taylor-distribution. The results demonstrated that the metamaterial has a good performance on SLLS of transmitted beams, with approximately −20dB SLL in a wide frequency region from 20GHz to 28GHz.
2. Theory and design
2.1 Theoretical analysis
Generally, there are two existing technologies that can suppress SLL. One is the conventional excitation amplitude tapering (AT) and the other the unusual element space density tapering (DT). The AT technique, such as triangular, cosine, squared cosine and raised-cosine amplitude distributions, as well as the Dolph-Chebyshev or Taylor current coefficients, provides effective means for SLLS. The antenna designed with DT technology is a uniformly excited non-uniformly spaced array,and the unit position is thinner from the center unit (odd array) or the center double unit (even array) [29–31].
For the antenna, the Fourier transform relation between the far-field lobe pattern and the intensity of the surface electric field can be expressed as:
Analog the antenna achieves side-lobe suppression through arraying the field amplitude emitted by the antenna according to the Taylor-distribution. In this paper, the effect of side-lobe suppression is achieved by controlling the Taylor distribution of the transmission electric field amplitude of the plane wave incident to the metamaterials.
As is well known, when a beam of EM wave incidents onto a metamaterial, the far-field scattering pattern is mainly determined by the spatial phase and amplitude distributions of the metamaterials. If the spatial phase distribution is uniform, the far-field scattering pattern will only depend on the amplitude spatial distribution. As shown in Fig. 1, the far-field scattering pattern can be derived from the amplitude spatial distribution by Fourier transform. On the contrary, the spatial amplitude distribution can be derived from the far-field scattering pattern by inverse Fourier transform. Therefore, the SLLS for the far-field scattering can be achieved by the modulation of the amplitude spatial distribution.
Fig. 1. The schematic diagram of the metamaterial with SLLS: Fourier transform and inverse Fourier transform between far-field scattering patterns and amplitude distributions.
2.2 Design of the folded SSPP structures
The proposed SSPP structures is designed to manipulate the transmission amplitude with freedom by changing folded angle. As shown in Fig. 2, the structure is composed of two symmetrical parts, which can be folded into different angles along the central axis. In order to achieve high transmission efficiency, the matching characteristic of the wave-vector in the air-to-dielectric and dielectric-to-air transformations need to be considered. Therefore, the height of the corrugated metallic strips needs to be modulated gradually according to the spatial distribution of SSPPs propagation constant k(z) and the tapered design is used at both ends of the structure. The metallic structure is fabricated on a 0.5mm-thick FR-4 (εr = 4.3, tanδ = 0.025) dielectric substrates. The length of the planar plasmonic structure along the z-direction is l = 15.8 mm, and the folded angle of the planar plasmonic structure along the central axis is α. The geometrical parameters are designed to be: h = 2.9 mm, p = 0.2 mm, q = 0.4 mm, m = 0.125, n = 0.125, d = 0.5, and r = 0.32 mm.
Fig. 2. Design of the proposed SSPP structures. (a) The structure diagram the SSPP structures. (b) The schematic diagram of the folded SSPP structures.
In fact, with the increase of the folding angle, the larger surface area of the SSPP structures is in the same direction as the polarization of the electric field, leading to an increase in the coupling efficiency, which will cause the electromagnetic wave to be more absorbed by the medium and the transmission amplitude will decrease. Then we use the electric field distribution and the excited surface current to verify the adjustable amplitude but unchanged phase of the SSPP structures from a microscopic and quantitative perspective.
CST Microwave Studio software was used for numerical simulation under the linearly polarized wave normal incidence from + z direction. In the simulation, the boundary conditions of z-axis are set as “open add space”, and the boundary conditions of x- and y-axis are set as “unit cell”, where the periodic dimension is N = 5.2mm. Figure 3 shows the electric field and the excited surface current at different angles. It can be observed that EM waves can be well transmitted through the designed SSPP structure with different folded angles. When the electric field of the incident wave is along the + y-direction, the direction of the excited current is shown as the blue arrow in Fig. 3(d-f). As the folding angle α increases, the electric field component of the excited current I2 along the − y-direction will increase, which is opposite to the direction of the incident wave electric field, resulting in a decrease of the co-polarized transmission amplitude. Figure 4 shows the co-polarized transmission phase φyy and co-polarized transmission amplitude Tyy at six different folded angles. It can be seen that the simulated phase differences under the six folded angles are kept within ±10° over a wide frequency range, from 20GHz to 28GHz. Additionally, the corresponding amplitude are remained mostly unchanged, except for a small fluctuation.
Fig. 3. Simulated Ey-component of electric field distributions and surface current under linearly polarized waves normal incidence. (a-c) Ey-component of electric field distributions at 60°, 90°, 120°. (d-f) Surface current at 60°, 90°, 120°.
Fig. 4. (a) Co-polarized transmission phase φyy of the proposed SSPP structures at six different folded angles. (b) Co-polarized transmission amplitude Tyy at six different folded angles.
2.3 Arrangement of the folded SSPP structures
To obtain co-polarized transmission amplitude of the SSPP structures under different folding angles from 0° to 150°, CST Microwave Studio software was used for numerical simulation under the linearly polarized wave normal incidence from + z direction in the frequency bands of 20-28 GHz. we perform nonlinear fitting of the normalized average amplitude Tyy and different angles through MATLAB software as shown in Fig. 5(a). Then we can obtain the corresponding relationship equation between amplitude and angle:
Fig. 5. (a) Co-polarized transmission amplitude and nonlinear fitting of the designed SSPP structures. (b) The discrete Taylor amplitude distributions.
As shown in Fig. 5(b), the eight amplitudes corresponding to the sixteen discrete points of the Taylor distribution are selected as: 0.17, 0.25, 0.38, 0.54, 0.70, 0.83, 0.94, 1. According to Eq. (5), the folded angles corresponding to the eight amplitudes are obtained as: 131.2°, 121.0°, 106.5°, 89.4°, 70.2°, 50.5°, 28.0°, 0°. We take the 4 × 4 consistent SSPP structures as the subunit array with the periodic dimension N = 5.2mm. In this way, the amplitude spatial distribution of the co-polarized transmission coefficients is designed according to the Taylor distribution in the x-direction, and the consisted subunit array are same in the y-direction. As shown in Fig. 1, the transmissive metamaterial with SLLS was designed according to the corresponding transmission amplitude, which is composed of a 16×12 subunit array.
3. Simulation
In order to verify the SLLS for the transmitted beams of the designed metamaterial, CST microwave Studio software was used for simulating the forward-scattering patterns under y-polarized wave normal incidence from + z direction. In the simulation, y-polarized plane waves are used as the source, and the boundary conditions in x-, y- and z- directions are set as “open add space”.
In Fig. 6, The SLL of forward-scattering patterns in the xoz- planes at 20 GHz, 24 GHz and 28 GHz are given. The simulated results convincingly demonstrate that the SLL of forward-scattering in the xoz-plane is significantly decreased due to the Taylor distributed co-polarization transmission of the metamaterial in the x-direction. It can be observed that, for y-polarized plane waves normal incidence, the SLL of the forward-scattering in the xoz-plane is highly reduced over a wide frequency range. Moreover, the SLL of the forward-scattering is lowered by − 20dB from 20GHz to 28GHz and almost reduces − 25dB at several frequency points.
Fig. 6. The simulated forward-scattering patterns in the xoz-planes under y-polarized plane waves incidence at 20 GHz, 24 GHz and 28 GHz.
4. Experiment
To further verify SLLS for the transmitted beams of the designed metamaterial, we fabricated a prototype with a size of 332.8 mm × 249.6 mm, shown in Fig. 7(a). The plasmonic structures are fabricated using PCB photolithography. The commercial FR-4 dielectric substrates are used as dielectric layers, while 17-ply copper films are used as metal components. The final prototype was obtained by folding the SSPP structure into different angles. As shown in Fig. 7(b), the experimental measurements of the prototype were carried out in a microwave anechoic chamber. The far-field experimental rotating system was used to measure the forward-scattering patterns, which consisted of an experimental platform, a vector network analyzer (VNA), a transmitting horn antenna, and a receiving horn antenna. The fabricated prototype is placed between the transmitting horn antenna and the receiving horn antenna. Here, the horn antenna is placed at a distance of 400 mm from the prototype to ensure quasi-plane incidence.
Fig. 7. (a) The fabricated prototype consisted of a 16×12 subunit array. (b) The far-field measurement system.
The Measured forward-scattering patterns are shown in Fig. 8. The solid blue line and the red dash line give the SLL of the forward-scattering pattern in the xoz- and yoz-planes, respectively. It is clearly indicated that the SLL of forward-scattering in the xoz-plane is significantly decreased compared with that in the yoz-plane due to the Taylor-distributed Co-polarized transmission of the metamaterial in the x-direction and the SLL of the forward-scattering is lowered by more than −20dB. It can be observed that the measured SLLS is slightly different from the simulated results. This phenomenon is mainly due to the fact that the origin of incident wave is not plane wave in the strict sense. In addition, the uncertainty of the environment may lead to the difference between the measured results and the simulated results.
Fig. 8. The Measured forward-scattering patterns in xoz- and yoz-planes under y-polarized wave normal incidence at 20 GHz, 24 GHz and 28 GHz.
5. Conclusion
In summary, we propose a method of achieving SLLS for transmitted waves based on foldable SSPP. The SSPP structure is designed and folded into different angles to obtain adjustable amplitude but unchanged phase. Then, a nonlinear fitting was performed on the mapping between the transmission amplitudes and the folded angles. In this way, we can easily obtain the transmission amplitude we want. As an example, a transmission metamaterial composed of 16×12 units was designed and fabricated to suppress side-lobes, according to the amplitude arrangement of discrete Taylor-distribution. The SLLS of the transmission metamaterial is demonstrated through simulation and far-field measurements. Different from general side-lobe level suppression metamaterials, we can design the desired forward-scattering patterns according to the corresponding relationship between the amplitude and the folded angle, without the need to redesign the metamaterial unit cell. In conclusion, this work provides another strategy of achieving SLLS and may find applications in antennas, radomes and stealth techniques, etc.
Funding
National Key Research and Development Program of China (SQ2017YFA0700201); National Natural Science Foundation of China (61601507, 61671466, 61671467, 61801509, 61901508, 61971435, 61971437).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
References
1. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef]
2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]
3. J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012). [CrossRef]
4. X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. 110(1), 40–45 (2013). [CrossRef]
5. F. Miyamaru, M. Kamijyo, N. Hanaoka, and M. W. Takeda, “Controlling extraordinary transmission characteristics of metal hole arrays with spoof surface plasmons,” Appl. Phys. Lett. 100(8), 081112 (2012). [CrossRef]
6. X. Wan, J. Y. Yin, H. C. Zhang, and T. J. Cui, “Dynamic excitation of spoof surface plasmon polaritons,” Appl. Phys. Lett. 105(8), 083502 (2014). [CrossRef]
7. X. Wan, S. L. Jia, T. J. Cui, and Y. J. Zhao, “Independent modulations of the transmission amplitudes and phases by using Huygens metasurfaces,” Sci. Rep. 6(1), 25639 (2016). [CrossRef]
8. J. Zhao, Y. Zhang, X. Yu, Y. Li, K. Fang, L. He, and H. Chen, “Ku-band low side-lobe level fixed-frequency electrically scanning leaky-wave antenna,” Microw. Opt. Technol. Lett. 58(10), 2512–2516 (2016). [CrossRef]
9. A. B. Varuna, S. Ghosh, and K. V. Srivastava, “A miniaturized-element bandpass frequency selective surface using meander line geometry,” Microw. Opt. Technol. Lett. 59(10), 2484–2489 (2017). [CrossRef]
10. R. Zhu, T. Qiu, J. Wang, S. Sui, C. Hao, T. Liu, Y. Li, M. Feng, A. Zhang, C.-W. Qiu, and S. Qu, “Phase-to-pattern inverse design paradigm for fast realization of functional metasurfaces via transfer learning,” Nat. Commun. 12(1), 2974 (2021). [CrossRef]
11. L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband Metasurfaces with Simultaneous Control of Phase and Amplitude,” Adv. Mater. 26(29), 5031–5036 (2014). [CrossRef]
12. K. I. Konov and K. N. Klimov, “Suppression of the Side Lobe Level in the Model Problem on Radiation of an Antenna Array with Given Partial Diagrams,” J. Commun. Technol. Electron. 66(6), 694–706 (2021). [CrossRef]
13. S. Zaiter, N. Raveu, and R. Oussaid, “A new inhomogeneous partially reflecting surface for Fabry-Perot antenna to reduce side lobe level,” Int. J. RF Microw. Comput. Eng. 30(7), e22229 (2020). [CrossRef]
14. A. Sharma and S. Mathur, “A novel adaptive beamforming with reduced side lobe level using GSA,” COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 37(6), 2263–2278 (2018). [CrossRef]
15. N. Javanbakht, R. E. Amaya, J. Shaker, and B. Syrett, “Side-Lobe Level Reduction of Half-Mode Substrate Integrated Waveguide Leaky-Wave Antenna,” IEEE Trans. Antennas Propag. 69(6), 3572–3577 (2021). [CrossRef]
16. A. Das, D. Mandal, S. P. Ghoshal, and R. Kar, “A Heuristic Approach to Design Linear and Circular Antenna Array for Side Lobe Reduction,” Iran. J. Sci. Technol. Trans. Electr. Eng. 43(S1), 67–76 (2019). [CrossRef]
17. J. L. Pita, I. Aldaya, O. J. S. Santana, L. E. E. de araujo, P. Dainese, and L. H. Gabrielli, “Side-lobe level reduction in bio-inspired optical phased-array antennas,” Opt. Express 25(24), 30105–30114 (2017). [CrossRef]
18. H. Yang, T. Li, L. Xu, X. Cao, J. Gao, J. Tian, H. Yang, and D. Sun, “A New Strategy to Design Microstrip Antenna Array with Low Side-Lobe Level and High Gain,” IEEE Access 7, 152715–152721 (2019). [CrossRef]
19. N. Javanbakht, B. Syrett, R. E. Amaya, and J. Shaker, “Reducing Side-Lobe Level of Surface Mounted Printed Leaky-Wave Antenna,” European Conference on Antennas and Propagation. pp. 1–3 (2020).
20. H.-W. Yu, Y.-C. Jiao, and Z. Weng, “Spoof surface plasmon polariton-fed circularly polarized leaky-wave antenna with suppressed side-lobe levels,” Int. J. RF Microw. Comput. Eng. 30(3), e22080 (2020). [CrossRef]
21. X. Gao, J. H. Shi, H. F. Ma, W. X. Jiang, and T. J. Cui, “Dual-band spoof surface plasmon polaritons based on composite-periodic gratings,” J. Phys. D: Appl. Phys. 45(50), 505104 (2012). [CrossRef]
22. B. C. Pan, H. C. Zhang, and T. J. Cui, “Multilayer Transmissions of Spoof Surface Plasmon Polaritons for Multifunctional Applications,” Adv. Mater. Technol. 2(1), 1600159 (2017). [CrossRef]
23. B. Zheng, R. Zhu, L. Jing, Y. Yang, L. Shen, H. Wang, Z. Wang, X. Zhang, X. Liu, E. Li, and H. Chen, “3D Visible-Light Invisibility Cloak,” Adv. Sci. 5(6), 1800056 (2018). [CrossRef]
24. J. Y. Yin, J. Ren, H. C. Zhang, B. C. Pan, and T. J. Cui, “Broadband Frequency-Selective Spoof Surface Plasmon Polaritons on Ultrathin Metallic Structure,” Sci. Rep. 5(1), 8165 (2015). [CrossRef]
25. Y. Zhai, J. Wang, T. Liu, Y. Jia, R. Zhu, X. Fu, Y. Li, Y. Pang, and S. Qu, “Quasi-continuous linear phase-gradient metamaterial based on conformal spoof surface plasmon polaritons,” Opt. Express 29(6), 8666–8675 (2021). [CrossRef]
26. H. C. Zhang, T. J. Cui, Y. Luo, J. Zhang, J. Xu, P. H. He, and L. P. Zhang, “Active digital spoof plasmonics,” Natl. Sci. Rev. 7(2), 261–269 (2020). [CrossRef]
27. L. Zhang, H. Zhang, M. Tang, P. He, L. Niu, L. Liu, J. Lu, W. Tang, J. Mao, and T. Cui, “Integrated multi-scheme digital modulations of spoof surface plasmon polaritons,” Sci. China Inf. Sci. 63(10), 202302 (2020). [CrossRef]
28. Y. Han, Y. Li, H. Ma, J. Wang, D. Feng, S. Qu, and J. Zhang, “Multibeam Antennas Based on Spoof Surface Plasmon Polaritons Mode Coupling,” IEEE Trans. Antennas Propag. 65(3), 1187–1192 (2017). [CrossRef]
29. B. P. Kumar and G. R. Branner, “Design of unequally spaced arrays for performance improvement,” IEEE Trans. Antennas Propag. 47(3), 511–523 (1999). [CrossRef]
30. K. Tomiyasu, “Combined equal and unequal element spacings for low sidelobe pattern of a symmetrical array with equal-amplitude elements,” IEEE Trans. Antennas Propag. 39(2), 265–266 (1991). [CrossRef]
31. X. Zhang, K. M. Luk, W. Song, W. Zhao, and Y. Liu, “An Efficient Density Weighting Approach for Side-lobe Level Suppression of Linear Array Antennas,” PIERS Proc. pp. 1390–1393 (2008).
