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Abstract
In this paper, we propose the design of a metasurface that can achieve three functions in different frequency bands. The proposed metasurface is composed of two kinds of unit cells which are designed on the basis of the spatial k-dispersion engineering of spoof surface plasmon polaritons (SSPPs). By arranging these two kinds of unit cells in the chessboard configuration, the three functions of transmission, anomalous refraction and absorption can be integrated into one metasurface. High transmission and strong absorption can be achieved in 2.0-9.0 GHz and 12.6-20.0 GHz, respectively. Meanwhile, anomalous refraction can be achieved in 10-11.7 GHz due to forward scattering cancellation of two unit cells. To verify the design, a prototype was fabricated and measured. The measured results are consistent with the simulation ones. The metasurface can integrate multiple functions into one aperture and therefore has potential application values in multifunctional microwave devices such as shared-aperture antennas, etc.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Manipulation of electromagnetic waves has always been an important topic in many fields. In recent years, with the development of wireless communication technology, one kind of the emerging artificial materials, called as metamaterials, has drawn lots of attention from both scholars and engineers. Due to their tailorable permittivity and permeability, metamaterials have been widely used in microwave devices such as antennas, filters, randomes, etc. Metasurfaces are the two-dimensional version of metamaterials, and have the advantages of low-profile and light-weight. There are many studies on metasurfaces such as planar perfect lens [1–3], vortex beam generations [4–6], polarization conversion [7–10] and wave-front shaping [11–13]. Presently, most metasurfaces are designed to bear a single function. For example, absorption can be achieved using irregular metal or carbon fibers [14], anomalous refraction using coding metasurface [15–18], polarization conversion using partially reflecting surface (PRS) [19–21], absorption using electrical or magnetic coupling metasurfaces [22–24] or by resistance or active devices loaded metasurfaces [25,26]. In fact, the metasurfaces with a single function are unable to meet the needs of modern technology, and thus multifunctional metasurfaces are much desired [27–33]. Also, it is hard for the most metasurfaces to manipulate the reflected and transmitted waves at the same time. In [27], a multifunctional metasurface is designed to exhibit three basic functions, reflection, absorption and transmission, but its working bandwidth is much narrow and it has multi-layered configuration.
In this paper, a trifunctional metasurface based on spoof surface plasmon polaritons (SSPPs) is presented. It is known that the SSPPs have the properties of field confinement and deep sub-wavelength [34–38]. By designing the phase-frequency dispersion relation of the SSPPs, the reflection and transmission properties can be manipulated readily. The proposed metasurface consists of 8×8 blocks which consists of 8×8 SSPP units. The dispersion relation of the spoof SPPs can be tailored by simply changing the corrugation height, so the phase and amplitude of the transmission/reflection waves can be easily designed. Simulated and experimental results show that our metasurface has three functions of transmission, anomalous refraction and absorption. Our proposed metasurface shows a high-efficient manipulating capability for the reflection and transmission waves, and can be easily designed by tailoring the dispersion properties of the SSPPs.
2. Design of the unit cell
The 2D periodic corrugated metal structure is used to generate the SSPPs. The topology of the SSPP unit is shown in Fig. 1(a). The corrugation repeats periodically along the z-axis and the period is twice the width of the strip. The dispersion properties of the SSPPs can be regulated through changing the height of the unit. In this paper, to excite the even mode, y polarized waves are used to illuminate the SSPPs. As can be seen from Fig. 1(b), the dispersion curves with different h are depicted. The dispersion curves all have the same trend with a linear part at the beginning of the curves, a dispersion from the light line above the linear area, and a flat area eventually. Such trend makes the phase constant easy to be controlled. The linear part makes the SSPPs transparent to the free-space waves. The dispersion area shows different phase constant from the vacuum. The SSPPs in flat area has an infinite phase constant which makes the EM waves absorbed by the structure. By combining the strips with different lengths, a wide band absorption can be achieved.
Fig. 1. (a) Topology of the unit cells for exciting the SSPPs. The geometric parameters are: l = 7.5 mm, a = 0.15 mm, b = 0.2 mm. (b) Dispersion relation of the SSPPs.
Based on the analysis of the spatial k-dispersion relation, two kinds of SSPP unit cell are presented. The configurations of two units are depicted in Fig. 2(a). The metallic corrugated grooves are printed on a FR-4 substrate, which has the permittivity of 4.3 and loss tangent of 0.02. The thickness of the substrate is 0.4 mm. The period of both units in x and y direction is 9 mm. The height of both units is 23 mm. The units both have the part of the short gradient corrugated grooves. From the dispersion relation in Fig. 1(b), the longer corrugated groove has a dispersion at lower frequencies. By designing the number of it, a refraction can be obtained. Two kinds of units are simulated in CST Microwave Studio. The units are solved under Frequency Domain Solve and the boundary conditions are both unit cell for ± x and ± y direction. The y polarized electromagnetic waves transmits along z axis and the boundary of + z and -z directions are both open boundaries with a space of 50 mm. The floquet ports are added to both sides with the ports attached on the unit edge. The frequency range is set to 2 GHz to 20 GHz.
Fig. 2. (a) Topology of unit 1 (left) and unit 2 (right). (b) The S parameters of unit 1 and unit 2. (c) The transmission phase difference of two units.
The simulation results of these two units are also depicted in Fig. 2. The reflection and transmission coefficients are shown in Fig. 2(b) and the transmission phase difference of two units are shown in Fig. 2(c). It can be seen that the S11 and S21 are both under −10 dB in the frequency band of 12.6 GHz to 20 GHz. The S21 curve has a high value in 2-12 GHz. In addition, one can find from Fig. 2(c) that the transmission phase difference is about π around 10 GHz, which is needed for the anomalous refraction function.
The electric fields distributions in different frequencies of two units are shown in Fig. 3(a). Because the SSPPs has the properties of field confinement and deep sub-wavelength, the electric field is localized on the interface of the metal SSPP structure and the dielectric when the incident waves is in the dispersion band. As can be seen in the figure, there are no interaction between the electromagnetic waves and the SSPPs at 3 GHz. The electric field on the longer corrugated grooves at 10 GHz is stronger than it at 3 GHz, which indicates an interaction between SSPPs and the incident waves. The incident waves excite the SSPP mode and the SSPP mode transmit along the SSPP structure causing a phase difference compared to the unit that without longer corrugated grooves. At 15 GHz and 20 GHz, the electric fields are strong in the short gradient SSPP structure for both units due to the low-pass and high-resistance characteristics of the SSPPs. A broadband absorption is achieved by the gradient structure. The distributions of surface current at different frequencies are shown in Fig. 3(b). The surface currents of unit 1 and unit 2 are both weak at 3 GHz which indicates there is no SSPP mode exists at 3 GHz. At 10 GHz, the surface currents of both units are strong. The free-space waves excite the SSPP mode on both units then the SSPP mode propagates along the SSPP structure. At 15 GHz and 20 GHz, the frequencies is in the flat area of the dispersion relation. Thus the surface currents are absorbed by the gradient SSPP structure.
Fig. 3. (a) The electric fields distributions of two units at several frequencies. (b) The surface currents distributions of two units at several frequencies.
3. Metasurface design and simulation
The configuration of the proposed metasurface is shown in Fig. 4. The metasurface is composed of 8×8 blocks. Each block consists of 8×8 SSPP units. Two kinds of blocks with π phase difference are named as 0 and 1 block respectively. Alternately arranging 0 and 1 blocks to make the metasurface have a chessboard structure. Part of the blocks can be observed in the detailed configuration in Fig. 4(a). The overall dimension of the metasurface is 423 mm × 423 mm. The length of the metasurface is about thirteen times the wavelength of the center frequency, thus most incoming EM waves can be received. The period in x and y direction are both 9 mm. The frequency range of the simulation environment is from 2 to 20 GHz. The metasurface is solved under Time Domain Solve and the feeds are chosen to be waveguide ports. To approximate plane wave, two ports are both set to be 150 mm far from the metasurface.
Fig. 4. (a) Configuration of the metasurface. The geometric dimensions are: W = 423 mm, H = 23 mm. (b) Simulated S-parameters of the metasurface. (c) Simulated far-fields at 3 GHz to 15 GHz.
The simulation results are depicted in Fig. 4(b) and Fig. 4(c). As we can see from Fig. 4(b), S11 is less than −10 dB from 2 GHz to 20 GHz. S21 is high from 2 GHz to 9 GHz. Thus the transparent transmission band is from 2 to 9 GHz. From 9.46 to 11.38 GHz, S21 is less than −10 dB, which is caused by the forward scattering cancellation. Thus the refraction function is in 9.46-11.38 GHz. From 12.6 to 20 GHz, the S11 and S21 are both less than −10 dB causing an absorption behaviour. For clarity, the simulated far field patterns at different frequencies are given in Fig. 4(c). The slight reflection of the incoming waves may be caused by the mismatch of the wave vector. With the increment of the frequency, the side lobe level becomes higher due to the increment of the phase difference. At 10.2 GHz and 11 GHz, there are four main lobes due to the π phase difference between the adjacent blocks. As can be observed from the far field pattern at 15 GHz, the outgoing beams both have very low level which illustrates the strong absorption.
In order to explore the absorption behaviour of the metasurface, the feed is changed from waveguide port to Gaussian beam port for analyzing the power pattern. The power pattern is shown in Fig. 5. The total input power is 1 W for the Gaussian beam port. The power at 15 GHz is 0.14 W because of the absorption property.
From the simulation results, three functions of the metasurface in three frequency bands is obtained. From 2 GHz to 9 GHz, the EM waves can transmit through the metasurface without distortion, i.e., the metasurface can achieve a transparent transmission. In 9.46-11.38 GHz, the outgoing beams have a beam-dividing behaviour which is caused by anomalous refraction. From 12.6 GHz to 20 GHz, the metasurface have an absorbing ability. The results prove our idea which is to apply the novel properties of the SSPPs to the multifunctional metasurface design.
4. Metasurface fabrication and measurement
To verify our idea, a prototype of the metasurface is fabricated using PCB technology and then measured under several conditions. The prototype is shown in Fig. 6(a). The fabricated metasurface is assembled using a square foam. The period of the blocks is 9 mm which is the same as the simulation. The S-parameters are measured by vector network analyzer in microwave chamber. The transmitting and receiving antenna are a pair of lens horn antenna whose operating frequency band are both from 8 to 18GHz. Then the far-field is measured. The test environment of far field is illustrated in Fig. 6(b). The metasurface is placed between two horn antennas. Based on the simulated far field, the divided beams are be in the diagonal line of the metasurface. Therefore, the receiving horn can receive two main beams at one time once rotating the metasurface along with the antennas 45°. The measured far field is depicted as the blue dash line in Fig. 7(a). Comparing with the simulated far-field at 10.2 GHz which can be seen as the black line with symbol in Fig. 7(a), the measured main lobe angle is precisely the same with the simulated one. The simulated and measured far-field patterns both have a strong side lobe in the normal direction. As can be seen from the figure, the measured side lobe level is higher than the simulation. It may be caused by the assembly error. One of the main lobes has a depression caused by measurement error. The test environment of S-parameters is shown in Fig. 6(c). The horn antennas in the test system have an operating band of 8-18 GHz. Limited by measurement instrument, the S-parameters from 8 GHz to 18GHz are depicted in Fig. 7(b). As can be seen from the figure, the reflection coefficient is lower than −10 dB from 8 to 18GHz. The transmission coefficient is high before 12.4GHz and has a steep drop at 12.4 GHz. The S21 is low than −10 dB from 10.0-11.7 GHz due to the scattering cancellation. The S21 curve remains under −20 dB from the 12.4 GHz to 18 GHz.
Fig. 6. (a) Prototype of the metasurface. (b) Far-field measurement environment of the metasurface. (c) S-parameter measurement environment.
Fig. 7. Measured results. (a) Simulated and measured far field of the metasurface at 10.2 GHz. (b) Measured S-parameters of the metasurface.
5. Conclusions
In conclusion, a trifunctional metasurface is presented in this paper. Based on the spatial k-dispersion engineering of SSPPs, the design schedule and operating mechanism can be simple and clear. The proposed metasurface can achieve three functions in three frequency bands. The metasurface is simulated and measured. The measurement results show that the presented metasurface is “invisible” from 2GHz to 9 GHz and has an anomalous refraction behavior around in 10.0-11.7 GHz. The absorption function is in a wide band from 12.6 to 20GHz. These results provide a simple design method for the multifunctional metasurface.
Funding
National Natural Science Foundation of China (61501497, 61971341).
Disclosures
The authors declare no conflicts of interest.
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