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Abstract
In this paper, a multi-bit dielectric reflective metasurface is presented for control of electromagnetic (EM) wave scattering and anomalous reflection. The unit cell is designed to act as a 1-, 2-, and 3-bit coding metasurface to attain better control of EM waves. For the 3-bit coding metasurface, the eight digital states have phase responses of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. The top layer of the proposed metasurface consists of high permittivity material to realize a high Q factor. The proposed multi-bit coding metasurface can reflect the incident EM wave to the desired angle with more than 93% power efficiency. For radar cross section reduction applications, the discrete water cycle algorithm is utilized to obtain an optimal coding matrix for the unit cell arrangement, leading to better diffusion-like scattering, dispersion of the EM wave in all directions, and hence minimal specular reflection. The simulation and experimental results verify that the proposed metasurface is a suitable candidate for control of EM wave scattering and anomalous reflection.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces are the two-dimensional (2D) equivalent of metamaterials and have attracted considerable attention because of their intriguing applications, including electromagnetic (EM) cloaking [1,2], perfect absorption [3–5], subwavelength focusing [6], and negative refraction [7], none of which can be realized with natural materials. Unlike traditional materials with fixed inherent properties, metamaterials can be used to customize material properties for a particular application. Because they exhibit low thicknesses and easy fabrication, metasurfaces are more advantageous than are metamaterials for various applications in microwave and visible light communication. C. D. Giovampaola proposed the concept of digital metamaterials in [8], and T. J. Cui introduced coding and programmable metasurfaces [9]. In a coding metasurface, the meta-atom is represented as a digital bit that could have a value of “0” or “1” depending on the magnitude, phase, and polarization of the metasurface element. After the design and optimization of unit cells, the array constitutes an arrangement of unit cells and different arrangements allow optimization for numerous applications. In the digital metasurface, the physical design is represented as digital codes; therefore, the concept of the metasurface is extended to signal processing techniques and information theory [10].
Metasurfaces offer many possibilities for manipulation of EM waves by introducing sudden changes in polarization, phase, and amplitude of the incident waves over the subwavelength scale [11–14]. The phase distribution at the aperture of the reflector is tuned by the arrangement of unit cells in an organized way, and thus the metasurface exhibits excellent potential for anomalous reflection with high efficiency [15–19]. In [20], a metasurface based on the generalized Snell’s law is proposed to achieve a high efficiency perfect anomalous reflection via the transfer of power through leaky waves. However, known structures designed to shape reflection wave-fronts according to the generalized laws of reflection suffer from significant parasitic reflection in undesired directions, resulting in a substantial reduction in efficiency [21].
For EM wave manipulation, the artificial magnetic conductor (AMC) is arranged like a chessboard to minimize specular reflection by converting the incident wave into four beams [22,23]. Diffusion-like scattering can be achieved by a random arrangement of unit cells to form a suboptimal array design. The optimized arrangement of unit cells is realized by using the binary particle swarm optimization (BPSO) or genetic algorithm (GA) in [24,25] for a 1-bit coding metasurface. Here, we apply the discrete water cycle algorithm (DWCA) to find the optimal array formation for better diffusion-like scattering. Many designs of the coding metasurface presented in the literature are composed of metallic structures [26–30], which suffer from non-radiative losses and intrinsic losses in metals. To cope with the losses of the metallic metasurface, another mechanism is introduced, which relies on the concept of interaction of EM waves and dielectric materials [31–33]. The electric and magnetic resonances are achieved through the use of high index dielectric materials [34–36]. The ability to tune the electric and magnetic field of dielectric materials using different geomaterial arrangements make it desirable for many applications in microwave, terahertz, and visible light communication [37–39].
A multi-bit dielectric metasurface is proposed for anomalous reflection and optimized diffusion-like scattering and a high permittivity material is used to achieve a high Q factor. The anomalous reflection is demonstrated with 93% power efficiency. The size of the air-filled holes is changed to get the desired phase difference between respective states of the coding metasurface. It is important to mention that changing the size of the air-filled holes causes shifts in the resonance points, by which we obtain the phase difference between respective states of the digital metasurface. An optimal coding matrix is used for array formation to achieve better radar cross section (RCS) reduction. The simulation and experimental results are compared with data for a copper sheet of the same size.
2. Unit cell design and simulations
The conceptual illustration of the proposed multi-bit dielectric metasurface and the isometric view of the unit cell are depicted in Fig. 1. The coding metasurface unit cell is designed by using dielectric material (ɛr = 10.2 and tan δ = 0.001) with a thickness of 7.5 mm.
Fig. 1. Conceptual illustration of the multi-bit dielectric metasurface. Here, p = 8 mm, h = 7.5 mm, g varies from 1.7 mm to 6.6 mm.
The proposed design consists of a dielectric metasurface that has drilled square holes of different sizes in the center, and the bottom of the dielectric material is covered with metal to realize the reflective metasurface. The thickness of the metal ground is 0.035 mm. The size of the unit cell is 8 mm, and, because of its symmetrical nature, the proposed design is polarization-insensitive.
The unit cell simulations were carried out by using periodic boundary conditions and a Floquet port in CST Microwave Studio. The magnitude response of the unit is presented in Fig. 2(a), which shows that a value of more than 0.94 is achieved for eight digital states. The phase response of proposed unit cells with hole “g” of varying size and for a frequency band of 10 GHz to 12 GHz is shown in Fig. 2(b). It is essential to mention that changing the size of air-filled holes causes the resonance points to shift, resulting in phase differences between respective states of the digital metasurface. The dimensions of the unit cell have been optimized to achieve eight phases, and the phase difference between two adjacent unit cells is 45°. The proposed dielectric metasurface can be used as a 1-, 2-, and 3-bit metasurface, as shown in Fig. 2(c), by careful selection of the parameter “g” representing the size of the hole. The 1-bit metasurface has two digital states with phases of 0° and 180°, while the 2-bit metasurface has four digital states with phases of 0°, 90°, 180°, and 270°. For a 3-bit metasurface, eight digital states have phases of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. The 3-bit coding metasurface is more robust to control EM waves than 1-bit and 2-bit coding metasurface, as the 3-bit coding metasurface has 8 states with a phase difference of 45° between respective phases. The lengths for the sides of the square holes are optimized as 1.7 mm, 3.28 mm, 3.88 mm, 4.28 mm, 4.66 mm, 5.1 mm, 5.86 mm, and 6.6 mm to realize the 3-bit coding metasurface.
Fig. 2. Simulation results of the unit cell with variations in the size of drilled-hole “g.” (a) magnitude response vs. frequency, (b) phase response vs. frequency, and (c) design principles of 1-, 2-, and 3-bit coding metasurfaces.
3. Results and discussion
3.1. Anomalous reflection
The conceptual illustration of the multi-bit dielectric metasurface and its application for anomalous reflection are depicted in Fig. 3. We consider a plane wave illuminating the periodic metasurface with an incident angle ${\theta _i}$ and yielding a resultant reflection angle ${\theta _r}$.
The period of the metasurface super-cell is given by the expression in Eq. (1), [19]
where $\lambda $ is the operational wavelength. The desired reflection is along the direction of $ n = 1 $, while the other orders distributes the energy to undesired directions and causes the loss of efficiency. For perfect anomalous reflection with 100% efficiency, all the incident energy should be transferred to the desired direction without any loss. Here, we apply the dielectric coding metasurface for anomalous reflection, which is different from conventional impedance matching and leaky-wave antenna concepts. By using the specific arrangement of phase gradients, anomalous reflection with high efficiency is achieved without tedious calculations. The dimension of the coding unit cell is p = 8 mm, h = 7.5 mm, and g varies from 1.7 mm to 6.6 mm.The super-cell is created according to the following formula in Eq. (2),
where ${D_x} $ is the size of super-cell, $ N$ is the number of unit cells, and p is the size of each unit cell. To explain the design mechanism, we will consider ${\theta _r}$ = 34.6°. Using Eq. (1), the super-cell size is calculated as $ {D_x}$ = 48 and, by inputting this value into Eq. (2), the number of unit cells is calculated as $N$=6. The final sequence required to achieve anomalous reflection at ${\theta _r}$ = 34.6° is “012467”. To illustrate this concept, we also calculate the coding sequence for anomalous reflection at $ {\theta _r}$=16° and ${\theta _r}$=25°.The coding sequences for ${\theta _r}$ = 16° and ${\theta _r}$=25° are calculated as “011233455677” and “01234567”, respectively. Fig. 4 shows the far-field patterns of multi-bit coding metasurfaces yielding anomalous reflection at ${\theta _r}$ = 16°, ${\theta _r}$ = 25°, and ${\theta _r}$ = 34.6°. It is clear from Fig. 4 that most of the incident wave is reflected in the anticipated direction with very weak reflections seen at undesired angles as harmonics; hence, high efficiency of anomalous reflection is achieved.
Fig. 4. Far-field pattern for anomalous reflection at (a) $ {\theta _r}$ = 16°, (b) $ {\theta _r}$ = 25°, and (c) $ {\theta _r}$ = 34.6°. Designed multi-bit coding metasurface for the sequence (d) “011233455677”, (e) “01234567”, and (f) “012467.”
In order to calculate the efficiency of the proposed design, the metasurface is replaced by a copper plate of the same size. The reflected signal received from the copper plate is measured by the receiving antenna. The reflection efficiency is calculated by dividing the power received of metasurface by the power received after reflection from the copper plate at the same angle. The efficiency of the proposed dielectric metasurface is improved relative to those of metallic designs, which suffer from non-radiative losses. In the linear scale and expressed in terms of power, the reflection efficiency for ${\theta _r}$ = 16° and ${\theta _r}$=25° is 96% while the efficiency for ${\theta _r}$ = 34.6° is calculated as 93%.
3.2. EM wave manipulation
After the design and optimization of the unit cell, unit cells are arranged to manipulate the incident EM wave. To realize one, two, three, or four reflected beams at 11 GHz the metasurface unit cells are arranged in different configurations, as shown in Fig. 5. For a single beam, identical unit cells with 0° phase response are arranged in the array, while two beams are generated by the alternative placement of 0° and 180° elements aligned along the x-direction. The other famous structure is a chessboard structure, in which 1-bit and 0-bit unit cells are arranged like a chessboard. When the incident wave interacts with the chessboard structure, it does not exhibit specular reflection, but is divided into four beams.
Fig. 5. Layout and scattering performance of proposed design for (a) one beam, (b) two beams, (c) three beams, and (d) four beams.
3.3. Optimized diffusion-like scattering
The diffusion metasurface is introduced to overcome the limitations of narrow bandwidth because it has a random arrangement of unit cells; this serves to disperse the scattering waves in many directions and reduces the specular reflection and thus increases the effective bandwidth [40,41]. To achieve a better RCS reduction, an optimized arrangement of unit cells is essential. For an array of $M \times N$ coding elements, the scattering pattern [42] is expressed as in Eq. (3),
where $\theta $ and $\varphi $ are the elevation and azimuth angles, respectively. $EP $ is the element pattern; we assume it as a constant in our model. According to the array theory, the $AF$ is expressed as in Eq. (4),The optimization process is executed in the MATLAB environment by considering 200 maximal iterations and 200 populations. Fig. 7(a) shows the convergence characteristics for the algorithm and indicates that the algorithm reaches an optimal solution within the first 30 iterations. The MATLAB simulation results for a 2D far-field pattern are shown in Fig. 7(b), and the 3D far-field pattern shown in Fig. 7(c) is achieved from full-wave simulations in CST Microwave Studio. The coding matrix associated with the minimum value of the array factor is then determined to design the final array for optimal RCS reduction. The optimal coding matrix and corresponding array are shown in Figs. 8(b) and 8(a), respectively. In our design, an array is designed with 24 × 24 unit cells, and the size of the array is 192 × 192 mm2. In order to reduce complexity and to maintain the periodicity of the metasurface, a super-cell of 3 × 3 identical unit cells is introduced in this paper. In contrast to a single beam in specular reflection of PEC, the multi-bit coding metasurface disperses the incident wave in many directions.
Fig. 7. Simulation results of (a) Convergence graph of DWCA, (b) 2D scattering pattern obtained from MATLAB, and (c) 3D far-field pattern of the optimized dielectric coding metasurface.
The 3D far-field pattern of the optimized coding metasurface and a same-sized PEC are shown in Figs. 8(a) and 8(c), respectively. The RCS of the metasurface is compared with that of a same-sized metal, and an RCS reduction of 13 dBsm is achieved at 11 GHz. The simulation results show that RCS reduction of more than 7 dB is realized for the frequency band 10 GHz-12 GHz, while an RCS reduction of 10 dB is achieved for the frequency band 10.5 GHz-11.5 GHz; the comparison of RCS for multi-bit coding metasurface and for the same-sized PEC is presented in Fig. 8(d). The multi-bit coding metasurface sample was fabricated to validate the performance of the proposed design, as shown in Fig. 9(b).
Fig. 8. (a) 3D scattering patterns of the proposed dielectric metasurface. (b) Optimized coding matrix. (c) 3D scattering patterns of the PEC. (d) Simulated RCS of metal and optimized dielectric coding metasurface.
Fig. 9. (a) Experimental setup in an anechoic chamber. (b) Fabricated sample of dielectric metasurface (c) Comparison of PEC and proposed dielectric metasurface.
The multi-bit coding metasurface sample was fabricated using a computer numerical control (CNC) milling machine. The fabricated sample consists of 24 × 24 unit cells, and the size of the array is 192 × 192 mm2. The top layer comprises a dielectric substrate supplied by Taizhou Wangling Insulating Materials Factory, China with relative permittivity ɛr = 10.2 and loss of tangent tan δ = 0.001. It should be noted that the permittivity and loss of tangents are the same we have used in the simulations. The dielectric substrate with the dimensions 192 × 192 mm2 was drilled with a CNC milling machine, and the size of air-filled holes “g” was selected according to the coding matrix in Fig. 8(b). The bottom of the dielectric material was covered with copper. The permittivity of the fabricated sample was determined by the vector network analyzer (Agilent N5227) to be in the frequency range of 10 GHz-12 GHz. The experiment was carried out in an anechoic chamber to validate the performance of the coding metasurface, and the experimental setup is shown in Fig. 9(a).
Two ports of the vector network analyzer (Agilent N5227) were connected to X-band transmitting and receiving antennas, and the fabricated sample was placed in the far-field of antennas. The simulation and experimental results for the proposed multi-bit coding metasurface are compared with those of a copper sheet of the same size, as shown in Fig. 9(c). The measurement results show that the RCS reduction of more than 7 dB is realized for the frequency band 10 GHz-12 GHz, while the RCS reduction of 10 dB is achieved for the frequency band 10.5 GHz-11.5 GHz. The small difference between the simulated and experimental results is the result of fabrication and measurement tolerances.
4. Conclusions
In this paper, a multi-bit dielectric reflective metasurface is presented for control of EM wave scattering and anomalous reflection. The proposed multi-bit coding metasurface can reflect the incident EM wave to the desired angle with more than 93% power efficiency. By employing different arrangements of unit cells, the proposed metasurface may be used to manipulate the EM wave. For RCS reduction applications, the optimal coding matrix is obtained from a discrete water cycle algorithm. The optimal unit cell arrangement is the key for better diffusion-like scattering, since it can minimize the specular reflection by distributing the incident wave in many directions. The RCS of the metasurface is compared with that for a metal of identical size, and the RCS reduction of 13 dBsm is achieved at 11 GHz. The simulation results show that RCS reduction of more than 7 dB is realized for frequencies of 10 GHz - 12 GHz while RCS reduction of 10 dB is achieved for frequencies of 10.5 GHz – 11.5 GHz. The simulation and experimental results verify that the proposed metasurface is a suitable candidate for control of EM wave scattering and anomalous reflection.
Funding
National Key Research and Development Program of China (2017YFA0100203); National Natural Science Foundation of China (61571130).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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