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Abstract
In this paper, a novel composite metasurface (MS) with diffuse scattering and absorbing characteristics is proposed to reduce the radar cross section (RCS) of a metal target in a broad band. The combination of absorption and diffusion is realized based on lossy Pancharatnam-Berry (PB) phase particles. The units are arranged according to a coding sequence which is obtained by an optimization algorithm based on simulated annealing algorithm. Simulation results show that the MS obtained based on the optimized coding sequence is insensitive to polarization. Due to the combination of absorption and diffusion, the MS has good performance in both monostatic and bistatic scenarios. Finally, the proposed MS is fabricated and measured, and the experimental results are in good agreement with simulation results. A 10 dB backward reflection reduction can be achieved from 21GHz to 38GHz and a 15 dB backward reflection reduction can be achieved from 22GHz to 35GHz under normal incidence. Furthermore, the MS has good performance under large angle (<45°) incidence.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the 1990s, the emergence of metamaterials [1,2] provided new horizons for scholars in the electromagnetic field. But the characteristics of large size, narrow band, and high loss [3,4] also limit its further development. In 2011, the research team of professor Capasso of Harvard University proposed a phase gradient MS based on the Generalized Snell's Law [5], which showed that MS has great potential for electromagnetic waves manipulation. Furthermore, MS breaks the limitations of traditional metamaterial, and has broad potential in terms of planarization and integration. In recent years, many novel electromagnetic devices have emerged, such as planar lenses, polarization converters, vortex wave generators, etc [6–11], which greatly promoted the development of the electromagnetic technology. The electromagnetic manipulation capability of the MS devices mentioned above is based on the phase response of subwavelength units. Variation of structural parameters is a frequently-used way to realize 360° phase coverage; however, the phase response is unevenly distributed and the bandwidth is limited. Some efforts have been made by researchers to expand the bandwidth. Multiple resonances configuration [12] has been introduced and optimization method [13] has been developed. These methods either increase the complexity of geometries or increase the difficulty of design. The geometric phase, also known as PB phase [14,15], is a competitive alternative solution. PB phase is only related to the rotation angle and is independent of the geometry or material. Therefore, PB phase unit has simple structure and inherent broadband characteristics.
One of the most important application scenarios of MS is electromagnetic stealth. Perfect absorber [16–18] and diffuse scattering MS [19–21] are two efficient ways to achieve reflection suppression. The operating principle of absorber is converting the electromagnetic energy of the incident wave into thermal energy by introducing loss. The perfect metamaterial absorber (PMA) was first proposed by Landy et al. in 2008 [16], which can achieve nearly 100% absorption within a narrow band. Some methods such as loading lumped elements [22,23] or adopting multi-layer structures [24] are proposed to improve the working bandwidth of MS absorber. However, the processing difficulty and manufacturing cost might be increased. At the same time, the conversion and accumulation of thermal energy also increase the risk of being exposed under infrared detection. Researches based on diffuse scattering were widely reported with the advent of coding MS [19,25]. With the introduction of random phase distribution, the reflected waves will be redirected to numerous directions in the upper half space. A backward RCS reduction can be achieved since the originally concentrated beams are now dispersed into various directions. In recent years, a lot of work [26–32] has focused on broadening the bandwidth of diffuse MS. Zheng et al. [28] proposed a shared aperture MS with relative bandwidth of 113.9%. However, due to the introduction of air gap, the thickness of the MS is nearly doubled. Efforts have been made to improve the performance of low scattering MS by combining absorption and diffusion. Multiband low-scattering MSs have been proposed in reference [33] and reference [34], which can realize absorption and diffusion in different frequency bands. In literature [35] and [36], lossy scatters are utilized to realize the combination of absorption and diffuse scattering in the same frequency band. Although both MSs achieve ultra-wideband reflection reduction (greater than 100%), the structures are multi-layered and difficult to fabricate.
In this paper, a novel MS based on lossy PB phase particles is proposed to reduce the RCS of a metal target. Carbon film with low surface resistance is utilized as the material of the surface pattern to regulate the magnitude of the reflection coefficient. Meanwhile, the phase response is modulated based on PB phase. In order to avoid the high side lobes that may be caused by random arrangement, a program based on simulated annealing algorithm is developed to find the optimal coding sequence. Both left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) cases are taken into accounts in the process to make sure that the obtained MS has good performance under circular polarization and linear polarization incidence. It is verified by simulation results that the performance of the proposed MS is not sensitive to polarization. Due to the combination of absorbing and diffuse scattering, the reflection reduction efficiency is further improved. Finally, the proposed MS is fabricated and measured. Simulated and measured results demonstrate that a 10 dB backward reflection reduction can be achieved within 21-38 GHz and a 15 dB backward reflection reduction can be achieved within 22-35 GHz under normal incidence. Furthermore, the MS has good performance under large angle incidence, and the performance deteriorates slightly till the incident angle is greater than 45°.
2. Design of MS
2.1 Unit cell
Variation of structural parameters is a frequently-used way to realize 360° phase coverage; however, the absence of general guidance leads to strong dependence on simulation and optimization. Furthermore, the limitation of narrow bandwidth, large size and uneven phase distribution can’t be ignored. PB phase is a good solution because of the simple structure and wide bandwidth. For MS composed of anisotropic unit cells, the introduction of rotation angle can be regarded as the rotation of two-dimensional coordinate system. Figure 1(a) shows the coordinate system. The axes of the local coordinate system are u and v respectively and the angle between u axis and x axis is .
Fig. 1 (a) The coordinate system and the definition of rotation angle (b) Schematic of the copper patch unit cell topology. (c) Schematic of the carbon film patch unit cell topology. The geometric parameters of the units are mm, mm, mm, mm, mm.
The reflection matrix in local coordinate can be defined as:
In general, for anisotropic MS . In the case of normal incidence, . Then the reflection matrix in rectangular coordinate system can be expressed as:For circular polarized incidence wave, the reflection can be derived as:where , −1 represents LCP incidence, + 1 represents RCP incidence. Under circularly polarized incidence, the reflected wave has both co-polarization component and cross-polarization component which can be concluded from Eq. (3). It is worth noting that the propagation direction of the reflected wave changes, so the polarization of the reflected wave is different from that of the incident wave. Therefore, the first term of Eq. (3) represents cross-polarization reflection, and the second term represents co-polarization reflection, which carries additional PB phase , where - represents LCP wave, + represents RCP wave. The PB phase can simplify the design process of the unit cell. The above analysis shows that a phase difference of co-polarization reflection can be introduced by rotation, and the phase difference can be adjusted by rotation angle. In addition, this type of unit cell has the characteristics of simple structure, small size, and broad bandwidth.A traditional copper patch MS unit is designed based on PB phase. An H-shaped pattern is utilized as the surface patch of the unit cell as Fig. 1(b) shows. The magnitudes and phases of the reflection coefficients are shown in Fig. 2. As analyzed above, the co-polarization reflection will exhibit a phase difference of 90° as the unit cell rotates 45°. Then a set of unit cells with phase coverage of 360° can be obtained by rotating the original pattern around the z-axis with angle of 45°, 90° and 135°, respectively. Although the co-polarization reflection is much larger than the cross-polarization reflection in the operating frequency band, further reduction of the cross-polarization reflection will improve the RCS reduction performance.
Fig. 2 Magnitudes (a) and phases (b) of reflection coefficients of copper patch unit cells with different rotation angles under LCP incidence. (The lowercase r represents the reflection coefficient, and the uppercase R and L represent RCP and LCP respectively.)
In this paper, lossy carbon film is used instead of copper as the material of surface pattern as shown in Fig. 1(c). The top layer is an H-shaped carbon film patch which is mounted on a grounded F4BME substrate with relative dielectric constant of 4.1 and loss tangent of 0.001. The PB phase is only related to the rotation angle and independent of the surface resistance of carbon film. Carbon film with square resistance of 15 is chosen to minimize the cross-polarization reflection. Figures 3(a) and 3(b) shows the magnitudes and phases of the reflection coefficients of units with different rotation angles. With the change of material, both the cross-polarization and co-polarization reflection are reduced, while the phase differences between these four units are not changed. The series of units analyzed above have phase differences of 0, π/2, π, 3π/2 under LCP incidence. Under RCP incidence, the magnitudes of the reflection coefficients are consistent with the LCP case, while the phase differences become 0, 3π/2, π, π/2 as shown in Figs. 3(c) and 3(d). Figure 3(e) shows the absorption performance and co-polarization efficiency of units with different material. The introduction of lossy material greatly improves the absorption rate, more than half of the energy is absorbed within 20 GHz to 40 GHz. And the cross-polarization reflection is almost negligible. Then diffuse scattering can be introduced based on PB phase of the co-polarization reflection.
Fig. 3 Magnitudes (a) and phases (b) of reflection coefficients of carbon film patch unit cells with different rotation angles under LCP incidence. Magnitudes (c) and phases (d) of reflection coefficients of carbon film patch unit cells with different rotation angles under RCP incidence. (e) The absorption performance and co-polarization efficiency of units with different materials.
2.2 Arrangement of MS
The scattering pattern of the whole array was the composition of the contributions of all the units. For an array in xoy plane consisting of M × N units with uniform spacing of dx, dy in x, y direction, respectively, the scattering pattern can be predicted by array theory. The total scattering field can be expressed as:
where EF represents the pattern function of a unit and AF represents the array factor. Since the four units adopted in this paper have approximately equal magnitudes under LCP and RCP incidence, so EF is fixed in this model. AF can be derived as:where is the relative phase of the unit (m, n), is the wave vector, and are the elevation and azimuth angles for an arbitrary scattering direction respectively.As is known to all, linear polarized wave can be represented as the superposition of LCP wave and RCP wave. Therefore, the performance under linear polarization can be guaranteed on condition that the obtained coding matrix has optimized results for both LCP and RCP cases. A program based on simulated annealing algorithm is developed to obtain 2-bits optimized phase arrangement. The flowchart of the optimization algorithm is shown in Fig. 4(a). The program begins with an initial coding matrix which will be randomly modified in the iterative process. The sampling step of and is set as 1°, AF values in LCP and RCP cases are calculated at each sampling point. Then the maximum values of LCP AFmax_L, and the maximum values of RCP AFmax_R are extracted respectively, and the bigger one between them is defined as AFmax. To make sure that the reflected waves are distributed to numerous directions in the upper half space as evenly as possible, the goal of this program is finding an optimal coding matrix to minimize AFmax. The initial coding matrix is constantly modified in the process until the temperature reaches the final temperature Te or the number of iterations reaches Nmax. In this program, the size of the coding matrix is 10 × 10, and the elements of the initial coding matrix are randomly chosen from 0, 1, 2, 3. The initial temperature T is set as 1, the decreasing rate a after each iteration is set as 0.95, the final temperature Te is set as 1 × 10^-20, and the number of iterations Nmax is set as 5000. After running the optimization program 10 times, the matrix with the best performance is selected as the optimal coding sequence, as shown in Fig. 4(b). The final model shown in Fig. 4(c) is constructed by 10 × 10 supercells according to the optimal coding sequence, and each supercell is composed of 2 × 2 basic units.
Fig. 4 (a) The flowchart of the optimization algorithm. (b) The optimal phase arrangement. (c) The final model of carbon film patch MS with optimal arrangement.
3. Simulation results and discussion
In order to compare the performance of copper patch MS and carbon film patch MS, simulations are carried out with the CST Microwave Studio. These two MSs have been simulated under normal incidence of LCP plane waves. The 3D scattering patterns of copper patch MS and carbon film patch MS at 28 GHz are shown in Fig. 5, and Fig. 5(g) shows the total scattering pattern of same-sized metal plate at 28 GHz. Under normal incidence, the main reflected energy of the metal plate is concentrated on the backward direction, while the reflected energy of each MS is redirected to various directions and the backward RCS is reduced. For copper patch MS, a uniform diffuse scattering distribution is shown in the co-polarized scattering pattern while a nonnegligible backward main lobe occurs in the cross-polarized scattering pattern. Therefore, good stealth performance can be achieved only in the case of co-polarization detection. For carbon film patch MS, the cross-polarized scattering pattern has obvious main lobe with very low intensity, which has little effect on the total scattering pattern. It is proved that the introduction of carbon film can reduce the cross-polarization reflection evidently.
Fig. 5 The total 3D scattering pattern (a), the co-polarized scattering pattern (b) and the cross-polarized scattering pattern (c) of copper patch MS at 28 GHz; The total 3D scattering pattern (d), the co-polarized scattering pattern (e) and the cross-polarized scattering pattern (f) of carbon film patch MS at 28 GHz, as well as (g) the total scattering pattern of same-sized metal plate at 28 GHz.
Figure 6(a) shows the bistatic total scattering RCS under normal incidence of LCP plane wave at 28 GHz. The scattering pattern of carbon film patch MS is greatly reduced in all directions of the upper half space compared with the scattering pattern of copper patch MS. This is because part of the energy is absorbed due to the introduction of lossy carbon film and the total scattering field is greatly reduced. Figure 6(b) shows the broadband backward RCS reduction of two types of MSs under normal incidence of LCP plane wave. From 22GHz to 35GHz, the RCS reduction is increased by 4-9dB after replacing the copper patch with carbon film patch. The above results prove that the proposed carbon film patch MS has good stealth performance under both co-polarization and cross-polarization detection in the case of normal incidence of circular polarized plane wave. Furthermore, significant monostatic backward scattering reduction and bistatic scattering reduction can be realized simultaneously.
Fig. 6 (a) The bistatic total scattering RCS under normal incidence of LCP plane wave at 28 GHz. (). (b) The broadband total backward RCS reduction of two types of MSs.
For linear polarized incidence, Figs. 7(a)-7(i) demonstrate the total 3D scattering pattern, co-polarization scattering pattern and cross-polarized scattering pattern at frequencies of 25 GHz, 30 GHz and 35 GHz. It is obvious that both the co-polarization component and the cross-polarization component have diffuse scattering distribution, and the total scattering pattern also presents a uniform diffuse scattering distribution. Figure 7(j) shows the broadband backward RCS of carbon film patch MS and metal plate. The total RCS, co-polarized RCS and cross-polarized RCS of the proposed carbon film patch MS are far below the backward RCS of metal plate in the working band. The co-polarized RCS is larger than the cross-polarized RCS at most frequencies, so the total RCS mainly depends on the co-polarized RCS.
Fig. 7 Under normal incidence of x-polarized plane wave, the total 3D scattering pattern of carbon film patch MS at (a) 25 GHz (b) 30 GHz (c) 35GHz; the co-polarized scattering pattern at (d) 25 GHz (e)30 GHz (f) 35GHz; the cross-polarized scattering pattern at (g) 25 GHz (h) 30 GHz (i) 35GHz. (j) The broadband backward RCS of carbon film patch MS and metal plate under normal incidence of x-polarized plane wave.
Figure 8(a) shows the broadband total backward RCS reduction under different polarizations. The curves in the four cases are almost identical, indicating that the RCS reduction performance of the proposed MS is not sensitive to polarization. Figure 8(b) shows the total 3D scattering pattern of the carbon film MS under x-polarized incidence with different incident angles. The scattering pattern of metal plate has obvious main lobe in the direction of specular reflection, while the main lobe of the scattering pattern of MS does not occur until the incident angle is greater than 45°.
Fig. 8 (a) The broadband total backward RCS reduction of four different polarization types under normal incidence. (b) The 3D scattering pattern of metal plate (top) and carbon film patch MS (bottom) under x-polarized incidence at angles of 0˚, 30˚, 45˚.
4. Experimental results
In order to verify the performance of the proposed carbon film patch MS, a sample with optimized coding sequence was fabricated based on silk screen printing technology. Photograph of the fabricated sample is shown in Fig. 9(a). The overall size of the sample is 80 × 80 mm2, equal to 8λ × 8λ at 30 GHz, which is composed of 16 × 16 units. The square resistance of carbon film is measured as 15.3. F4BME board with thickness of 1.2 mm is chosen as the substrate, and the copper layer with thickness of 0.018 mm is coated on the other side of the substrate as the ground. The schematic diagram of the measurement system is shown in Fig. 9(b). The distance d between the sample and the antennas satisfies the far-field condition and the plane wave condition. The actual measurement system is shown in Fig. 9(c). The sample was fixed on a foam base, and the relative dielectric constant of the foam is close to 1, which has negligible influence on the measurement results. A pair of double-ridged horn antenna are used as the transmitter and receiver. The reflection coefficients of the sample and same-sized copper plate are measured by vector network analyzer (VNA) Agilent N5227A.
Fig. 9 (a) Photograph of the fabricated sample. (b) Schematic diagram of the measurement system. (c) The measurement system.
The simulated and measured results of both co-polarized and cross-polarized normalized reflections of the proposed MS are demonstrated in Fig. 10(a) while the schematic diagram of measurement is shown in Fig. 10(b). The normalized cross-polarization reflection is lower than 20 dB in the whole operating band, which proves that excellent stealth performance can be achieved under cross-polarization detection. As the incidence angle increases, the reflection reduction performance of the proposed MS deteriorates gradually, especially in the direction of specular reflection. Therefore, in the case of oblique incidence, the reflection reduction in the direction of specular reflection is measured and the schematic diagram is shown in Fig. 10(b). Figure 10(c) shows the comparison of the reflection reduction between simulation and measurement in the case of x polarization with different incident angles. Figure 10(d) shows the simulation and measurement results under y polarization. In the case of normal incidence, the monostatic backward reflection reduction below 10 dB is realized from 21 GHz to 38 GHz. Under oblique incidence, the reflection reduction performance decreases a little in the direction of specular reflection. Inevitably, there are slight errors in fabrication and measurement, so the measured bandwidth is slightly narrower than that of simulation results. The measurement results agree well with the simulation results in both bandwidth and amplitude. The above results verify that the sample is not sensitive to polarization, and the performance deteriorates slightly with the increase of incident angle. Table 1 shows the comparison between this work and other related works. The comparison shows that the proposed MS has the advantages of wide band and low profile. It is worth noting that the backward reflection is further reduced within a broadband and a backward reflection reduction below 15 dB is achieved in the frequency band of 22 GHz-35 GHz. Our work has significant advantages in terms of thickness and reflection reduction efficiency, which are key factors in electromagnetic stealth, although our work has no superiority in terms of 10 dB bandwidth. The above results demonstrate that further reflection reduction can be achieved by the combination of diffusion and absorption.
Fig. 10 (a) The normalized reflections of the MS under normal incidence of x-polarized plane waves. (b) The measurement schematic diagrams of co-polarization reflection and cross-polarization reflection in the case of normal incidence (the first two figures), and the measurement schematic diagram of specular reflection in the case of oblique incidence (the last figure). The comparison of the reflection reduction performance between simulation and measurement in the case of x polarization (c) and y polarization (d) with different incident angles.
Table 1. Comparison between our work and previous designs
5. Conclusion
In summary, a novel composite MS with diffuse scattering and absorbing characteristics is proposed to reduce the RCS of a metal target. The absorption is introduced by the loss of carbon film patch, and the diffusion is realized based on the phase differences introduced by PB phase units. The units are arranged according to a coding sequence which is obtained by an optimization algorithm based on simulated annealing algorithm. Simulation results show that the MS obtained based on the optimized coding sequence is insensitive to polarization. By comparing the simulation results of copper patch MS and carbon film patch MS, it is verified that the introduction of lossy material reduces the scattering field of the whole upper half space, especially the backward direction. Finally, the proposed MS is fabricated and measured, and the experimental results are in good agreement with simulation results. A 10 dB backward reflection reduction can be achieved within 21-38 GHz and a 15 dB backward reflection reduction can be achieved within 22-35 GHz for both x and y polarization. Furthermore, the MS has good performance under large angle incidence, and the performance deteriorate slightly till the incident angle is greater than 45°. The MS proposed in this paper has the advantages of low profile, wide band, high reflection reduction efficiency, and easy processing. The combination of absorption and diffusion provides a novel and effective way to reduce the scattering of metal targets. In addition, the magnitude and phase of reflection coefficient can be manipulated independently, which may find applications in high quality holography and shaped beam antenna.
Funding
National Natural Science Foundation of China (NSFC) (61771304).
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