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Abstract
Retroreflection can be achieved by phase gradient imparted by super-cells of metasurfaces. Nevertheless, in most cases, retroreflection can only be achieved for one specific polarization. In this paper, we propose an alternative design strategy and reveal that a polarization-independent multi-channel metasurface based on extraordinary optical diffraction (EOD) can achieve high-efficient retroreflection. A unary unit cell, instead of binary unit cells, is employed to canalize impinging EM waves along targeted diffraction channels. Under oblique incidence, only the -1st diffraction order is maintained and the 0th order and others are suppressed through structural design while the reflection is unaffected under normal incidence. In this way, we can achieve retroreflection in three channels. A proof-of-principle prototype was designed, fabricated and measured to verify this design strategy. The prototype can operate at 20.0 GHz under the incident angle of ±48.6° and 0° with the efficiency of retroreflection about 90%. Both the simulated and measured results show an excellent performance of retroreflection along the three channels, regardless of the polarization state of incident waves. This method offers a fast implementation for retrodirective characteristics with facile planar fabrication and can also be easily extended to THz or optical regimes.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The retroreflector is a device which can reflect the incident electromagnetic (EM) wave back the way it came. Because of the advantages in improving the echoes of the small vehicles with poorly radar cross section (RCS) and saving the signal processing time in a wireless transfer system, retroreflection has a plethora of practical applications such as navigation safety, remote sensing, target labeling, unmanned aerial vehicles, satellite communications and so on [1–6]. Traditionally, retroreflection of oblique incident wave has been achieved by three-dimensional structures such as metallic corner cubes, metallic sawtooth gratings and Luneburg lenses. However, they are limited to practical applications as a result of large size, heavy weight and relatively expensive fabrication. Therefore, it is urgently desirable to obtain thin and light substitutes for retroreflection.
Metasurfaces, which is a two-dimensional form of metamaterial composed of sub-wavelength units, have emerged as a versatile tool in EM wavefront manipulation [7–12]. Recent years, many retroreflective metasurfaces have been proposed [13–18]. Jia et al. [19] used a modified metallic square loop structure to achieve the required phase gradient design and his metasurface can reflect incident waves backwards at 9.8GHz under the incident angle of 20° with transverse electric (TE) polarization. Estakhri et al. [20] reported that a gradient metasurface in the visible regime can achieve efficient retroreflection under the incident angle of 35.7°. Wong et al. [21] carried out retroreflective subwavelength arrays of rods (for TE) and slot (for TM) backed by a ground plane, at 24.0 GHz under the incident angle of 84.7°. Nevertheless, the aforementioned retroreflective metasurfaces are all operated in a single polarization, which will limit their practical applications in the complex and changeable operational environment. Tao et al. [22] achieved retroreflection of oblique incident wave with LP and CP at 10 GHz. Shang et al. [23] proposed a polarization-independent backscattering enhancement of cylinders based on conformal gradient metasurfaces. Nonetheless, these metasurfaces still need sophisticated structure design and elaborate phase control in order to achieve the desired effect.
The extraordinary optical diffraction (EOD) refers to that metasurfaces with identical unit cells instead of the gradient-phase metasurfaces can acquire the near-unitary diffraction efficiencies by means of utilizing the decaying pathways of the resonance cavity modes into high diffraction orders [24]. It means we can regulate the reflection channels of impinging EM wave using our proposed metasurface. If the impinging EM can be all directed into the diffraction channel that we can control, we will get a perfect retroreflection by redirect the diffraction angle to the incident angle.
In this paper, we propose an alternative design principle and reveal that the metasurfaces based on EOD can achieve retroreflection under oblique EM wave incidence with arbitrary polarization states. The schematic diagram is shown in Fig. 1 and the excellent performance of the polarization-independent retroreflection can be achieve along three channels represented by three different colors. Different from phase-gradient metasurfaces, a simply unary unit cell, where metal strips are placed on the top of a dielectric medium with a copper sheet background, is used to funnel the impinging EM into the desired diffraction channel such as zeroth and -first diffraction orders, according to the EOD theory [25–27]. We can retroreflect the -first diffraction order by adjusting the period of the metal strips and suppress the zeroth order by changing the structure parameters. Finally, a high-efficient retroreflective metasurface can be achieved. In order to prove this strategy, we take a retroreflective metasurface under the incident angle of 48.6° at 20 GHz as an example, and then a prototype is designed, fabricated and measured. Both the simulated and measured results show an excellent performance for retroreflection no matter in linear polarization (LP), circular polarization (CP) or elliptical polarization (EP).
2. Theory and design
2.1 Theoretical analysis
Figure 2(a) shows a schematic illustration of the metasurfaces based on EOD theory in xoz incident plane. When incident EM waves illuminate the metasurface, most of them will ideally go into the diffraction channel (the blue solid line) and few go into the reflection channel (the red dotted line). Unlike most phase-gradient metasurfaces, the facile EOD metasurfaces can achieve near-unity efficiency of EM wave steering without the necessity of spatially varying meta-atoms. The EOD metasurfaces work in specific diffractive regimes, where only the zeroth and -first (or first) diffraction orders are allowed to propagate in free space. Therefore, in order to get the desired diffraction orders, we need to have a knowledge of the diffraction order chart.
As shown in Fig. 2(b), the diffraction order chart in the k-space is depicted, which is constructed by multiple wood’s anomaly (WA) lines. The WA lines can be expressed in a formula as ${k_x} \pm m2\pi /{p_0} ={\pm} {k_0}$ (m=0, 1, 2, …), where ${k_x}$ is the parallel wavevector, ${k_0}$ is the overall wavevector, ${p_0}$ is the periodicity of the structure and ${\pm} m$ are the diffraction order number. The ${\pm} m$-th propagating diffraction order begin to appear when ${k_0}$ is above the ${\pm} m\textrm{ - th}$ WA.
Fig. 2. (a) Schematic illustration of the EOD metasurfaces and (b) the diffraction order chart in the k-space.
Therefore, aiming to get only the zeroth and -first (or first) diffraction orders, we have to put the ${k_0}$ and ${k_x}$ in the green area of Fig. 2(b). In other words, the overall wave vectors ${k_0} = 2\pi /\lambda $ and parallel wave vectors ${k_x} = {k_0}\sin {\theta _0}$ should be located in the momentum subspace surrounded by the 0th, 1st, -1st, and 2nd (or -2nd) WA lines. According to the diffraction order chart, those regimes can be determined by the following conditions,
According to Eqs. (3), we can obtain the periodicity ${p_0}$ of retroreflective metasurface if we want to achieve a certain angle of retroreflection at a certain frequency. However, partial energy of EM waves will still enter the specular reflection channel. Hence, in order to increase the diffraction efficiency in the 1st (or -1st) order, we can adjust the structural parameters to completely suppress the specular reflection. Finally, a high-efficient retroreflective metasurface will be achieved.
It is worth mentioning that the angle of retroreflection is limited to a certain range. As the diffraction order chart is symmetric with respect to the ${k_0}$ axis, we only consider the ${k_x}$>0 case in the following discussions. Plugging Eqs. (3) into (1a), we can obtain:
In the end, the range of ${\theta _0}$ is 19.47°$< {\theta _0} < $90°.
2.2 Structural design
As a proof-of-principle example, we designed a retroreflective metasurface at 20GHz under the incident angle ${\theta _0}$=48.6°. According to Eqs. (3), we can figure out p0=10 mm. Meanwhile, in order to verify the EOD regimes conditions, ${\theta _0}$ and p0 are plugged into Eqs. (1a) because of ${k_x} = {k_0}\sin {\theta _0} > 0$. Then, we can obtain 114.3 rad/m <${k_0}$< 228.6 rad/m. On account of ${k_0} = 2\pi /\lambda $ and $\lambda = c/f$, we can obtain the range of frequency (17.14GHz $< {f_0} < $34.26 GHz). Therefore, it is reliable to achieve the retroreflection at 20 GHz under the incident angle ${\theta _0}$=48.6° when the ${p_0}$=10 mm.
In order to easily suppress the specular reflection, we choose a very simply unit cell, in which metal strips are placed on the top of a dielectric spacer with a copper background, as shown in Fig. 3(a). It is periodically arranged along the x- and y-directions with a periodicity of p=10 mm. The thickness of the top copper strip is 0.018 mm with a conductivity of 5.8×107 S/m and the geometrical parameters of the copper strip are illustrated as follows: l=3.45 mm, w=3.9 mm. The second layer is F4B (a dielectric constant 2.65 and a loss tangent 0.001) dielectric spacer with a thickness h=1.5 mm. And the bottom layer is a 0.018 mm copper ground sheet.
3. Simulation
Numerical simulations are carried out to verify the retroreflective metasurface proposed above, using the time domain solver in CST Microwave Studio. A finite size metasurface (240 mm×240 mm) is simulated with open conditions along the x, y and z directions. The schematic diagram of numerical simulation is shown in Fig. 3(b). Polarization angle (α) of linearly polarized EM is the angle between the electric field and the horizontal line. The EM wave as a plane wave enters at ${\theta _0}$ degrees into the metasurface. In order to facilitate the observation of the retroreflection, a metallic plate of the same size is used as a comparison under the same simulation conditions.
Firstly, the bistatic RCS under different states of polarization are simulated and scattering patterns in the xoz plane are exhibited in Fig. 4 and insets are the 3D farfield pattern of metasurface. As shown in Fig. 4(a), when the transverse electric waves (α=0°) are illuminated in the metal plate at ${\theta _0}$=48.6°, the reflected wave will be reflected at -48.6° (the red lines). However, when the EM waves are illuminated in the metasurface at the same incident angle ${\theta _0}$, it will be retroreflected at 48.6° (the blue lines). Meanwhile, it can be clearly observed that the retroreflection component of metasurface is strong while the specular reflection component is weak. Compared with flat metallic plate, the retroreflection of the metasurface is enhanced by more than about 32dBm2 around the designed frequency in 20.0GHz. The efficiency ${\xi _\textrm{r}}$ of retroreflection can be calculated using the following formula:
Fig. 4. The bistatic RCS scattering patterns in the xoz plane under different states of polarization including (a) LP α=0°, (b) LP α=20°, (c) LP α=40°, (d) LP α=60°, (e) LP α=80°, (f) LP α=90°, (g) left-hand circular polarization (LCP), (h) right-hand circular polarization (RCP) and (i) elliptic polarization with an axial ratio (RA) of 0.7.
Besides, aiming to figure out the polarization-independence, we simulate the same metasurface under different states of polarization including LP (α=0°,20°,40°,60°,80°,90°), left-hand circular polarization (LCP), right-hand circular polarization (RCP) and elliptical polarization (EP). Simulation results are depicted in Fig. 4(a)-Fig. 4(i). By comparing each other, we can find that the states of polarization have few impacts on retroreflection and it has only a slight effect on specular reflection. The efficiency of retroreflection in Fig. 4 are all above 90%. Therefore, we can get the conclusion that the proposed metasurface can achieve high-efficient retroreflection under any state of EM polarization.
Furthermore, because the metasurface is symmetric along the y-axis, the metasurface will achieve a high-efficient retroreflection under multi-incident angles. On account of the polarization-independence proven above, we only give the simulated monostatic RCS of TE and LCP waves. As shown in Fig. 5(a) and Fig. 5(b), the proposed metasurface can achieve high-efficient retroreflection at 20GHz under the incident angles of 48.6°, -48.6° and 0°, respectively.
Fig. 5. The simulated monostatic RCS scattering patterns in the xz-plane at 20 GHz under (a) TE and (b) LCP and (c) the photograph of fabricated sample.
4. Experiment
To further verify these properties, we fabricate a prototype of retroreflective metasurface covering an area of 240 mm×240 mm. The photograph of the prototype is shown in Fig. 5(c), where the inset is a zoom-in view of the sub-cells. The sample, which is surrounded by absorbing materials to avoid unwanted reflections from the environment, is measured using two horn antennas and the Agilent E8363B network analyzer. In the process of experiment, one horn antenna is used as the transmitter and the other is used for receiving reflected waves. The measurement consists of two parts: bistatic reflectivity measurements and monostatic RCS measurements.
The setup of reflectivity measurement is shown in Fig. 6(a). By fixing the receiving antenna and rotating the transmitting antenna that is kept an angle with metasurface, the bistatic reflectivity pattern can be measured. In Fig. 6(b), EM waves impinging into copper sheet are mostly reflected to about -49° at 20GHz. In Figs. 6(c)–6(f), most EM waves are reflected to about 50° and the specular reflection is about -15dB that is much smaller than retroreflection. It indicates that the metasurface can achieve retroreflection in different polarization states. However, we can find that there is a sharp decrease at about 49° in Figs. 6(e)–6(f). That's because the circular-polarized horns are larger than line-polarized ones. When two circular-polarized horns are in the same line, the EM waves are blocked leading to the sharp decrease.
Fig. 6. (a) Setup of reflectivity measurement, (b) reflectivity of metal and reflectivity of metasurface under the incident of (c) TE (d) TM (e) LCP (f) RCP at 20 GHz.
The setup of monostatic RCS measurements is shown in Fig. 7(a). Two antennas are fixed and the prototype is rotated to achieve different incident angles. A copper plate with the same area is also measured for comparison. Monostatic RCS under TE and LCP are depicted in Fig. 7(b) and Fig. 7(c). We can find that the measured results are basically consistent with the simulation results of Fig. 5 and there are three mainly peaks of retroreflection at 20GHz, respectively in about 50.5°, 0°and -50.5°.
Fig. 7. (a) Setup of monostatic RCS measurements and the monostatic RCS in the xoz-plane at 20 GHz under (b) TE and (c) LCP.
From the above test results, the measured angle of retroreflection is slightly larger than the simulated one and amplitude between the simulated and measured result also has some differences. The reasons for these phenomena include two aspects: measurement errors and practical fabrication errors. The measurement errors mainly come from the angle between the two horn antennas and the placement of sample. Because a single horn antenna cannot receive EM waves when transmitting, two horn antennas are placed close and symmetrically to replace the transceiver antenna. It is the angle between receiving and transmitting antennas and the placement of the sample that lead to the differences from the simulation. On the other hand, practical fabrication errors also have an impact on the test results such as sample size processing and instability of dielectric constant.
5. Conclusion
In this paper, we propose an alternative design strategy and reveal that a polarization-independent multi-channel metasurface based on extraordinary optical diffraction (EOD) can achieve high-efficient retroreflection. The unary unit cell, instead of binary unit cell, does not rely on sophisticated structure design and elaborate phase control and thus significantly simplifies the metasurface design procedures and lowers the fabrication demand, which is highly desirable for applications. A proof-of-principle prototype was designed, fabricated and measured to verify this design strategy. The prototype can operate at 20.0 GHz under the incident angle of ±48.6° and 0°. Both the simulated and measured results show an excellent performance of retroreflection along the three channels, regardless of the polarization state of incident waves. Although this paper only considers the xoz incident plane, it is not difficult to see that the theory can be easily extended to yoz incident plane. In this way, more channels of retroreflection will be achieved. In conclusion, this method offers a fast implementation for retrodirective characteristics with facile planar fabrication and can also be easily extended to THz or optical regimes.
Funding
National Key Research and Development Program of China (SQ2017YFA0700201); National Natural Science Foundation of China (61971435).
Disclosures
The authors declare no conflicts of interest.
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