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Abstract
Due to the strong capability to control electromagnetic (EM) wave, metasurfaces have garnered considerable interest and brought in many intriguing EM functional devices. However, most of such devices can only work in either transmitted or reflected mode, and it is still very challenging to achieve a simultaneous control of reflection and transmission in one device. Here, we present a cascaded metasurface which integrates the resonant and geometrical phase cells, to manipulate the transmitted and reflected wave independently. By specific design of phase distribution, the reflected and transmitted wavefront can be respectively reshaped on the shared aperture at two different frequency bands. As a proof of concept, a bidirectional beam deflector is realized by our metasurface and experimentally demonstrated at the microwave region. Both simulated and experimental results show that the transmitted and reflected beams can be simultaneously deflected to the predesigned angles. Furthermore, this metasurface exhibits isotropic EM responses under the different linear polarized wave in the reflected mode, while behaves anisotropic EM responses under the different circular polarized waves in the transmitted mode. Our approach provides a simple way to realize full-space EM manipulation, which could be developed for potential applications in mutlifunctional devices and integrated systems.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The invention of metamaterials opens an encouraging way to control electromagnetic (EM) wave due to their unique EM properties that cannot be found in nature. In the past decades, metamaterials have attracted intensive attentions in scientific communities, and many intriguing physical phenomenon and novel functional devices have been demonstrated [1–6]. Nevertheless, some insuperable difficulties in manufacture and material loss prevent its development. Recently, metasurface [7–10], as a planar version of metamaterial, has rapidly caused much research interest due to its easy fabrication and powerful capability in the arbitrary control of EM wavefront. Compared with the bulk metamaterials, metasurfaces significantly relax the fabrication requirement and reduce the material loss due to its small characteristic thickness much smaller than a wavelength. In addition, metasurfaces can achieve anomalous reflection and refraction by producing the abrupt phase change across the interface, breaking the traditional Snell’s laws and opening a new era of flat optics. There have been many fascinating planar EM devices emerged based on metasurfaces [11–22], such as flat lenses [12,17], low-scattering material [13,14], ultrathin cloaks [11,21–23] and beam steering antennas [19].
With the increasing development of modern integration technology, there are great demands on the multifunctional EM devices. However, the above-mentioned meta-devices can only exhibit a single functionality, which is hard to meet the development trend in the future. Recently, several metasurfaces have been reported to achieve different EM functionalities [24–28]. These multifunctional metasurfaces are usually realized by properly arranging different sizes or geometries of meta-atoms on one layer, or stacking them on different layers. By changing incidence polarization or frequency, they can behave different EM functionalities. In addition, the reconfiguration technique has been also used to achieve multifunctional control of EM wave by constructing active metasurface [29–31]. By tuning the lump components or tunable materials, the active metasurface can dynamically generate different EM functionalities. Compared with the passive metasurface, the design of active metasurface is more complicated and also requires another biasing network, increasing system cost, and loss. Besides, most of the current multifunctional metasurfaces can only control EM waves in half space (either in the reflected or transmitted regime), it is still challenging to achieving a simultaneous control of reflection and transmission in one device. Apparently, in order to integrate the control of the reflected and transmitted wave, not only the efficiency and phase coverage must be considered at each mode, but also the mutual coupling between two modes cannot be ignored. Furthermore, it should be noted that the transmission efficiency of a single-layer transmissive metasurface has a low theoretical upper limit of 25% [32,33], so the multi-layer structures are generally employed to improve the efficiency [34,35]. Recently, the anisotropic multi-layer metasurfaces have been presented to realize full-space EM manipulation, which can respectively control the transmitted and reflected wavefront under two different orthogonal polarizations. Although these metasurfaces can achieve high efficiencies in both reflected and transmitted mode [36–41], the transmitted and reflected waves can be only manipulated at a single polarization.
In this paper, we propose a simple method to achieve the control of the transmitted and reflected wave based on the cascaded metasurface. By integrating the resonant and geometric phase cells, the designed metasurface can control the reflection wavefront in X-band under linear polarization incidence, while exhibit the polarization-conversion property and also reshape the transmission wavefront in C band under circular polarization (CP) incidence. Both the wave manipulation in the transmitted and reflected modes can be independently realized. More importantly, this metasurface behaves polarization-insensitive property in the reflection mode, and indicates anisotropic EM responses under the different CP waves in the transmitted mode. Through the specific design of phase distribution, the transmitted and reflected beam deflection (focusing) effects can be obtained within the shared aperture at two different frequency bands. We fabricated this metasurface and demonstrated its excellent beam manipulation performance in both the transmitted and reflected modes by experiment.
2. Theoretical design and analysis
Figure 1 shows the schematic model of the proposed metasurface that can achieve simultaneous control of the transmitted and reflected waves. This metasurface is composed of the resonant phase cells and geometric phase cells. By the independent control of the resonant and geometric phase distributions, our metasurface can manipulate the transmitted wave under CP incidence at λ1, while it operates in the reflection mode under illumination of LP wave at λ2. The detailed description of the meta-atom is given in the right inset of Fig. 1. It is constructed by three kinds of functional structure layers. The top layer is a reflection layer that adopts the square loop structure as the resonant phase cell. The loop width is w1 = 0.15mm, and the loop length of a is tuned from 0.5mm to 3.6mm for obtaining the gradient reflection phases. The bottom two-layer structure operates in the transmitted mode, which employs two layers of the split rings with the same orientation as the geometric phase cells. The parameters of the split ring are set as follows: the radius R is 6.8mm, the width w2 is 3.7mm, and the split angle α0 is 45°. By rotating the split ring structure, the transmission phase can be continuously tuned under illumination of CP waves, based on the Pancharatnam–Berry (PB) phase modulation principle [42]. In order to reduce EM cross-talk between the transmission and reflection layers, the filtering layer is inserted between them to make the transmitted CP wave pass through with low loss at λ1 and reflecting all the LP waves at λ2, respectively. This layer consists of a square patch with a length of l1 = 9.3mm inside and a square loop with a length of l2 = 11.5mm outside. All of the metallic patterns for the three functional structures are printed on one identical substrate made of F4B (dielectric constant εr = 2.65 and loss tangent δ = 0.003). The thicknesses of each substrate are set as h1 = 3.5mm, h2 = 3.5mm and h3 = 2.2mm, respectively. So the total thickness of the meta-atom is 9.2mm, and its period of p is 15mm.
Fig. 1 Schematic model of the cascaded metasurface and its meta-atom. This metasurface operates in a transmitted mode under the circularly-polarized incidence at λ1, while it behaves the reflection property under illumination of the linearly polarized wave at λ2. The meta-atom consists of three functional structure layers which are a reflection layer, a filtering layer, and two transmission layers, respectively.
According to the generalized Snell’s law, the special design of the resonant and geometric phase distributions would respectively result in the anomalous reflection and transmission. Their abnormal reflected and transmitted angles (θr and θt) could be derived using the following equations.
where θi is an incidence angle, λ0 is the free-space wavelength, and nt and ni represent the refractive indexes of the two media. The dΦ/dx indicates a phase gradient along the array. In the transmitted mode, the phase gradient distribution is obtained by the split ring structures with different rotation angles, and the proposed metasurface could manipulate the transmitted CP wave. The square loop structure with different sizes is utilized for generating the phase gradient distribution in the reflected mode, which can modulate the reflected beam. By independent design of each phase distribution in both transmitted and reflected modes, our metasurface is expected to achieve simultaneous control of the reflected and transmitted beams on the shared aperture.In order to investigate the transmission and reflection characteristics of the proposed metasurface, we use the CST Microwave Studio software package to simulate and optimize the element. For the transmitted mode, the LCP plane wave is incident onto the meta-atom, while it is illuminated by the LP wave in the reflected mode. The periodic boundary condition is set to the four sides of the element.
As Fig. 2(a) shows, the eight rotation angles of the split rings with an interval of 30° were chosen to exhibit the corresponding transmittance and phase coverage. It is seen that the incident LCP wave is converted to the RCP outgoing wave, and the transmission phase coverage can occupy the whole 360° between 6.1 and 6.3 GHz when the rotating angle is varied from 0° to 180°. The transmission amplitude reaches almost 0.8 for each of the rotating angle of the split ring structure. In the reflected mode, when changing the edge length of the square loop from 0.5 to 3.6 mm, the reflection phase shift of the meta-atom reaches almost 300° in the frequency band of 10.8-11.6 GHz where the near-unit reflection is generated, as seen in Fig. 2(b). The coupling level between the transmission and reflection layers is also discussed. For the transmitted mode, the rotating angle is fixed as β = 30° and the edge length a of the reflection layer is set as 0.5 mm, 3.1 mm and 3.6 mm, respectively. It is seen in Fig. 2(c) that there is a weak phase variation for the different edge lengths. In the reflected mode, the varying rotating angles of the transmission layer have almost no influence on the reflection amplitude and phase, as shown in Fig. 2(d). Therefore, it is considered that the cross-talk between the above two layers is very weak, which can be ignored in the design. In addition, the role of the filtering layer is studied in Figs. 2(e) and 2(f). It is obvious that there is almost no influence for the transmitted wave whether the filtering layer exists or not. However, it is very important for the reflection layer because it can significantly improve the reflection efficiency, assisting the reflection layer to achieve near-unit reflection.
Fig. 2 Transmission and reflection characteristics of the meta-atom. (a) Transmission amplitude and phase of the outgoing RCP wave for the proposed meta-atom under LCP incidence. The inset displays the cross-talk performance of the meta-atom. (b) Reflection amplitude and phase as a function of the edge length (a) of the square loop. (c) Transmission amplitude and phase variation under different values of a, when β is fixed as 30°. (d) Reflection amplitude and phase variation under different values of β, when a is fixed as 3.1mm. (e) Transmission amplitude with/without the filtering layer. (f) Reflection amplitude with/without the filtering layer.
By special design of the phase distribution for the proposed meta-atoms, the different EM functional devices could be created to operate in both reflected and transmitted modes. Here, full-wave simulation is carried out to investigate the phase control performance of the novel bidirectional deflector based on our metasurface. In the simulation, the deflector composed of 26 × 1 meta-atoms are adopted with periodic boundary condition set along the y-axis, which can significantly reduce the amount of calculation with the high accuracy remaining. Figure 3(a) shows the simulated electric field distribution of the proposed deflector under illumination of an x-polarized wave at 10.8 GHz. To observe the reflected wave more easily, only the reflection wave is illustrated in the upper region (z > 0 mm). In the lower region (z < 0 mm), the transmitted wave is very weak owing to the high reflectivity of the metasurface. With the modulation of the gradient square loop structures, the reflected wavefront is reconstructed, and there is an obvious deflection phenomenon occurring in the reflected mode. From the far-field radiation pattern exhibited in the inset of Fig. 3(a), it is seen that the reflected beam is redirected towards the angle of 29.6° that is in a good agreement with the theoretically calculated value (30°). Due to the polarization-insensitive design of the meta-particles, the similar deflection effect would be expected under the y-polarized incidence. Furthermore, the reflected phase profiles of all the square loop structures are given in Fig. 3(b). The fitted phase curve shows an excellent agreement with the ideal one as expected. For the transmitted mode, the designed deflector is illuminated by the normal LCP wave, and the transmission field distribution of the RCP wave is depicted in Fig. 3(c). It shows that the outgoing wave direction is obviously deflected from the normal, and its wavefront propagates towards the angle of 210.5°, complying with the predesigned value (210°), as seen in the inset of Fig. 3(c). When this metasurface is illuminated by the RCP wave, the LCP outgoing wave is generated with the beam direction redirected to the angle of 150° due to the chirality of the split ring structure, as shown in Fig. 3(d). In general, a LP beam can be regarded as a superposition of its circular components. So, it is expected that our metasurface could achieve CP beam splitting effect in the transmitted mode under LP incidence [43–46]. Figure 3(e) shows the fitted transmission phase profile of the rotating split rings, which also matches well with the ideal phase curve.
Fig. 3 Electric field distributions of the designed bidirectional deflector in the reflected and transmitted modes and their corresponding phase profiles. (a) The electric field distribution in the reflected mode at 10.8 GHz and (b) its corresponding phase profile. (c, d) The electric field distribution in the transmitted mode under LCP and RCP incidence at 6.1 GHz and (e) their corresponding phase profile in the transmitted mode. Insets schematically depict the far field radiation patterns in both two modes.
Furthermore, we still employ the designed meta-atoms to construct a bidirectional focusing lens that is numerically verified. Here, this meta-lens is composed of 26 × 26 meta-atoms with an aperture size of 390 mm. The focal length is respectively set as 200 mm in the transmitted mode and 300 mm in the reflected mode. Therefore, we can use 26 × 26 pixels to control the transmitted beam, while 104 × 104 pixels are applied for the reflected beam. In addition, it is worthwhile to point out that the actual lattice period of the reflected meat-atom is quarter of the unit period, which is far less than λ/2 in the reflected frequencies. So, no grating lobes would be generated in our metasurface. The beam focusing effects are examined by vector diffraction method using the phase parameters extracted in CST Microwave Studio. As Fig. 4(a) shows, the meta-lens placed at the position of z = 0 can converge all the outgoing RCP wave energy into the position of z = 200 mm. When it operates in the reflected mode, most of the reflected wave energy can be collected at the position of z = 300 mm, as seen in Fig. 4(b). Therefore, the proposed meta-lens can respectively realize beam focusing effect in both transmitted and reflected modes, and its focal length is well matched with the predesigned goal. The phase profiles are given in the insets of Figs. 4(a) and 4(b) reveal a good agreement between ideal phases and the fitted phases in both two modes, ensuring the good beam focusing performance.
Fig. 4 Beam focusing performance of the designed meta-lens in the transmitted and reflected modes. (a) The transmission intensity in the xz cross section. The inset shows the ideal focusing phase profile and its fitted phase curves by using 26 pixels. (b) The reflection intensity in the xz cross section. The inset shows the ideal focusing phase profile and its fitted phase curves by using 104 pixels.
3. Fabrication and measurement
To experimentally demonstrate the beam manipulation performance of the proposed metasurface, we fabricated a sample by using the low-cost printed-circuit-board technique. This sample is composed of 26 × 26 unit cells, occupying a total area of 390 × 390 mm2. The multilayer F4B boards are bonded together by the RO4403 films (ε = 3.38, h = 0.09 mm). The reflection measurement system is set up in a microwave anechoic chamber. As Fig. 5 shows, two LP horn antennas connected to a vector network analyzer are utilized as the transmitter and receiver, respectively. The sample and the transmitting horn antenna placed in front of it are fixed on the rotation equipment. When revolving the rotation equipment, the sample is always illuminated by the normal incident wave produced by the transmitting horn. The reflected wave for the (- 90° to + 270°) rotating angles can be received by the other horn antenna.
Fig. 5 Experimental setup of the far field radiation pattern scanning system used to characterize the beam deflection performance of the proposed metasurface.
Figure 6 shows the measured result of the sample in the reflected mode, which also includes the simulated result as the comparison. It is seen that there is an obvious beam deflecting phenomenon in the reflected mode. The main reflection peak is redirected to the angle of about 30° that agrees well with the simulated angle, as seen in Fig. 6(a). When changing the incidence polarization from x-pol to y-pol, the similar deflection performance can be obtained in Fig. 6(b). That means the sample can control the reflected wavefront and make the reflected beam deflected into the predesigned direction. In addition, this sample behaves the polarization-insensitive property in the reflected mode. It is still found that the beam deflection can be realized at both 10.8 GHz and 11.6 GHz, which indicates at least 0.8 GHz deflection bandwidth. When measuring the beam-control performance of the sample in the transmitted mode, the two LP horn antennas are replaced by a pair of RCP and LCP horn antennas, where the LCP horn antenna is adopted as the transmitter and the RCP one is the receiver. Both two CP horn antennas are placed at two sides of the sample.
Fig. 6 Measured and simulated beam deflecting results of the sample in the reflected mode. (a) x-pol incidence and (b) y-pol incidence.
Figure 7 depicts the simulated and measured radiation patterns at 6.1 GHz and 6.3 GHz. It is seen the sample can convert the incident LCP wave into the RCP outgoing wave, and deflect the transmitted beam to the angle of about 210° at both two frequency points. Both the simulated and measured deflection angles show a good agreement in the transmitted mode. It should be pointed out that the deflection angles decrease a little in both transmitted and reflected modes with the increase of frequency, which can be explained by Eq. (1) and Eq. (2). In addition, there are some deviations between the measured and simulated results, which may be due to the imperfect matching of the experimental environment with the simulated one. For instance, the ideal infinite uniform plane wave in the simulation is difficult to be realized by the horn antenna in the experiment, which may influence the transmitted and reflected field distribution. Part of the unexpected scattering wave energy from the testing bracket and rotation equipment may be directly redirected to the receiving horn, causing some scattering noises in the measurement. Moreover, the efficiency of the proposed cascaded metasurface is also studied. The relative loss of the reflection peak (relative to a metallic plate with the same dimension) measured at 10.8 GHz is 1.2 dB, while the transmission loss (relative to the incident beam) is about 2.76 dB at 6.1 GHz. The above experimental results have fully demonstrated our sample is able to simultaneously manipulate the reflected beam at 10.8 ~11.6 GHz and transmitted beam at 6.1~6.3 GHz. It is still noted that the higher efficiency may be expected by adopting more-layer transmissive metasurface [10,36], but it may increase the total thickness of the full-space EM metasurface.
Fig. 7 Measured and simulated beam deflecting results of the sample in the transmitted mode under LCP incidence.
4. Conclusion
In conclusion, we have designed a cascaded metasurface that can achieve the simultaneous control of the transmitted and reflected beams. By integrating the geometrical phase and resonate phase cells, the metasurface can independently manipulate the transmitted phase and reflected phase. We have numerically demonstrated its bidirectional beam deflecting and focusing functionalities at the microwave frequency region. The bidirectional beam deflector has been also fabricated and its deflecting performance has been experimentally verified. The good agreement between the simulated and experimental results is obtained, which demonstrates that the designed metasurface is able to reshape the transmitted and reflected wavefront into the predesigned deflection angle. Compared to the previous works, our metasurface not only can control the reflected beam at any LP modes but also behave diversified EM responses under different incident polarizations in the transmitted mode. This design reveals a promising way to achieve full-space control of EM wave and further promotes the integration of EM devices and systems.
Funding
National Natural Science Foundation of China (61475160, 61605213, 61775218).
Acknowledgments
Jianing Yang and Xiaoyu Wu contributed equally to this work.
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