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Abstract
Highly integrated planar meta-devices have attracted much attention in optics and communication, which can achieve multitasking wavefront manipulations at multiple frequencies. Integrated meta-devices can increase data capacity and functional diversity. However, further expansion of functions in integrated devices is still challenging. Here, a multilayer geometric phase metasurface is proposed. The functions are expanded via decoupling the resonance of different layer structures or decoupling its phase modulation. Under circularly polarized (CP) wave incidence, the proposed multifunctional metasurface performs four functions at three distinct frequencies. When left-handed circularly polarized (σ+ CP) waves at 8 GHz is incident from the lower half of space, deflection is realized. When a CP wave with different handedness at 10 GHz is incident from the upper half of space, focusing and diverging lenses are realized, respectively. When σ+ CP waves at 17 GHz is incident from the lower half of space, the reflective holography is realized. We designed, manufactured, and experimentally proved the multifunctional integrated full-space metasurface. The simulation and measurement results are in good agreement, verifying the four-function and tri-band metasurface design strategy. The method proposed in this paper opens up a new opportunity for increasing the information capacity and has application prospects in communication systems, optical storage, and image display.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a new technology, electromagnetic (EM) metamaterials have received extensive attention due to their unique EM properties [1–3]. Metasurfaces are the planar form of metamaterials. The transformation optics method can be used to design ideal anisotropic and non-uniform metasurfaces, allowing metasurfaces to arbitrarily control the characteristics of EM waves, such as propagation, polarization, absorbing, and scattering [4–8]. Therefore, the metasurface can realize some novel physical phenomena and novel functional devices such as the spin Hall effect [9], holographic imaging [10], illusion devices [11], and novel lenses [12–13]. Metasurfaces are more widely used in wireless communication applications because they have powerful EM wave manipulation capabilities, whose advantages are small size, low loss, and easy processing. In this way, metasurface provides a new way for multifunctional integrated system design [14–19].
With the rapid development of modern integrated systems, most electronic devices are becoming miniaturized and highly integrated. The research on multifunctional devices has attracted much attention. After designing a specific geometric phase or resonant phase unit cell, a function that satisfies a preset condition is obtained through a particular field distribution to manipulate the reflected or the transmitted wave. The metasurface loaded with tunable devices can also realize multi-functions, but it has some flaws, such as complicated design, high insertion loss, poor stability, and high cost. The composite two-dimensional multifunctional structure can realize multiple functions simultaneously, which meets the purpose of miniaturization, low loss, and promotes highly integrated systems.
In the early research stage on multifunctional metasurfaces, manipulating electromagnetic waves by metasurfaces is limited to half-space, and most devices can only work in reflection mode or transmission mode [20]. Subsequently, some devices with full-space EM wave control capabilities have realized two to three linear or circular polarization functions using a multilayer structure [18,19]. The above-mentioned multifunctional metasurfaces generally use frequency, polarization, and oblique incident angle independent characteristics to achieve functional expansion. These findings all provide a method for constructing multifunctional integrated optical devices on a single planar device.
This paper proposes a hybrid method in the microwave region to expand the functions of the integrated meta-atom under the high-efficiency circularly polarized (CP) wave normal incidence. The key of design is to suppress the crosstalk among the substructures working in the three frequency bands, including the crosstalk between the distinct structures in the different layers and the same layer. Thus, the independent control of the three groups of Pancharatnam-Berry (P–B) phases can be realized in the reflection and transmission modes. As shown in Fig. 1, by changing the incident direction of the CP wave, the metasurface can perform four functions at three frequencies in total. At f2=10 GHz, the designed metasurface realizes the beam focusing and divergence lens (F2 and F3) under CP wave incidence. In addition, the designed metasurface achieves deflection (F1) at f1=8GHz (-Z-direction) and realizes the hologram (F4) at f3=17GHz (-Z-direction). Finally, we fabricated a five-layer integrated metasurface and completed the near-field measurement, which verified the four functions designed in this paper. The experimental and simulation results show the excellent wavefront control ability of the multifunctional integrated meta-device, which may be widely used in microwave photonics.
Fig. 1. The schematics of the proposed four-functional metasurface. (a) The metasurface behaves as a beam splitter under the excitation of the left-handed circularly polarized (σ+ CP) wave incident from the lower half of space. The metasurface behaves as (b) transmissive focusing lens and (c) reflective beam diverging lens under excitations of σ+ CP and right-handed circularly polarized (σ- CP) waves incident from the upper half of space. (d) Reflective meta-hologram under the excitation of the σ+ CP wave incident from the lower half of space.
2. Meta-atom design
The design of the meta-atom is the key to realize the four-functional metasurface at three frequencies (f1, f2, and f3). In order to realize the full-space kaleidoscope wavefront control of electromagnetic waves, a multilayered resonant structure is adopted, as shown in Fig. 2. The multilayered meta-atom consists of five copper layers with a thickness of 0.017 mm. The five copper layers are separated by four F4B substrates, in which the thickness of the two top layers is the same (d1 = d2 = 2 mm), and the thickness of the two bottom layers is the same (d3 = d4 = 1 mm). Layers I, II, and III are composite sandwich structures, and layers I and III are used as quarter-wave plates. The role of the oblique bar of layer II is equivalent to a linear polarizer, which determines the transmission and reflection of the meta-atom at f1. The layers I, II, and III are used as a resonant phase unit through the geometric phase distribution to achieve the functions F2 and F3 under CP wave incidence. When the CP wave is incident from below, the split ring resonator (SRR) and the bar of layer V realize the corresponding functions F1 and F4 through the geometric phase distribution. The design of layer IV follows the principle of frequency selective surface (FSS) design, which is used to distinguish reflection and transmission modes at different frequencies. Since the structure of the upper three layers and layer V are rotated to obtain phase changes, the FSS structure is designed as a circular groove to eliminate the relative displacement between layers. The FSS structure serves as the reflector of layer V to improve the reflection amplitude of the CP wave at f1 and f3. Meanwhile, the FSS structure provides an aperture-coupling for achieving high-efficiency transmission at f2 when CP wave illuminated from the above.
Fig. 2. Geometry of the proposed meta-atom. (a) Perspective view of the meta-atom composed by stacking five copper layers and four F4B substrates alternately. (b) I and III layers are two S-shaped structures. (c) The middle oblique bar. (d) A circular-slot frequency selective surface (FSS) structure. (e) Split ring resonator (SRR) and bar rotate independently. Some geometrical parameters are fixed as: p = 10 mm, d1 = d2 = 2 mm, d3 = d4 = 1 mm, r1 = 4.5 mm, r2 = 3.5 mm, w = 2 mm, l = 9 mm, a = 2.5 mm, b = 9 mm, r3 = 3 mm, r4 = 3.4 mm, c = 0.5 mm, d = 5 mm, r5 = 3.8 mm, r6 = 4 mm, k = 0.3 mm.
In order to better characterize the reflected and transmitted properties of the meta-atom, the full-wave simulations are calculated in the Computer Simulation Technology (CST) Microwave Studio commercial packet. In addition, the unit-cell boundaries are applied in the x and y directions, and Floquet ports are set in the + Z and -Z directions. At f2 (10 GHz), Figs. 3(b) and (c) show the electric field distributions of layers I-V cutting at X-O-Y plane, under the illumination of σ+ CP and σ- CP incident wave toward the −Z direction, respectively. And Figs. 3(f) and (g) show the electric field distribution of layers I-V, under the illumination of σ+ CP and σ-CP incident wave toward the + Z direction, respectively. As illustrated in Figs. 3(b) and (f), under the σ+ CP irradiation, the electric field strength of the layers I-IV is stronger, which means that a good transmission window appears at f2. As shown in Figs. 3(c) and (g), under the σ- CP irradiation, the electric field strength of the layers I-II is stronger, and the electric field strength of the other layers is weaker, which means that at f2, the σ- CP wave is basically completely reflected. Figure 3 also shows the electric field distribution of f1 (8 GHz) and f3 (17 GHz) under the illumination of σ+ CP incident wave. Since the SRR and bar structures in layer V are both anisotropic structures, f1 and f3 exhibit the same electric field distribution effect under σ- CP wave incident, there is no repetition here. It can be seen from Figs. 3(a) and (e) that the SRR structure of layer V is the main working element at f1. It can be seen from Figs. 3(c) and (g) that the bar structure of layer V is the main working element at f3. All in all, meta-atom shows good isolation in the frequency domain.
Fig. 3. Schematic of the electric field distributions on every layer of meta-atom. (a, e) The electric field distribution of layers I-V illuminated by the σ+ CP wave at 8 GHz toward the -Z and + Z direction, respectively. (b, f) The electric field distribution of layers I-V illuminated by the σ+ CP wave at 10 GHz toward the -Z and + Z direction, respectively. (c, g) The electric field distribution of layers I-V illuminated by the σ- CP wave at 10 GHz toward the -Z and + Z direction, respectively. (d, h) The electric field distribution of layers I-V illuminated by the σ+ CP wave at 17 GHz toward the -Z and + Z direction, respectively.
According to the geometric phase theory, the phase coverage from 0° to 360° can be achieved by independently rotating each structure of the meta-atom. Here, the rotation angle of the SRR of layer V is q1, the rotation angle of the bar of layer V is q3. The upper three layers (I-III) are simultaneously rotated, and the rotation angle is defined as q2. In the reflection mode, the reflection phases $\varphi _{\;1\;\; +{+} }^r$, $\varphi _{2\;\;\textrm{ - }\;\textrm{ - }}^r$, and $\varphi _{3\;\; +{+} }^r$ are all obeyed Dφn = 2σnqn (n = 1, 2, 3, σ1,3 = 1, σ2 = -1). In the transmission mode, the transmission phase $\varphi _{2\;\;\textrm{ - } + }^t$ obeys Dφ2 = 2q2. As shown in Figs. 4(a)-(d), the reflection and transmission phase have a phase shift of 2qn as the rotation angle qn changes from 0° to 180°. The overall structure changes the phase in reflection and transmission modes while maintaining a high amplitude, which shows that the FSS structure of layer IV has a good isolation effect, which lays a good foundation for the proposed metasurface to control EMs in different spaces independently. At the same time, the SRR and the bar structures of layer V work at two far apart frequency points, avoid coupling between structures. Two merits mentioned above are the keys to realized frequency multiplexing at f1, f2, and f3.
Fig. 4. Simulated EM response of each independent structure of the meta-atom by rotating. The q1 (the SSR of layer V), q3 (the bar of layer V), and q2 (the top three layers I-III) are individually rotating within the range of the 0°-180° with eighteen 10° rotation steps when keep the other two angles at 0°. (a) The reflection amplitude $|{{r_{1\;\; +{+} }}} |$ and phase $\varphi _{\;1\;\; +{+} }^r$ as a change of q1 when illuminated by the σ+ CP wave from the -Z direction at 8 GHz. (b) The reflection amplitude $|{{r_{3\;\; +{+} }}} |$ and phase $\varphi _{\;3\;\; +{+} }^r$ as a change of q3 when illuminated by the σ+ CP wave from the -Z direction at 17 GHz. (c) The reflection amplitude $|{{r_{2\;\;\textrm{ - }\;\textrm{ - }}}} |$ and phase $\varphi _{2\;\;\textrm{ - }\;\textrm{ - }}^r$ as a change of q2 when illuminated by the σ- CP wave from the + Z direction at 10 GHz. (d) The transmission amplitude $|{{t_{2\;\; -{+} }}} |$ and phase $\varphi _{3\;\;\textrm{ - } + }^t$ as a change of q3 when illuminated by the σ+ CP wave from the + Z direction at 10 GHz.
3. Function realization and experimental verification
The finite-difference time-domain (FDTD) technique is employed to analyze the near-field and far-field characteristics of the four-functional metasurface. The phase difference between the two propagation paths is initially zero when the EM wave irradiates on the surface of the meta-atom at the incident angle qi. However, when there is a phase gradient (constant) at the interface, the phenomenon of anomalous deflection occurs. As for the function F1 (realized at f1), according to the generalized Snell's law of reflection, the phenomenon of anomalous deflection can be expressed as [21]:
Under the σ+ CP wave vertically incident (θi = 0), the electric field distribution of the designed metasurface is simulated, and the path distribution of the reflected wave is obtained in the lower half of the space region. As shown in Fig. 5(a), it can be seen that there is a clear difference between the propagation paths of the incident and reflected EM waves. There is a certain angle between the incident and reflected EM waves, which indicates that anomalous deflection occurs at the interface of the metasurface. Figure 5(b) shows the far-field pattern at f1 (8 GHz). Since there is a phase gradient in the X-axis direction of the designed metasurface, the wave vector of the reflected wave is generated in the X-axis direction so that the anomalous deflection angle is generated in the + X-axis direction. The angle of deflection is consistent with the theory.
Fig. 5. Simulated results in the reflected mode under σ+ CP incident wave at 8 GHz: (a) Three-dimensional (3D) far-field radiation pattern. (b) The simulated electric field distribution on the X-O-Z cutting plane for the incidence of -Z-direction. (c) The simulated and experimental measured far-field polar map. (d) The -Z-direction picture view of the sample.
In the experiment, we used two σ+ CP horn antennas as transmitting and receiving antennas, respectively. The sample and the transmitting horn antenna are fixed on a rotatable turntable, while the receiving antenna remains stationary. As shown in Fig. 5(c), the far-field polar plot of the experimental and simulation results can identify the abnormal reflection angle. The simulated maximum efficiency value is 92%, and the measured maximum efficiency value is 88%. Both the simulated and experimental abnormal reflection waves are deflected to about 30 degrees, which is consistent with the theoretical value. As shown in Fig. 5(d), a multilayer metasurface is fabricated, consisting of 50 ´ 50 elements with a total size of 500 ´ 500 mm2.
At f2 (10 GHz), the proposed metasurface works in reflection and transmission modes simultaneously, realizing a dual-function meta-lens (F2 and F3). Under the incidence of σ+ CP, the meta-lens is a transmissive focusing lens. On the contrary, under the incidence of σ- CP, the meta-lens is a reflective diverging lens. In addition, the geometric phase has a helicity-dependent response to incident EMs with different CP states, which results in the two functions that cannot be independently controlled under σ+ CP and σ- CP incidence. In the design, it is only necessary to arrange the transmission phase φ (x) related to the focus lens function (F2) under the incidence of the σ+ CP wave, as shown in Fig. 6(c). When the incident EM wave is switched to the σ- CP wave, the reflected phase is precisely the opposite of the transmitted phase, which is -φ (x). In this way, the diverging lens function (F3) is realized. In order to realize the two functions (F2, F3), the transmission phase $\varphi _{2\;\;\textrm{ - } + }^t$ and the reflection phase $\varphi _{2\;\;\textrm{ - }\;\textrm{ - }}^r$ should satisfy the following distributions [19]:
Fig. 6. The proposed multifunctional metasurface behaves as a transmissive focusing lens under the excitation of σ+ CP waves. (a) FDTD simulated electric field distribution on the X-O-Z plane at the low-half region of the metasurface at f2 = 10 GHz. (b) The top-view picture of the fabricated sample. (c) Phase distribution of the designed focus lens. (d) The simulated and measured normalized |E|2 distributions at the X-O-Z plane.
First, we examine the F2 (transmissive focusing lens) of the sample. The two CP horn antennas act as transmitter and receiver, respectively. And they are connected to the vector network analyzer. The σ+ CP horn antenna is placed in front of the sample and illuminates the meta-lens vertically. Because the sample has rotational symmetry, in order to simplify the measurement, the electric field intensity is measured along the Z-axis (X=0). According to the electric field intensity in the z-direction in Fig. 6(d), the focal length of the focusing lens can be found. Figure 6(a) shows the electric field intensity distribution on the X-O-Z plane, which is calculated by FDTD simulation. The simulation results (Z=296 mm) and measurement (Z=303 mm) are consistent with the theoretical values, and the focus points appear near Z=300 mm. In addition, the full width at half maximum (FWHM) is used to illustrate the sizes of the focal spots, as shown in Fig. 6(b). The simulated and experimental results of the FWHM are 190 mm and 235 mm at 10 GHz, respectively. According to the work efficiency calculating method of the lens in [22], the absolute efficiency of the focusing lens is 87% in measurement and 90% in simulation.
Next, we experimentally characterize the divergence performance of the multifunctional metasurface in the reflection mode. At this time, the σ- CP wave is used as an excitation wave. The experimental procedure is similar to the transmission focusing lens, but the two CP horn antennas should be placed on the same side of the sample. Figure 7(a) shows the simulated electric field distribution at 10 GHz. The maximum simulated and measured efficiencies of the reflective diverging lens are 88% and 86%, respectively. The electric field intensity was measured along the X-axis at Z=100 mm, 150 mm, and 200 mm, as shown in Fig. 7(b). The consistency between the numerical and measured results proves that the divergence effect is excellent.
Fig. 7. Performances of the designed beam diverging lens in the reflection mode under the excitation of the normally incident σ- CP wave. (a) Simulated electric field distribution at 10 GHz on the X–O–Z plane. (b) The measured normalized |Ex|2 distributions at Z = 100 mm, 150 mm, and 200 mm.
Meta-hologram is an imaging technique via recording the phase and amplitude profile to reappear the objects [23–28]. According to the recording method, holography could be classified into three types: one is a phase and amplitude holography. It is original holographic imaging and has a higher imaging quality and a simpler calculation process. One is amplitude-only holography, and it is limited in imaging quality and efficiency. The other is phase-only holography, which has relatively high-power efficiency so has a broad application prospect. At f3 (17 GHz), the proposed metasurface works in reflection mode, realizing reflective meta-hologram (F4). We use the Rayleigh-Sommerfeld diffraction theory to calculate the phase profile on the metasurface. Due to the absence of amplitude information, iteration or optimization is necessary. Here, Gerchberg–Saxton algorithm is utilized to achieve high-quality imaging. We assume there is a virtual symbol on the imaging plane with a distance of d=350 mm from the metasurface. Firstly, the superposition of the fields radiating by pattern can be expressed as:
The virtual imaging pattern covers an area of 480×480 mm2. The imaging pattern covers an area of 300×300 mm2 with a distance of 380 mm away from the metasurface at 17 GHz. Based on MATLAB convenient Fourier transform, we use homemade code to calculate the phase profile on SLM, showed in Fig. 8(b). To compare the imaging efficiency of complex-amplitude hologram and phase-only hologram, the calculated scattered fields of complex-amplitude and phase-only hologram are showed Fig. 8(c)-(d). It can be seeing the complex-amplitudes hologram has a sharp outline, evenly E-field distribution, and the background noise points are well suppressed. However, its imaging efficiency is low to 0.5, which is obviously lower than 0.98 the efficiency of the phase-only hologram. In 3D full-wave simulation, due to our pixel is subwavelength, the change gradient of geometric parameters is small. Hence, the coupling of different adjacent units is negligible. Simultaneously, the decoupling effect between layers is also negligible. The simulated model is constructed according to the PB phase. An σ+CP plane wave illuminates on the metasurface, and E-Fields monitors are set to record the E-field intensity distribution. Figure 8(d) shows the simulation results, showing that the proposed metasurfaces reconstruct the desired images at the desired frequency and distance. In order to experimentally verify the performance of the designed meta-holography, the printed circuit board technology was utilized in the fabrication process, and a prototype has been fabricated, as shown in Fig. 8(f). The experiment is performed in an anechoic chamber showed in Fig. 8(f). The radiation antenna is 1.5 m away from the metasurface and connects to a vector network analyzer via low-loss coaxial cables to radiating σ+CP plane wave. We fixed the fabricated samples at the center of the rotate stage. A y-polarization probe is moved to record the field intensity distribution information. Corresponding holographic images were obtained, as shown in Fig. 8(f). Here, the signal-to-noise ratio (SNR) is used to illustrate the imaging quality. SNR is defined as the average intensity ratio in the pattern region to the average intensity of background noise whose sampling area is the whole rectangular region (480×480 mm2) apart from the pattern region. The SNR ratio calculated from the experimental results is 89.1, which means high imaging quality. The measured results are agreed well with theoretical results calculated by CST.
Fig. 8. Holographic imaging. (a) The imaging pattern. (b) The calculated distribution of the phase of the phase-only hologram on SLM at 17 GHz. (c) The imaging effect of the complex-amplitude hologram of the pattern. (d) The imaging effect of the phase-only hologram of the pattern. (e) The measured E-Field intensity distributions on the image plane. (f) Microwave hologram measure stage.
4. Conclusion
The paper shows a design method of multifunctional integrated metasurface to manipulate CP waves at three independent frequencies. The meta-atom consists of five-layer structures, and the crosstalk between the structures is negligible. By rotating the corresponding resonator, a full 2π PB phase modulation at three frequencies can be achieved. We use different phase arrangements to achieve various functions. The multifunctional metasurface proposed in this paper works in reflection and transmission modes. The simulation demonstrates beam deflection, focusing, diverging, and reflective holography functions of the metasurface in the microwave region. The four-function integrated metasurface has been manufactured and experimentally verified. In summary, we provide a way to expand the full-space functions in different frequency bands, which has advantages in highly integrated, easy manufacturing, and flexible polarization design. The designed multifunctional integrated metasurface has application prospects in metalens, beam splitters, holograms, and communications systems.
Funding
National Natural Science Foundation of China (51802349, 61801508, 61801509, 61971435, 61971437, 62101589).
Disclosures
The authors declare no conflicts of interest.
Data availability
The datasets presented in this paper are available from the corresponding author upon reasonable request.
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