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Abstract
Multiform electromagnetic beams (multi-direction, multi-polarization, multi-frequency, and multi-beam) generated by ultrathin metasurfaces show promising prospects in multiple optical traps, modern communication systems, and identification in complex environments. However, their application is limited by their inability to generate desired multiform beams simultaneously. Here, a multifunctional surface using a polarization selection structure and integrated electric and magnetic structures is proposed to solve the above problem. This surface is composed of three layers with weak coupling that can achieve different quasi-nondiffracting beams. The top and bottom layers are reflective surfaces that can reflect two different incident waves to generate two types of quasi-non-diffracting beams. The middle layer is a transmissive surface that can transmit another incident wave to generate the third type of quasi-non-diffracting beams. For verification, the surface was fabricated and tested. The results of a full-wave simulation and measurements revealed that three different forms of quasi-non-diffracting beams could be generated by the proposed surface.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic metasurfaces, which are two-dimensional structures formed by arranging meta-atoms in a periodic or quasi-periodic order on an ultrathin surface, have been extensively investigated in the fields of optics and microwaves. Owing to attributes such as low profiles, low losses, easy fabrication, and unprecedented wave-front controlled capability, metasurfaces have been applied to realize perfect anomalous refraction and reflection [1,2], polarization manipulation [3–6], perfect absorption [7], flat optics [8], spin control [9–11], asymmetric transmission [12] and multi-beams [13]. In particular, novel beams generated by metasurfaces to satisfy special requirements have attracted considerable attention in recent years, such as nondiffracting beams [14–16], three-dimensional spatially curved beams [17], vortex beams [18,19], and airy beams [20,21]. Among them, the non-diffracting beam possesses the remarkable property of an extremely narrow beam radius that is almost unaltered in the propagating path. By restraining diffraction to improve beam directivity, the non-diffracting beam has been applied in point-to-point data transmission [22], near-field detection and imaging [23], and communication [24].
Several methods have been proposed to generate non-diffracting beams using metasurfaces [25–27]. However, all these methods have only produced a single beam radiated directly from the surface. Although efficient phase and polarization control metasurfaces have been demonstrated [5,6], only pure reflection or transmission can be realized. An asymmetric electromagnetic wave transmission structure has been developed [12]. However, there are few such structures with attributes such as frequency selectivity, polarization control, and the required reflection and transmission phase shifts. Thus, it is worth researching approaches that will allow single surfaces to meet complex and diverse demands. Although a reconfigurable metasurface can achieve diverse electromagnetic functions, it cannot switch from one function to another instantaneously and requires additional active components such as tunable diodes, which increases the cost and loss of the system, and may even cause potential electromagnetic coupling interference [18,28–30]. Passive multifunctional surfaces without active devices can simultaneously realize different functionalities. Several passive multifunctional metasurfaces have been proposed in recent years, yet four or more layers of surface elements are required for good matching, which increases fabrication costs [31–33]. In addition, the multifunctional properties of these devices are designed only for the reflection and transmission of plane waves. Therefore, further research is needed to obtain a multifunctional metasurface with fewer layers for beam shaping.
In this study, we propose a method for designing multiform beams using a single metasurface. As a proof of concept, a three-layer ultra-thin metasurface with a size of 200 mm × 200 mm fabricated by a printed circuit board (PCB) was designed to operate in the microwave frequency band. Each layer of the metal patch on the surface was composed of square rings and cross rectangular patches with polarization selection properties. The metasurface can simultaneously generate three different forms of quasi-non-diffracting beams with reflection modes in the front and rear of the surface and transmission through the surface. In particular, these functions remained independent. Subsequently, the properties of the metasurface were determined, and the performance of the design was validated.
2. Theoretical concept and meta-atom analysis
In order to analyze the working mechanism of the proposed multifunctional metasurface, which exhibits frequency selectivity, selective polarization, a working band, and reflection and transmission phase control, the scattering parameters that vary with the structure of a meta-atom were utilized:
Because the designed surface does not produce cross polarization, the four scattering matrices of the surface are written as
A schematic diagram of the multifunctional metasurface is shown in Fig. 1. It is assumed that regions 1 and 2 are in the front and rear of the surface, respectively. The proposed metasurface exhibits functions including reflection in region 1 (F1, f1 = 17 GHz), reflection in region 2 (F2, f1 = 17 GHz), and transmission from region 2 to region 1 (F3, f2 = 14 GHz).
Fig. 1. Schematic illustration of the multifunctional metasurface. In region 1, the red beams denote the reflective beams of x-polarization at the frequency of f1. In region 2, the green beams denote the reflective beams of x-polarization at the frequency of f1. From region 2 to region 1, the purple beams denote the transmissive beams of y-polarization at the frequency of f2.
The corresponding scattering parameters whose values are dependent on the meta-atom structure of the metasurface should have the following characteristics: At ${f_1}$, when the x-polarized incident wave is reflected in region 1, $|{S_{11}^{xx}} |$ is greater than $|{S_{21}^{xx}} |$, and the phase range of $S_{11}^{xx}$ is greater than 300°. At ${f_1}$, when the x-polarized incident wave is reflected in region 2, $|{S_{22}^{xx}} |$ is greater than $|{S_{12}^{xx}} |$, and the phase range of $S_{22}^{xx}$ is more than 300°. It should be noted that ${S_{11}}$ can be completely different from ${S_{\textrm{22}}}$, i.e., the reflection characteristics of incident waves in different regions can be controlled independently. At ${f_2}$, when the y-polarized incident wave propagates from region 2 to region 1, $|{S_{22}^{yy}} |$ is much less than $|{S_{12}^{yy}} |$, and the phase range of $S_{12}^{yy}$ is more than 300°.
To satisfy the above requirements, a meta-atom composed of three copper layers using a polarization selection structure and integrated electric and magnetic structures was utilized. First, a cross patch with two orthogonal arms, which can control two orthogonally polarized electromagnetic waves by the length of its arms, was selected. However, this structure can work only in the transmission mode. Second, to enhance the functionality of the reflection mode of the meta-atom, a grating structure was considered. In addition, to achieve an asymmetric function, the grating structure was placed in the middle layer, which implies that the meta-atom can independently reflect the x-polarized wave from both sides. The improved structure possessed two working modes: asymmetric reflection of x-polarized electromagnetic waves and transmission of y-polarized electromagnetic waves. However, the three-layer structure could not satisfy the requirements of transmissive and reflective phase coverage. Third, a square ring promoting the magnetic response was added to the meta-atom, which resulted in a significant improvement in both the transmissive and reflective phase coverage.
The proposed meta-atom of a multifunctional metasurface is illustrated in Fig. 2(a). At a reflective frequency of 17 GHz and transmissive frequency of 14 GHz, the meta-atom consists of three copper layers with a thickness of 0.01 mm, which are separated by two dielectric plates with a thickness of 1.52 ${\varepsilon _\textrm{r}} = 3.48,\tan \delta = 0.009$. The detailed geometric parameters are illustrated in Figs. 2(b)–2(d), where the tunable parameters are ${a_1}$, ${a_3}$, and b, and the fixed parameters are p = 6.6 mm, h = 3.04 mm, ${d_1} = {d_2} = $ 1.8 mm, ${d_3} = $ 0.3 mm, and ${a_2} = $ 6 mm.
Fig. 2. Schematic configuration of the meta-atom composed of three layers of copper patches with two dielectric plates between the copper patches. (a) Perspective view of the meta-atom. (b) Top layer of the meta-atom. (c) Middle layer of the meta-atom. (d) Bottom layer of the meta-atom.
To further understand the benefit of the designed meta-atom, we compared the performances of two types of structures in the absence and presence of a square ring. The scattering properties of the two structures were analyzed using a full-wave simulation with periodic boundary conditions. First, considering x-polarization at 17 GHz, Figs. 3(c) and 3(d) show the amplitude and phase of $S_{11}^{xx}$ as a function of ${a_1}$ or ${a_3}$ in the absence and presence of the square ring. In this simulation, b is fixed at 4 mm and ${a_1}$ is equal to ${a_3}$. For the first structure shown in Fig. 3(a), when ${a_1}$ is larger than 4.5 mm, the high reflection effect of the meta-atom is significant. At this time, $|{S_{11}^{xx}} |$ is greater than –3 dB. When ${a_1}$ is less than 4 mm, the current will flow on the orthogonal arm b, resulting in $|{S_{11}^{xx}} |$ less than –3 dB. For the second structure shown in Fig. 3(b), by adding a rectangular ring, the number of strips along the x-polarized direction of the incident wave is increased, which restrains the effect from the cross-arm in the y-direction. It can be seen that the second structure achieves high reflection in a certain range of ${a_1},$ and the reflective phase range is more than 310° with a –3 dB reflected amplitude ($|{S_{11}^{xx}} |$).
Fig. 3. Transmission and reflection performance of the two proposed structures. The schematic structure of meta-atoms in the (a) absence and (b) presence of the square ring. The reflection coefficient as a function of the patch length (c)${a_1}$ or (d)${a_3}$ of the corresponding meta-atoms. (e) and (f) The transmission phase as a function of the patch length b of the corresponding meta-atoms.
Furthermore, considering y-polarization at 14 GHz, Figs. 3(e) and 3(f) show the amplitude and phase of $S_{\textrm{21}}^{yy}$ as a function of the patch length b in the absence and presence of a square ring. In this case, ${a_1}$ and ${a_3}$ were fixed at 4 mm. For structure 1, $\varphi _{21}^{yy}$ changes slightly when b is greater than 2 mm and less than 4 mm. Only when b is greater than 4 mm does $\varphi _{21}^{yy}$ clearly change. This is because structure 1 can excite the additional resonance through an equivalent capacitance structure formed by the adjacent patch when the size of patch b is relatively large, for instance, greater than 4 mm. However, for the entire range of b, the phase range is only approximately 200° when the transmitted amplitude ($|{S_{\textrm{21}}^{yy}} |$) is greater than –3 dB, which does not satisfy the requirements of the phase range. For structure 2, the added rectangular frame structure can excite the ring current, which is equivalent to the magnetic structure. When b is less than 4 mm, the added rectangular frame can form a resonant loop, which expands the covering range of the phase effectively. Structure 2 achieves an over 320° phase range of the transmitted amplitude of −3 dB.
To illustrate the reflective and transmissive performance of meta-atoms, the meta-atom with parameters ${a_1}$ = ${a_\textrm{3}}$ = 4 mm and b = 4 mm was studied. Figures 4(a)–4(c) show the distribution of electric current density on the top, middle, and bottom layers excited by incident waves polarized in the x-direction. From the figure, it can be seen that the electric current density on the top layer is obviously high and that on the bottom layer is relatively low, which demonstrates that the incident wave of x-polarization is mainly reflected. It is also known that the size change of the meta-atom in the bottom layer has little effect on the top layer, which implies that the two layers are functionally independent. Figures 4(d)–4(f) show the distribution of electric current density on the top, middle, and bottom layers excited by incident waves polarized in the y-direction. It can be seen that the current densities on the middle and bottom layers are relatively higher than that on the top layer, which demonstrates that most of the energy of the incident wave of y-polarization is transmitted.
Fig. 4. Distribution of the electric current density of the meta-atom shown in Fig. 3(b) in different cutting planes. (a) The top, (b) middle, and (c) bottom layers excited by the incident wave of x-polarization. (d) The top, (e) middle, and (f) bottom layers excited by the incident wave of y-polarization.
The isolation of functions ${F_1}$, ${F_2}$, and ${F_3}$ will be discussed below. Because the degree of coupling between reflection modes ${F_1}$ and ${F_2}$ is low, we focused on the coupling between ${F_1}$ and ${F_3}$, and ${F_2}$ and ${F_3}$. Taking the reflection mode as an example, the reflection coefficient of the meta-atom is obtained by assuming that ${a_1}$ and b are constant. However, for different meta-atoms in a metasurface, b is different; therefore, it is necessary to analyze the influence of the size of b on the reflection and sizes of ${a_1}$ and ${a_3}$ on the transmission. Figures 5(a) and 5(b) show the phases and amplitudes of the reflection with varying ${a_1}$, ${a_3}$, and b when the incident wave is x-polarized, and Figs. 5(c) and 5(d) show the simulation with the incident waves of y-polarization. From the results, it can be seen that the phases of the reflection exhibit little change with changes in the size of b, and the phases of the transmission exhibit little change with changes in the size of ${a_1}$ or ${a_3}$. Meanwhile, the amplitudes of the reflection and transmission were greater than −3 dB over the entire range. The above analysis proves good independence between different functions, which ensures good reflectivity and transmittance.
Fig. 5. Isolation analysis of the proposed meta-atom. (a) and (b) The reflection phase and amplitude distributions as a functions of ${a_1}$ or ${a_3}$ and b. (c) and (d) The transmission phase and amplitude distributions as a function of ${a_1}$ or ${a_3}$ and b.
3. Design of the multifunctional metasurface and experimental verification
A metasurface containing 30 × 30 of the above designed meta-atoms with a total size of 200 mm × 200 mm was designed. Figure 6 shows the coordinate schematic of beams generated by a metasurface, and further information about the metasurface is given below.
Fig. 6. Coordinate schematic of beams generated by the metasurface. (At ${f_1}$ = 17 GHz, the incident wave of x-polarization from region 1 or 2 is reflected to produce the quasi non-diffracting beam ${F_1}$ or ${F_\textrm{2}}$. At ${f_2}$ = 14 GHz, the incident wave of y-polarization from region 2 is transmitted to generate double quasi non-diffracting beams in region 1 ${F_\textrm{3}}$.)
The results highlighted in the previous section revealed that each layer of this surface can realize different beams. To realize different quasi-non-diffracting beams, the phase distribution of each layer should first be obtained.
For reflection in region 1 (${F_1}$), the x-polarized wave at 17 GHz was employed for excitation in region 1. The surface was placed in the xoy plane, which was centered at (0, 0, 0). The excitation source was located at –15 cm, 0 cm, and 15 cm. The designed reflective angle was ($\theta = {0^0}$, $\varphi = {90^0}$), and the phase distribution $\Phi _{11}^{xx}(x,y)$ of the surface was
For reflection in region 2 (${F_2}$), the x-polarized wave at 17 GHz was employed for excitation in region 2. The excitation source was located at the position (−15 cm, 0, −15 cm). The designed direction of the reflective beam was ($\theta = {150^0}$, $\varphi = {90^0}$), and the phase distribution of the surface was
For transmission from region 2 to region 1 (${F_3}$), the y-polarized wave at 14 GHz was employed for excitation in region 2. The excitation source was located at the position (0, 0, and –20 cm). The designed directions of the transmission beams were (${\theta _1} = {30^0}$, $\varphi = {90^0}$) and (${\theta _2} = {30^0}$, $\varphi = {270^0}$), and the phase distribution $\Phi _{12}^{yy}(x,y)$ of the surface was
Fig. 7. Phase distributions of the three layers: (a) phase $\Phi _{11}^{xx}$, (b) phase $\Phi _{22}^{xx}$, and (c) phase $\Phi _{12}^{yy}$.
The size of a1 of each meta-atom in the top layer of the surfaces was determined by the phase distribution $\Phi _{11}^{xx}(x,y)$ for ${F_1}$. Similarly, the sizes of a3 and b of each meta-atom in the bottom and middle layers of surfaces was determined by the phase distribution $\Phi _{22}^{xx}(x,y)$ and $\Phi _{12}^{yy}(x,y)$ for reflection in regions 1 for ${F_2}$ and ${F_3}$.
Full-wave simulations of metasurfaces excited by different sources were performed using CST Microwave Studio. for ${F_1}$, Figs. 8(a) and 8(b) show the amplitude distributions of the normalized electric fields in the z = 300 mm and x = 0 mm planes at 17 GHz. From Fig. 8(a), it can be seen that there is a narrow spot in the central region, which represents a reflective beam confined in a narrow area. The amplitude distributions of the normalized electric fields at 16, 17, and 18 GHz are shown in Figs. 8(c)–8(e), respectively.
Fig. 8. Full-wave simulation results of F1. (a) and (b) The normalized amplitude distributions of the electric fields in the xoy plane at z = 300 mm and yoz plane at x = 0 mm at 17 GHz. (c)–(e) The normalized amplitude distributions of the electric fields in the xoy planes at z = 200, 300, 400, 500 mm, and yoz plane at x = 0 mm from 16 to 18 GHz with a step of 1 GHz.
For F2, Figs. 9(a) and 9(b) show the amplitude distributions of the normalized electric fields in the z = 300 mm and x = 0 mm planes at 17 GHz. A narrow spot can be seen on the left in Fig. 9(a), and an oblique beam reflected by the surface is shown in Fig. 9(b). The amplitude distributions of the normalized electric fields at 16, 17, and 18 GHz are shown in Figs. 9(c), 9(d), and 9(e), respectively. It can be observed that the beam propagates in the designed direction.
Fig. 9. Full-wave simulation results of F2. (a) and (b) The normalized amplitude distributions of the electric fields in the xoy plane at z = 300 mm and yoz plane at x = 0 mm at 17 GHz. (c)–(e) The normalized amplitude distributions of electric fields in the xoy planes at z = 200, 300, 400, 500 mm, and yoz plane at x = 0 mm from 16 to 18 GHz with a step of 1 GHz.
For F3, Figs. 10(a) and 10(b) show the normalized amplitude distributions of the electric fields in the z = 200 mm and x = 0 mm planes at 14 GHz. It is obvious that the two transmission beams propagate along two oblique directions. From Fig. 10(a), it can be seen that there are two narrow bright spots in the plane. The normalized amplitude distributions of the electric fields at 13, 14, and 15 GHz are shown in Figs. 10(c), 10(d), and 10(e), respectively. From the figures, it can be seen that good transmission performance is achieved at 13 and 14 GHz.
Fig. 10. Full-wave simulation results of F3. (a) and (b) The normalized amplitude distributions of the electric fields in the xoy plane at z = 200 mm and the yoz plane at x = 0 mm at 14 GHz. (c)–(e) The normalized amplitude distributions of the electric fields in the xoy planes at z = 100, 200, 300, 400 mm and yoz plane at x = 0 mm from 13 to 15 GHz with a step of 1 GHz.
To verify the theoretical analysis and full-wave simulation results, a metasurface was fabricated based on a PCB. The test environments for reflection and transmission are shown in Figs. 11(a) and 11(b), respectively. The main equipment used in this experiment were the excitation source (the feed horn generating the incident wave), a vector network analyzer, a scanning frame, and a receiving probe. The absorbing materials were arranged around the test instruments to reduce unnecessary electromagnetic interference. The electric field distributions of the two orthogonal planes parallel and perpendicular to the metasurface were measured.
Fig. 11. Experimental setup of the multifunctional metasurface (a) for reflection measurements and (b) for transmission measurements.
Figure 12 shows the measured results for the different modes ${F_1}$, ${F_2}$, and ${F_3}$. The measured results of the beam width, propagation distance, spot position, and energy distribution are consistent with the simulation results in the corresponding working modes. It can also be seen that the measured results of the electric field distributions have partial discontinuity and background clutter, which are mainly caused by the limitation of scanning accuracy, the fabrication error of the surface, and the measurement error in the experiment.
Fig. 12. Experimental measurement results of the three modes. (a) The normalized amplitude distributions of the electric fields in the xoy plane at z = 300 mm (${F_1}$ at 17 GHz), z = 300 mm (${F_2}$ at 17 GHz), and z = 200 mm (${F_3}$ at 14 GHz). (b) The normalized amplitude distributions of the electric fields in the yoz plane at x = 0 mm (${F_1}$ at 17 GHz, ${F_2}$ at 17 GHz, and ${F_3}$ at 14 GHz). (c)–(d) The normalized amplitude distributions of the electric fields in the xoy planes at z = 200, 300, 400, 500 mm and yoz plane at x = 0 mm from 16 to 18 GHz with a step of 1 GHz (F1, F2). (e) The normalized amplitude distributions of the electric fields in the xoy plane at z = 100, 200, 300, 400 mm and yoz plane at x = 0 mm from 13 to 15 GHz with a step of 1 GHz (F3)
4. Conclusion
In summary, a multifunctional wavefront-controlled ultra-thin surface is proposed. The metasurface can realize reflections in the front and rear of the surface in the x-polarized direction, and transmission through the surface in the y-polarized direction by independently controlling the wavefront at two frequencies. For verification, a metasurface generating three different forms of quasi-non-diffracting beams was designed and fabricated for operation in the microwave frequency band. The measurement results were in good agreement with the simulation results, which proves that the proposed metasurface can effectively generate or receive different forms of beams. With advantages such as miniaturization, multifunctional integration, and ease of fabrication, the surface designed in this study has potential application prospects in near-field multi-target identification, intelligent communication, and point-to-point data transmission. It is worth mentioning that the method is not limited to the microwave frequency band and can be further extended to terahertz and optical frequencies.
Funding
International Educational Foundation of Beihang University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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