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Abstract
Metasurfaces have enabled precise electromagnetic (EM) wave manipulation with strong potential to obtain unprecedented functionalities and multifunctional behavior in flat optical devices. One promising aspect to achieve multifunction is polarization-dependent metadevices enabled by simultaneous phase control over orthogonally polarized waves. Among these, metasurfaces with geometric phase shows their natural and robust phase control ability over different circularly polarized waves. However, the phase responses under the circularly polarized incidence are locked to be opposite with each other, resulting in limited multifunctionality. In this study, we propose what we believe to be a novel transmission-type microwave metadevice constructed by linear-to-circular metasurface and spin-decoupled metasurface. By endowing independent phase adjustment capability to each unit structure in a spin-decoupled metasurface, the metadevice can reconfigure arbitrary phase wavefronts under orthogonal polarization state incidence, thereby achieving flexible multifunctionality. As a proof-of-concept, the feasibility and reliability of proposed metasurfaces were verified by simulating multifunctional directional deflection, off-axis focusing, and focused vortex beam generation. Finally, the multifunctional manipulation capability of the metadevice is successfully demonstrated by actually measuring the generation of orbital angular momentum modes. This work is expected to drive the application development of metasurface devices in wireless communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, metasurfaces, as an ultrathin planar artificial electromagnetic material, have attracted extensive attention and research in the field of wave field regulation [1,2]. Metasurfaces are usually composed of multiple subwavelength sized units with different electromagnetic responses, which can manipulate the polarization, phase, and amplitude of incident waves to achieve beam deflection [3–5], polarization conversion [6–8], focusing [9–11], holography [12], vortex beam generation [13–15], sensor [16,17] and so on. At the same time, metasurfaces have the advantages of small size, light weight, and easy fabrication, and can be applied in compact and miniaturized microwave communication systems [18,19]. However, most of the previous research mainly focused on the realization of customized single-function metasurfaces, which is difficult to meet the development needs of optical and wireless communications. Driven by the integration of communication systems, there is an urgent need for a multifunctional transmission-type microwave metadevice to meet the required wave field manipulation.
Circular polarization waves have stronger anti-interference ability and can maintain good signal quality for propagation in complex environments [20]. Therefore, it is widely used in satellite communication [21,22], radar [23], navigation [24] and other fields. The wavefront manipulation of circular polarization waves can be easily achieved depending on the geometric phase. Despite its intrinsic wavelength-independent or dispersion-free characteristics enable it to work in broadband, the spin-dependent geometric phase always results the metasurface to manipulate the orthogonal circular polarization incident wave into two symmetrical transmitted or reflected waves [25]. Therefore, in order to achieve a phase-controlled multifunctional metasurface under orthogonal circular polarization incidence, work [26–28] proposed an interleaved designed metasurface to realize two different functions under right-handed and left-handed circular polarizations (LCP and RCP) incidence, respectively. Moreover, the segmented designed metasurface proposed in work [29] can focus the LCP and RCP incident waves to different spots. Although circular polarization controlled multifunctional metasurfaces can be easily realized with interleaved and segmented designs, the unit structures in these metasurfaces cannot achieve independent phase manipulation of LCP and RCP waves, which reduces the working efficiency of metasurfaces and introduces extra background noise. In fact, in addition to the geometric phase, the phase response of the metasurface also has a transmission phase component [30–32]. The transmission phase can be obtained by carefully tuning the geometric parameters of the unit structure and has spin-independent properties. By combining these two phase components, the independent phase manipulation of the orthogonal circular polarization states has been successfully demonstrated in work [33–35], thus decoupling the correlation between phase shifts of LCP and RCP waves and overcoming the aforementioned drawbacks. Therefore, it is necessary to draw upon this method to develop a multifunctional transmission-type microwave metadevice to meet the urgent needs of microwave communication for channel capacity and flexible manipulation.
In this work, we propose a kind of multifunctional transmission-type microwave metadevice by carefully design linear-to-circular metasurface and spin-decoupled metasurface. The metadevice can carry two independent phase wavefront information and encode them onto spin-decoupled metasurface by utilizing geometric phase and transmission phase. Then, the phase information is reorganized by circular polarization waves provided by the linear-to-circular metasurface. The units constituting the metadevice are respectively single-layer and three-layer C-shaped split ring resonators (CSRRs) structure, imparting linear-to-circular polarization conversion and spin-decoupled independent phase manipulation functions. For that purpose, we explored the relation between the geometric dimension of the CSRRs and the polarization-dependent phase respectively. Based on that, we design the metadevice and simulate multifunctional directional deflection. The deflection angles shown in the simulated electric field cross-sections are consistent with the design, confirming the spin-decoupled ability. Furthermore, we designed two alternative spin-decoupled metasurfaces to simulate multifunctional off-axis focusing and focused vortex beam generation, exhibiting a high-efficiency and negligible functional crosstalk. Notably, the linear-to-circular metasurface is reusable in all multifunctional metadevice designs, immensely reducing design complexity and manufacturing costs. As experimental verification, a linear-to-circular metasurface and a spin-decoupled metasurface for generating vortex waves with l = −2, + 1 were fabricated using the printed circuit board (PCB) processing technology. Measuring the metadevice with a linear polarization feeder source in microwave darkroom. The consistency with the simulation results is verified by scanning and checking the intensity distribution and phase distribution of electric field. Finally, the proposed metadevices operate in the Ku-band (14.8 GHz), giving it potential applications in satellite communications, radar systems, and other practical scenarios.
2. Design and results
2.1 Analysis
Different electromagnetic beam manipulation characteristics usually correspond to different metasurface structures and arrangements. How to effectively and quickly obtain the corresponding metasurface structure and arrangement according to various electromagnetic beam manipulation requirements is the key to construct new electromagnetic beam manipulation devices. Here, we carefully designed eight spin-decoupled units that can overcome the conjugate response between orthogonal circular polarization waves, and there is a π/4 cross-polarization transmission phase gradient between them. Furthermore, an additional linear-to-circular polarization conversion unit is designed, enabling the incident x- and y- linear polarizations (x-LP and y-LP) are converted to RCP and LCP. The orthogonal circular polarizations are converted to output states of opposite spins by the spin-decoupled metasurface and endowed with mutually independent phase wavefront. The phase distributions that generate arbitrary two independent wavefronts can be represented by ${\psi _1}(x,y)$ and ${\psi _2}(x,y)$. Based on the circular polarization spin-dependent geometric phase $2\sigma \theta (x,y)$ and the spin-independent transmission phase $\phi (x,y)$, ${\psi _1}(x,y)$ and ${\psi _2}(x,y)$ can be expressed as:
where σ = + 1 corresponds to RCP incidence and σ = −1 corresponds to LCP incidence, and $\theta (x,y)$ is the rotation angle. At the same time, the correspondence between RCP, LCP incidences and producing ${\psi _1}(x,y)$, ${\psi _2}(x,y)$ phase distributions is also determined. Figure 1 shows a schematic illustration of a metadevice for multifunctional focused vortex beam generation, which consists of two parts: a linear-to-circular metasurface and a spin-decoupled metasurface. Among them, the linear-to-circular metasurface is responsible for converting incident orthogonal linear polarizations into transmitted orthogonal circular polarization. The spin-decoupled metasurface is responsible for independently manipulating the wavefronts of orthogonal circular polarizations. The realization of spin decoupling is shown in detail in section 1 of the Supplement 1. Additionally, Fig. 1 also plots three-dimensional (3D) exploded views of the two subwavelength sized units and makes concrete the process by which metasurfaces manipulate electromagnetic waves. It can be also clearly seen the conversions of x-LP into RCP wave and RCP into a vortex wave with l = −2. Similarly, a vortex wave with l = + 1 is generated under y-LP wave incidence. Notably, the designed two metasurfaces can be fabricated by printing unit array of metal layers on a dielectric material using low-cost PCB processing techniques. Based on the two types of metasurfaces, metadevices with two arbitrary functions can be designed and achieved. In addition, The Ku-band is commonly used in satellite communication and broadcasting fields benefiting from its shorter wavelength. Therefore, the proposed metadevices operating at 14.8 GHz have potential applications in satellite communication, radar systems and other practical scenarios.
Fig. 1. The schematic illustration of the metadevice consisting of linear-to-circular metasurface and spin-decoupled metasurface, and the 3D exploded views of the two units. Among them, the two optical paths illustrate the multifunctional focused vortex beam generation process that the metadevice converts x-LP, y-LP waves to RCP, LCP waves, and then converts RCP, LCP waves to vortex waves with l = −2 and l = + 1.
2.2 Design of linear-to-circular unit
In general, the microwave feeder sources emit linear polarization waves, so linear-to-circular polarization conversion is required to obtain circular polarization for spin-decoupled independent manipulation. It is well known that circular polarization can be synthesized by two orthogonal linear polarization with the same amplitude and a phase difference of ±π/2. This synthesis can be achieved by manipulating incident linear polarization using metasurface. Figure 2(a) and (b) show the top view and 3D view of the proposed linear-to-circular polarization conversion unit. The unit comprising a top C-shaped split ring and a bottom dielectric material. When the linear polarization wave is normally incident along the + z direction, the unit manipulates the incident electric field in the following equation [7]:
Fig. 2. The top view (a) and 3D view (b) of the linear-to-circular polarization conversion unit show its structure and various geometric parameters. (c) The electric field views of x-component and y-component under x-LP and y-LP incidences, respectively. Color represents the electric field intensity. The transmission amplitude (d) and phase (e) of the x- and y-components of transmitted wave under x-LP and y-LP incidences, respectively. Among them, Txx and Txy are the co-polarized and cross-polarized transmission components under x-LP incidence, respectively. Tyy and Tyx are the co-polarized and cross-polarized transmission components under y-LP incidence, respectively.
To convert the incident x-LP and y-LP into RCP and LCP, the rotation angle parameter θ0 of C-shaped split ring is set to 45°, as shown in Fig. 2(a). In this work, it is important to note that the symbol of clockwise rotation angle is denoted as ‘+’ and the symbol of counterclockwise rotation angle is denoted as ‘−’. The Jones matrix T0 of the unit and the Jones vector $E_{RCP}^t$, $E_{LCP}^t$ of transmitted RCP and LCP waves are represented as follows [7]:
2.3 Design of spin-decoupled unit
The fusion phase consisting of transmission phase and geometric phase is the main scheme to achieve independent manipulation of circular polarization. Here, the design process of the spin-decoupled unit structure based on the fusion phase is introduced. The top view of the proposed spin-decoupled unit is shown Fig. 3(a). The key geometric parameters of the unit, including the subwavelength sized unit period p, opening angle β, inner radius rin, outer radius rout and rotation angle θ, are also denoted Fig. 3(a), respectively. Figure 3(b) provides the cross-section of the intermediate metal layer. This layer incorporates a composite structure design consisting of a C-shaped split ring and a circular hole. Where the radius of the circular hole is rc = 2.4 mm. Figure 3(c) presents a 3D view that clearly illustrates the composition of the entire unit, which consists of three metal layers separated by two dielectric layers. Notably, the design of the bottom, middle, and top metal layers is identical, except that the middle layer includes an additional circular hole. The metal material and dielectric material are also copper and Taconic RF-35. All metal layers and dielectric materials have a thickness of 0.035 mm and 0.762 mm, respectively. Furthermore, Fig. 3(c) provides a cross-section diagram of the unit at the y = 0 mm plane. The red dielectric represents the prepreg material (ɛ = 4.4 with a loss tangent of 0.02, thickness hpp = 0.1 mm) and is utilized to bond two layers of dielectric material together during PCB processing.
Fig. 3. The top view (a), middle view (b) and 3D view (c) of the spin-decoupled unit show its structure and various geometric parameters, respectively. (d) Simulation results database with outer radius rout, inner radius rin, and opening angle β as variables. (e) The cross-polarization and co-polarization transmission amplitude (right coordinate axis) and cross-polarization transmission phase (left coordinate axis) of eight units under LCP and RCP incidences. (f) The surface current distributions at the bottom and top of the second unit under LCP and RCP incidences, respectively. The geometric phase 3D point-line view (g) and cross-polarization amplitude 3D point-line view (h) of each unit with changes in the rotation angle θ under LCP and RCP incidences. Among them, TLL and TLR are the co-polarized transmission and cross-polarized transmission components under LCP incidence, respectively. TRR and TRL are the co-polarized transmission and cross-polarized transmission components under RCP incidence, respectively.
To design a metasurface with close to ideal phase distribution and high work efficiency, a transmission phase gradient of π/4 is set. Therefore, eight units that cover the cross-polarization transmission phase range of 0-2π while maintaining a high cross-polarization transmission amplitude need to be designed. However, due to the complex structure and many parameters of the spin-decoupled unit, artificially filtrating the units in the simulation results is Inefficient and laborious. Here, the opening angle β, inner radius rin and outer radius rout are used as variables, and the frequency domain solver of CST combined with MATLAB software is used for simulation. That is, the MATLAB program can control the operation of CST and analyze the simulation results. In this way, the value range of the outer radius is (rout = 2.2 mm or rout = 2.3 mm), the value range of the inner radius is (1.0 mm ≤ rin ≤ 1.3 mm, step size 0.01 mm), and the value range of the opening angle is (5° ≤ β ≤ 50°, step size 0.2°). After performing two-dimensional linear interpolation on the initial simulation results, the database of cross-polarization transmission amplitude and phase is shown in Fig. 3(d). In fact, to identify eight units that satisfy the above conditions in the database is challenging. In order to solve this problem and simplify the design, we adopt a scheme that first determines the parameters of four units covering 0-π, and then uses the geometric phase to obtain the remaining four units covering π−2π after rotating 90°. The MATLAB program can be used to automatically filter and output four groups of geometric parameters that meet above conditions. The constraint condition of the MATLAB program can be described as:
Table 1. Geometric parameters of eight units
2.4 Multifunctional directional deflection
Colorful pixel dots can be combined in different ways to form various pictures. Similarly, a group of units with different electromagnetic responses can be combined into a planar structure to design a metasurface with a specific function. Directional antenna as a kind of antenna that emits electromagnetic waves particularly strong in a particular direction, while emitting electromagnetic waves extremely small in other directions. It is often used in communication systems to increase the effective utilization of the radiated power. Similarly, a spin-decoupled metasurface constructed using the above units can be manipulated for directional deflection of electromagnetic waves, which can achieve multifunctional directional control of wave beam. We designed a metadevice for multifunctional directional deflection. As a theoretical design, the metadevice is expected to deflect wave by −10° under x-LP incidence and by 20° under y-LP incidence. Firstly, the phase gradients are calculated according to the generalized Snell's law [36]:
Figure 4(a) and (b) show the phase distributions ${\psi _1}(x,y)$ and ${\psi _2}(x,y)$ for deflections of −10° and 20°, respectively. Since the metadevice is static, in order to generate different phase distributions under orthogonal circular polarizations incidence, the unit distribution on the spin-decoupled metasurface is determined by deriving the Eq. (1) and (2):
where transmission phase $\phi (x,y)$ and rotation angle $\theta (x,y)$ are used to determine the selection and rotation of the unit at the (x, y) position on the spin-decoupled metasurface, respectively. Figure 4(c) and (d) are the designed spin-decoupled metasurface and linear-to-circular metasurface, respectively, which were constructed by controlling CST software with MATLAB software. The simulation is performed utilizing periodic boundary conditions and time domain solver to simulate the infinite repetition characteristics of metasurface for accurate numerical results. Figure 4(e) represents the electric field cross-section of simulation result at y = 0 mm. It is observed that the incident x-LP wave propagating along the + z direction converts into RCP wave after passing through the linear-to-circular metasurface. Subsequently, circular polarization cross-polarization conversion occurs on the spin-decoupled metasurface, and the reorganized phase distribution ${\psi _1}(x,y)$ causes the wavefront to change. As a result, the wave beam undergoes a deflection −10° and propagates in the LCP state. Similarly, Fig. 4(f) demonstrates that under y-LP incidence, the wave beam deflects by 20° and propagates in the RCP state. The simulation results align well with the theoretically designed deflection angles, indicating the multifunctional spin-decoupled capability. For the combined metadevice, the deflection efficiency can be expressed as the product of the efficiency of the spin-decoupled metasurface and the efficiency of the linear-to-circular metasurface. Therefore, we first simulated spin-decoupled metasurface under RCP and LCP incidence, as shown in Fig. 4(g)(h). Further, we can calculate the deflection efficiency from Fig. 4(g)(h) by [37]In addition, the influence of the distance between the two metasurfaces is explored in section 4 of the Supplement 1. In general, the design of linear-to-circular metasurface remains fixed, while the spin-decoupled metasurface can be redesigned to achieve arbitrary symmetric or asymmetric deflection manipulation.
Fig. 4. (a) and (b) are the designed phase distributions to deflect −10° and 20°, respectively. (c) The spin-decoupled metasurface for independent manipulation of circular polarization waves. (d) Linear-to-circular metasurface that provides circular polarization waves. The simulated normalized electric field intensities of multifunctional directional deflection under the x-LP (e) and y-LP (f) incidences, respectively. Among them, the white dashed lines indicate the isophase plane of the plane wave. The deflected beam intensity of the spin-decoupled metasurface transmitted under RCP (g) and LCP (h) incidence is normalized to the incident wave.
2.5 Multifunctional off-axis focusing
In practical, microwave communications require components such as lenses to focus wave beams to transmit or receive information efficiently and consistently. Off-axis focusing can focus the beam to any position off the optical axis. Therefore, off-axis focusing technology has great potential for application in communication systems. In order to achieve multifunctional off-axis focusing, two independent phase wavefront information need to be redesigned and encoded onto a spin-decoupled metasurface consisting of 28 × 28 units. The design is carried out in three degrees of freedom, setting the appropriate focal length f in the z direction, and the appropriate off-axis distances dx and dy in the x and y directions. After that, f = 100 mm, dx = −30 mm and dy = 0 mm is one group, and f = 50 mm, dx = 30 mm and dy = 0 mm is another group. The phase distributions corresponding to these two groups of design targets are shown in Fig. 5(a) and calculated by the following equation [35]:
Fig. 5. (a) The off-axis focusing phase distributions at f = 100 mm and f = 50 mm, respectively. (b) The schematic illustration of the metadevice generating off-axis focused beams and its wavefield manipulation under x-LP and y-LP incidences. (c) The simulation results of designed metadevice under the x-LP and y-LP incidences, respectively.
2.6 Multifunctional focused vortex beam generation
Vortex wave is a kind of electromagnetic wave carrying OAM. The electromagnetic waves at the same frequency point can theoretically have infinite OAM modes, and different OAM modes transmit without interfering with each other. So that the spectrum utilization can be greatly improved. Therefore, OAM has potential applications in improving communication transmission capacity. By precisely engineering the distribution of subwavelength unit structures on a metasurface, the phase of the incident wave can be modulated and generate the desired vortex phase. Therefore, we further designed a spin-decoupled metasurface for multifunctional focused vortex beam generation. The phase distribution of the vortex wave is given by [41]:
where l is the designed OAM mode (or topological charge), and can take any integer value in (−∞, +∞). x and y are horizontal and vertical coordinates. The vortex beam naturally diverges as it propagates, causing the radius of the wavefront to increase with the propagation distance. However, this divergence is not conducive for complete reception of the vortex wave. To address above issue, a focused phase is added to the vortex phase to induce convergence. Focused phase distribution is described by [9]: where λ is the vacuum wavelength, corresponds to 14.8 GHz. (x, y) is the coordinate of the unit structure. (0, 0) is the central coordinate of the metasurface, and f is the designed focal length. The phase superposition of Eqs. (15) and (16) can obtain the distribution of the focused vortex phase.Through the above analysis, a spin-decoupled metasurface composed of 28 × 28 units with a size of 140 × 140 mm2 is designed to generate focused vortex waves with topological charges l = −2 and l = + 1. The designed focal length is f = 100 mm. Figure 6(a) displays the distribution of the focused vortex phase with l = −2, + 1. The spin-decoupled metasurface shown in Fig. 6(b) is determined by the calculation results of Eqs. (9) and (10). Linear-to-circular metasurface and spin-decoupled metasurface are constructed by controlling the CST software using MATLAB software and simulated using CST time domain solver and open boundaries. The schematic diagram of the whole model and the simulation results of metadevice is shown in Fig. 6(b). Figure 6(c) and (d) shows the simulation results of the normalized intensity distributions and phase distributions of transmissive electric field on the focal plane. Incident x-LP and y-LP waves are manipulated to generate focused vortex waves with l = −2 (top) and l = + 1 (bottom), respectively. Due to the phase singularity inherent in vortex waves, a ‘doughnut’ intensity profile can be observed, and the radius of ‘doughnut’ increases with the increase of topological charge order. To highlight the reconfigurability of the multifunctional transmission-type microwave metadevice, another spin-decoupled metasurface is designed to generate vortex waves with l = −3 and l = −2, while the same linear-to-circular metasurfaces can still be utilized. Figure 6(e) displays the distribution of the focused vortex phase with l = −3, −2. Meanwhile, Fig. 6(f) gives the schematic illustration of the whole model and the simulation results of metadevice. The simulation results of the normalized intensity distributions and phase distributions on the focal plane are presented in Fig. 6(g) and (h), confirming the generation of vortex waves with l = −3 (top) and l = −2 (bottom). Vortex wave generation for arbitrary two modes is a challenge for conventional metasurfaces, but can be easily and efficiently realized for proposed spin-decoupled metasurfaces. Furthermore, without combining with linear-to-circular metasurface, the spin-decoupled metasurface can directly manipulate orthogonal linear polarization to generate multiple vortex beams (see the section 6 of Supplement 1). In conclusion, above results not only validate the multifunctionality of the proposed metadevice, but also demonstrate the feasibility of the design method.
Fig. 6. (a) The phase distribution of focused vortex waves with l = −2 and l = + 1. (b) The schematic illustration of the metadevice generating focused vortex beams (l = −2 and l = + 1) and its wavefield manipulation under x-LP and y-LP incidences. The normalized intensity distributions (c) and phase distributions (d) of simulation results on focal plane f = z = 100 mm under the x-LP and y-LP incidences. (e) The phase distribution of focused vortex waves with l = −3 and l = −2. (f) The schematic illustration of the metadevice generating focused vortex beams (l = −3 and l = −2) and its wavefield manipulation under x-LP and y-LP incidences. The normalized intensity distributions (g) and phase distributions (h) of simulation results on focal plane f = z = 100 mm under the x-LP and y-LP incidences.
3. Fabrication and measurement
To further verify the practical functions of the proposed multifunctional transmission-type microwave metadevice, the metadevice was fabricated. In order to facilitate measurement, we set the actual focal length to 300 mm. Meanwhile, the number of units was expanded to 80 × 80, resulting in the size of the metadevice of 400 × 400 mm2. The equipment for testing the metadevice is shown in Fig. 7(a) and (b). The measuring device is located in the closed environment of the microwave darkroom. Among them, the linear-to-circular metasurfaces (Fig. 7(c)) and the spin-decoupled metasurface (Fig. 7(d)) were fabricated by PCB processing technology. The overall size is 440 × 400 mm2. The blank areas on both sides are used to make through holes, so that it is convenient to connect and fix the two metasurfaces with hexagonal copper pillars with a length of 15 mm. Detailed fabrication steps are illustrated in the section 7 of Supplement 1. Throughout the entire testing process, the metasurface is vertically placed on a foam platform and secured with tape, and remains stationary. The waveguide probe is located on a plane 300 mm away from the output end of the metasurface and fixed on a scanning frame. The feeder source is positioned at a certain distance from the incident end of the metasurface and placed on the central axis of the metasurface. The feeder source and waveguide probe are connected to the two ports of the Keysight PNA Network Analyzer N5225A, respectively.
Fig. 7. The incident surface (a) and transmitted surface (b) views of the fabricated metasurfaces in the experimental setup. The top views of fabricated linear-to-circular metasurfaces (c) and spin-decoupled metasurface (d). (e) The experimental results show transmission normalized intensity distributions and phase distributions of the vortex waves with l = −2 and l = + 1 under x-LP and y-LP incidences, respectively.
In the process of measurement, the feeder source outputs x-LP wave and y-LP wave with a frequency of 14.8 GHz, respectively. The waveguide probe scans the range of 400 × 400 mm2 in both vertical and horizontal directions with a step size of 5 mm to collect the intensity and phase data of the transmitted waves. A total of 6400 sampling points guarantee the accuracy and reliability of the results. The measurement results under x-LP incidence are displayed on the left side of Fig. 7(e). In contrast, the ‘doughnut’ shaped intensity radius is larger and the phase exhibits a 4π variation along the clockwise direction. Therefore, this transmitted wave has an ${e^{ - 2i\varphi }}$ phase rotation factor and carries a topological charge of l = −2. The measurement results under y-LP incidence are shown on the right side of Fig. 7(e). In the results, the normalized intensity exhibits a ‘doughnut’ shaped radius is smaller, while the phase exhibits a 2π variation in the counterclockwise direction. Therefore, the transmitted wave has a phase rotation factor of ${e^{i\varphi }}$ and carries a topological charge of l = + 1. Thus, the multifunctional focused vortex beam generation is confirmed. The difference between the simulated results and the measured results may be caused by the different parameters of the simulation system and the measurement system. In the simulation system, the incident wave is an ideal plane wave, which shows good results on the designed focal plane. In the measurement system, due to the limited distance between the feeder source and the metadevice, the actual plane wave is an approximation of the spherical wave emitted by the feeder source. And the compensation effect of the spherical wave and the focusing phase in the metasurface causes the actual focal length to increase. Eventually, there is a certain disagreement between the measured results on the designed focal plane and the simulated results. Benefit from the phase compensation of the focusing phase and the spherical phase ensures that the final result falls within an acceptable range.
4. Conclusion
This work proposes a multifunctional transmission-type microwave metadevice based on spin-decoupled and linear-to-circular metasurfaces. The linear-to-circular metasurface provides circular polarization waves by converting the linear polarization waves, while the fusion phase information on the spin-decoupled metasurface is reorganized under the incidence of the circular polarization waves. Among them, the design of unit with fusion phase is sophisticated and not easy to implement. Therefore, a design approach based on co-simulation using CST software and MATLAB software is employed to automatically output optimized structural parameters under the required conditions. This design approach can also be applied with high accuracy and convenience to the design of other types of metasurface-based devices, thereby shortening the development cycle of metasurface devices and advancing the practical application of metasurface devices in design. And then, the multifunctional directional deflection, off-axis focusing and focused vortex beam generation at 14.8 GHz were successfully realized, followed by experimental validation of the focused vortex beam generation with l = −2, + 1 in a microwave darkroom. The measured results have good agreement with the numerical simulations, demonstrating the feasibility of the method and the multifunctionality of the metadevice. Compared with the previous metasurfaces [42] and [31], the smaller unit period improves the continuity of the phase wavefront, and the smaller number of layers reduces the fabrication cost and difficulty. Compared with reflection-type metadevices with dielectric/metal-dielectric-metal structures [43], transmission-type metadevices are more suitable for practical applications. Moreover, the mature PCB process provides assurance for the fabrication of the designed metadevices. In conclusion, we believe the proposed multifunctional metadevices can offer a promise for applications in optical communication, optical information processing, and imaging.
Funding
National Natural Science Foundation of China (62105093); Science and Technology Project of Hebei Education Department (BJK2023036); Doctoral Research Initializing Fund of Hebei University of Science and Technology (1181382).
Disclosures
The authors declare no conflicts of interest related to this study.
Data availability
The 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.
Supplemental document
See Supplement 1 for supporting content.
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