
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39245772
72018
10.1038/s41598-024-72018-6
Article
Phase and amplitude simultaneously coding metasurface with multi-frequency and multifunctional electromagnetic modulations
Cai Chengxin cxcai2018@haut.edu.cn

123
Li Yinfei 1235
Li Mingxing 123
Qin Yao 123
Zhou Yangyang zhouyangyang0623@163.com

4
1 https://ror.org/03m01yf64 grid.454828.7 0000 0004 0638 8050 Key Laboratory of Grain Information Processing and Control (Henan University of Technology), Ministry of Education, Zhengzhou, 450001 People’s Republic of China
2 https://ror.org/05sbgwt55 grid.412099.7 0000 0001 0703 7066 Henan Key Laboratory of Grain Photoelectric Detection and Control, Henan University of Technology, Zhengzhou, 450001 People’s Republic of China
3 https://ror.org/05sbgwt55 grid.412099.7 0000 0001 0703 7066 College of Information Science and Engineering, Henan University of Technology, Zhengzhou, 450001 People’s Republic of China
4 https://ror.org/01f4k3b46 grid.482554.a 0000 0004 7470 4983 The Science and Technology on Reliability Physics and Application of Electronic Component Laboratory, China Electronic Product Reliability and Environmental Testing Research Institute, Guangzhou, 510610 China
5 The School of Communication and Information Engineering, Chongqing College of Mobile Communication, Chongqing, 401400 China
8 9 2024
8 9 2024
2024
14 2090417 4 2024
3 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The integration of multiple functionalities into a single, planar, ultra-compact metasurface has presented significant opportunities for enhancing capacity and performance within compact 5G/6G communication systems. Recent advances in multifunctional metasurfaces have unveiled comprehensive wavefront manipulations utilizing phase, polarization transmission/reflection, and coding apertures. Despite these developments, there remains a critical need for multifunctional metasurfaces with expanded channel capabilities, including multiple operational frequencies, minimal crosstalk, and high-efficiency computable array factors. This study introduces a multifunctional metasurface that integrates phase- and amplitude simultaneous coding meta-atoms at dual frequencies. By altering the polarization of electromagnetic (EM) waves, it is possible to reshape the wave-fronts of reflected waves at these frequencies. The coding metasurface proficiently manipulates both x and y linearly polarized waves through phase and amplitude coding at dual frequencies, thereby enabling distinct functionalities such as anomalous reflection, reflection imaging, and vortex wave beam generation. Both theoretical analysis and full-wave simulation confirm the anticipated functionalities of the designed devices, paving the way for advancements in integrated communication systems with diverse functionalities.

Subject terms

Metamaterials
Metamaterials
The research has been partially supported by the National Natural Science Foundation of China(No.62373136 (No.62373136 (No.62373136 (No.62373136 Cai Chengxin Li Yinfei Li Mingxing Qin Yao Key Scientific and Technological Project of Science and Technology Department of Henan ProvinceNo. 242102210154 No. 242102210154 No. 242102210154 No. 242102210154 Cai Chengxin Li Yinfei Li Mingxing Qin Yao Innovative Funds Plan of Henan University of TechnologyNo. 2022ZKCJ02 No. 2022ZKCJ02 No. 2022ZKCJ02 No. 2022ZKCJ02 Cai Chengxin Li Yinfei Li Mingxing Qin Yao Key Scientific Research Project of Henan Education DepartmentNo.23A510007 No.23A510007 No.23A510007 No.23A510007 Cai Chengxin Li Yinfei Li Mingxing Qin Yao High-level Talent Fund of Henan University of TechnologyNo.31401232 No.31401232 No.31401232 No.31401232 Cai Chengxin Li Yinfei Li Mingxing Qin Yao Key Laboratory of Grain Information Processing and Control (Henan University of Technology), Ministry of EducationNo.KFJJ-2023-002 No.KFJJ-2023-002 No.KFJJ-2023-002 No.KFJJ-2023-002 Cai Chengxin Li Yinfei Li Mingxing Qin Yao Fund for State Key Laboratory6142806230401 Zhou Yangyang issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The rapid advancement of 5G/6G technology has escalated the demand for integrated communication devices that combine high capacity with versatile functionality. metasurfaces, representing a revolutionary shift in device design, have become increasingly prevalent for generating diverse and innovative devices, ranging from optical to microwave applications. These devices include those for abnormal reflection1–3, meta-lenses4–8, holograms9–13, specialized beam manipulation14–19, and quantum manipulation20–24. Unlike natural materials or traditional three-dimensional meta-materials, metasurfaces are artificially engineered electromagnetic materials. They consist of either periodic or aperiodic arrays of two-dimensional sub-wavelength structures, notable for their ultralight and ultra-thin characteristics25,26.

In 2014, the concept of coding metasurfaces, a significant branch of metasurfaces, emerged27. These surfaces are composed of a finite number of elementary cells arranged in a specific coding sequence. By individually manipulating the electromagnetic characteristics, such as phase, amplitude, or polarization, of each meta-atom, coding metasurfaces28–32 enable the programmatic control of electromagnetic wavefronts, thereby serving as an interface between physical electromagnetism and information science. Subsequently, coding metasurfaces have facilitated the development of high-performance devices, including those for beam deflection33, spectral imaging34,35, polarization manipulation36–39, meta-lenses40–42, and holography43.

As high-density communication evolves, the limitations of mono-functional coding devices have become apparent, failing to meet the sophisticated demands of integrated systems. Multifunctional coding metasurfaces have thus garnered substantial interest for their potential in integrated communication systems, attracting attention from both scientific and engineering fields44,45. Employing single-dimensional multiplexing techniques such as phase, angle, wavelength, and polarization, these devices are designed to manipulate electromagnetic waves across both half-space46 and full-space scenarios47. Recent innovations in multifunctional coding metasurfaces have introduced composite dimensional multiplexing, which includes combinations of polarization and wavelength, polarization and phase, as well as polarization and amplitude multiplexing48–50. These advancements significantly enhance the functionality and integration of coding metasurface devices in communication technologies. However, challenges such as high channel crosstalk and the constraints of dimensional multiplexing continue to pose significant hurdles, necessitating further investigation to fully leverage the capabilities of multi-dimensional multiplexing coding metasurfaces.

In this study, a three-dimensional multiplexing multifunctional coding metasurface with low crosstalk and high efficiency is proposed, achieved through amplitude and phase coding at various operating frequencies. This metasurface allows for multidimensional control of terahertz waves by modulating amplitude and phase variations across different polarization states. We agree that the designed metasurfaces is static and cannot switch states. But different functions can be achieved by adjusting the polarization state of incident wave and frequency points. So this is the polarization multiplexing multifunctional device. Switchable imaging is facilitated through amplitude variations, enabling control over the incident frequency and reflection polarization state. Furthermore, by implementing transmission phase distributions in the coding units, we demonstrate various polarization multiplexing functionalities, including Orbital Angular Momentum (OAM) beams, abnormal reflections, and multiple beams at frequencies of 1.234 THz and 1.551 THz. Additionally, a two-dimensional focusing lens designed for x-polarized incidence achieves 2π phase coverage at 1.551 THz. Therefore, in same arrangement, we designed metasurface can achieve different functions under different polarization states and the coordination of polarization states can also be expressed as a reconfigurable characteristic. This integrated, multifunctional coding metasurface significantly enhances the manipulation efficiency of terahertz waves and holds promise for advancing high-frequency communication systems.

Theorical analysis and device design

Recent advancements have seen multifunctional metasurfaces, utilizing multiple degrees of freedom such as frequency, polarization, and wavelength, being increasingly employed in high-speed wireless communication, holographic imaging, radar, and other fields within information technology. We introduce a dual-frequency, multifunctional metasurface based on reflection. Figure 1a presents the conceptual diagram of the proposed coding metasurface, which consists of two metasurface meta-atoms depicted in Fig. 1b. Depending on orthogonal polarization states, the metasurface components, in combination with amplitude and phase modulations, enable the execution of various functionalities (F1, F2, F3, F4, F5, F6)) at two distinct frequency points. Based on the two metasurface atoms described in Fig. 1b, we respectively constructed four different metasurfaces. The metasurface 1 was constructed using the amplitude characteristics of the two meta-atoms in Fig. 1b, which can realize reflective imaging (function F1) for x-polarization at frequency f1 (1.234 THz) and reflective imaging (function F4) for y-polarization at frequency f2 (1.551 THz). The metasurface 2 was constructed using the phase characteristics of the two meta-atoms in Fig. 1b, which can realize different functions for x-polarization and y-polarization at frequency f1 (1.234 THz), that is, a vertical beam can be realized under x-polarization (function F2) and a vortex beam can be realized under y-polarization (function F3). The metasurface 3 was constructed using the phase characteristics of the two meta-atoms in Fig. 1b, which can realize a lens sensitive to x-polarization at frequency f2 (1.551 THz). In addition, the metasurface 4 was also constructed to realize the splitting of dual-beam and three-beam (functions F5 and F6) at frequency f2 (1.551 THz). The meta-device structure comprises an upper metal patch, a dielectric substrate, and a metal ground plane, with the upper structure featuring a circular ring and a diamond square. A detailed view of the coding component is illustrated in Fig. 1b, showcasing two layers of gold metal, each 0.2 μm thick, and a Mylar dielectric substrate (εr = 3.1, tan δ = 0.002) with a thickness of 30 μm. By adjusting the radius of the circular ring and the side length of the diamond square in the upper structure, the configuration of combined scatterers is optimized to enable dual-operation frequency bands.Fig. 1 Schematic and working principle of the multifunctional integrated coding metasurface. (a) Overview of the multifunctional integrated coding metasurface and its functions. (b) Design and characteristics of the proposed coding metasurface meta-atoms "0" and "1".

The design concept of encoding metasurfaces is mainly to digitize information such as phase and amplitude. For 1-bit encoded metasurfaces, when designing the unit, only the phase difference of 180° needs to be guaranteed while keeping the amplitude of the unit the same. In this way, different functional forms can be achieved by artificially designing the phase arrangement of different units. The detailed geometric parameters of the meta-atom are depicted in Fig. 1b. To streamline the design process, several geometric parameters of the basic components are fixed as follows: Px = Py = 120 μm, h = 30 μm, w1 = w2 = 6 μm, t = 0.3 μm. Moreover, the detailed structural parameters of meta-atom "0" (left structure) in Fig. 1b are: L1 = 50 μm, r1 = 42 μm, r2 = 39 μm, and the detailed structural parameters of meta-atom "1" (right structure) are: L2 = 36 μm, r3 = 58 μm, r4 = 48 μm. By adjusting the size parameters of the circular ring and diamond square structure, we can change the amplitude and phase shifts responds to x- and y-polarized incident waves.

Based on the principle of polarization-dependent reflection in polarized multiplexing, the behavior of polarization-multiplexing metasurface units can be analyzed using the Jones matrix. Within the Cartesian coordinate system, the relationship between the incident and reflected electric fields of a linearly polarized electromagnetic wave can be articulated as follows:1 ERxERy=rxxrxyryxryyEIxEIy=REIxEIy

2 R=rxx00ryy

where, ER and EI denote the reflected and incident electric fields, respectively; r represents the reflection coefficient, with subscripts indicating the x-polarized and y-polarized directions; is the reflection matrix, composed of reflection coefficients. Analysis from Fig. 2 shows that the metasurface meta-atom does not undergo polarization conversion, thus R can be defined by Eq. 2. Consequently, for a linearly polarized wave, the reflected electric field predominantly depends on the reflection coefficients for x-polarization and y-polarization.Fig. 2 The response of the meta-atom "0" under x-polarized and y-polarized wave incidence: (a) reflection amplitude coefficient; The meta-atom "1" under x-polarized and y-polarized wave incidence: (b) reflection amplitude coefficient.

The design of meta-atom "0" was achieved by decreasing the outer ring radius of meta-atom "1" and enlarging the side length of the inner diamond block. To elucidate the relationship between meta-atom "0" and meta-atom "1", numerical calculations of the current and electric field distributions on their surfaces were conducted. Two Floquet ports were utilized in the + z and -z directions, with periodic boundary conditions in the x and y directions. Figure 3a and b display the surface electric field distributions for the meta-atom when subjected to plane waves incident in the x and y polarizations, respectively. It was observed that under x polarization, the electric field in meta-atom "1" predominantly concentrated along the sides of the diamond ring and the circular ring. Conversely, under y polarization, the electric field was primarily concentrated on the upper part of the diamond ring and the center of the circular ring. When the circular ring's radius in meta-atom "1" was reduced and the diamond block's side length increased to transform into meta-atom "0", the simulation showed that under x polarization, the electric field predominantly concentrated along the sides of the circular ring, whereas the electric field along the sides of the diamond ring diminished. Under y polarization, the electric field remained concentrated on the upper part of the diamond ring, while the field in the middle part of the circular ring weakened.Fig. 3 The surface electric field distribution of the upper metal layer: Meta-atom "0" under x-polarized and y-polarized wave incidence (a); Meta-atom "1" under x-polarized and y-polarized wave incidence (b); The surface current distribution of the upper metal layer. Meta-atom "0" (c) under x-polarized and y-polarized wave incidence; Meta-atom "1" (b) under x-polarized and y-polarized wave incidence.

Figure 3c and d respectively depict the surface current distributions of the meta-atoms when a plane wave is incident under x-polarization and y-polarization. Observations show that under x-polarization, a monopole resonance appears on one side of the diamond ring and the annular notch ring in the meta-atom "1", which usually enhances the electromagnetic energy locally on the surface of the unit and binds the electromagnetic energy to a certain extent, and this enhanced electromagnetic energy may be dissipated through the ohmic loss effect of the metal and the absorption effect of the dielectric, thereby affecting the electromagnetic characteristics and performance of the unit structure; while under y-polarization, a distinct dipole resonance occurs within the annular notch ring, which can bind the electromagnetic energy on the surface of the unit, causing the electromagnetic energy to be dissipated through the ohmic loss effect of the metal and the absorption effect of the polyimide dielectric, thereby achieving the absorption of y-polarized waves. This behavior is also consistent in the meta-atom "0". Therefore, it can be inferred that the resonant electric field mainly involves the sides of the circular ring under x-polarization, while mainly involves the upper part of the diamond ring under y-polarization.

Based on the analysis above, the resonance characteristics of the structure under x-polarization and y-polarization are intricately linked to their geometric parameters, primarily dependent on the radius of the ring and the length of the diamond block. By manipulating these dimensions, the metasurface can effectively control the polarization state of the incident wave. In the parameter optimization process, we mainly use the 3D full-wave simulation software CST Studio Suite to optimize the design of the structure. In the optimization process, first of all, it is necessary to determine the structural parameters we needed to optimize, the ring radius (r1 & r3) of meta-atom 0 and meta-atom 1, and the rhombic side length (L1 & L3) of meta-atom 0 and meta-atom 1. Keeping other parameters unchanged, the built-in algorithm of CST Studio Suite is used to scan the maximum/minimum value we need to optimize to achieve the required phase and amplitude responses. Adjustments and optimizations of the geometric structure enable the derivation of varied sub-phase parameters for x-polarization and y-polarization, as evidenced in Fig. 4. The figures reveal that at an x-polarized incident wave of frequency 1.234 THz, the phase change is minimal, but the amplitude change is significant due to alterations in the radii of the rings of meta-atom "0" and "1". Conversely, at an x-polarized incident wave of frequency 1.551 THz, the phase change spans from 0 to 2π, while the amplitude change is minimal, also resulting from modifications in the radii of the rings of meta-atom "0" and "1".Fig. 4 (a) Reflection amplitude coefficient and (b) reflection phase coefficient diagrams upon adjusting the ring radii of meta-atoms "0" and "1"; (c) The reflection amplitude coefficient and (d) reflection phase coefficient diagrams following adjustments to the lengths of the diamond blocks of meta-atoms "0" and "1".

Similarly, Fig. 4c and d illustrate that at an incident frequency of 1.234 THz for y-polarized waves, modifications to the lengths of the diamond blocks of meta-atoms "0" and "1" result in minimal amplitude changes, while the phase change is considerable, achieving a full 2π phase shift. At a frequency of 1.551 THz for y-polarized waves, alterations to the lengths of the diamond blocks lead to a relatively stable amplitude, though an amplitude mutation point is noted. As the length of the diamond block in meta-atom "0" increases under y-polarized wave incidence, the outer ring also expands, causing meta-atom "0" to transition towards meta-atom "1." This adjustment induces a significant phase shift under y-polarization. Conversely, as meta-atom "1" evolves into meta-atom "0" with increasing diamond block length, its phase remains relatively stable under y-polarized incidence. This behavior corroborates the previously described changes in the surface electric field. Thus, the amplitude and phase of the metasurface can be adeptly controlled by manipulating the radius of the ring, the length of the diamond block, and the polarization state of the meta-atom structure.

Multifunctional integrated wavefront manipulation

In this section, a multiplexed and multifunctional coding metasurface is proposed, facilitating flexible control over the metasurface's amplitude and phase by adjusting the geometric dimensions, incident frequency, and polarization state of the unit structure. This enables multidimensional control of terahertz waves. Amplitude variations of the metasurface allow for regulation of the incident frequency and reflected polarization state, supporting switchable imaging capabilities. The introduction of transmission phase distributions within the coding units yields various polarization multiplexing functions at frequencies of 1.234 THz and 1.551 THz, including the generation of orbital angular momentum beams, anomalous reflection, and multi-beam splitting. Furthermore, a two-dimensional focusing lens for x-polarized incident waves is designed. This integrated multifunctional coding metasurface substantially enhances the efficiency of terahertz wave manipulation and promises significant advancements in high-frequency communication systems.

Polarization-multiplexed spatial imaging design

In recent years, terahertz imaging devices based on metasurfaces have garnered significant interest due to their broad applications in stealth communication, medical diagnostics, and security monitoring. This study introduces a terahertz device capable of achieving superior imaging functionality at various frequencies under different incident polarization states, leveraging the differential reflection amplitudes between meta-atoms “0” and "1". Figure 5a displays the reflection coefficients (rx and ry) for meta-atoms "1" and "0" at frequencies of 1.234 THz and 1.551 THz, respectively. At 1.234 THz, meta-atom "1" exhibits a higher reflection coefficient (rx), while at 1.551 THz, it shows a lower reflection coefficient (ry), with meta-atom "0" demonstrating the opposite behavior. Specifically, under x-polarized incidence, the reflection amplitude of meta-atom "0" at 1.234 THz (r1 = 42 μm, r2 = 39 μm, L1 = 50 μm) approaches 0%, whereas for meta-atom "1" (r3 = 58 μm, r4 = 48 μm, L2 = 36 μm), it is nearly 100%. Notably, at 1.551 THz, the reflection amplitudes of meta-atoms "0" and "1" are similar. Under y-polarized incidence at 1.551 THz, the roles of the reflection amplitudes for meta-atoms "0" and "1" are reversed, with meta-atom "0" approaching 100% and meta-atom "1" nearing 0%. Interestingly, at 1.234 THz, their reflection amplitudes converge. Thus, the differential reflection amplitudes between meta-atoms "0" and "1" facilitate the creation of a 1-bit encoded metasurface across different frequencies.Fig. 5 Reflection Amplitude of Meta-atom "0" and Meta-atom "1" (a) For x-polarized and y-polarized incidence. (b) Design of the image under x-polarized and y-polarized incidence at 1.234 THz and 1.551 THz, and (c) simulated electric field distribution under x-polarized incidence at 1.234 THz, and (d) simulated electric field distribution under y-polarized incidence at 1.551 THz.

Metasurface encoding sequences with varying polarization conversion performance were arranged as depicted in Fig. 5b. This study introduces a meta-material pattern capable of controlling different polarization states at various frequencies by organizing the encoding meta-atoms, as illustrated in Fig. 5c and d. In the simulations, each color pattern shown in Fig. 5b consists of a 4 × 4 array of meta-atoms. Figure 5c and d reveal that the designed patterns display the letter "L" under x-polarized incidence and the number "7" under y-polarized incidence along the z-direction at 800 μm. The simulation results closely align with the predefined images in terms of size, position, and contour, confirming the near-field imaging capabilities at different frequencies through the modulation of reflection amplitudes under various polarized states, as presented in Fig. 5c and d.

Polarization-multiplexed orbital angular momentum design

The rapid development of mobile communication technologies has fostered widespread applications of OAM in fields such as laser communication, target detection, and optical trapping, attributable to its perfect orthogonality. By strategically arranging the proposed meta-atoms, incident plane waves are transformed into vortex beams. The requisite phase variation for the metasurface meta-atoms correlates with the azimuthal angle and can be expressed as:3 ϕ(x,y)=lϕ=larctan(y/x)

where φ represents the azimuthal angle and l denotes the topological charge of OAM. When l =  + 1, the phase completes a 2π cycle over one revolution, and the phase difference between adjacent regions satisfies ππ44. When l =  + 2, the phase completes a 4π cycle over one revolution, and the phase difference between adjacent regions satisfies ππ44. It is worth noting that when the parameters of the other meta-atoms "0" and "1" are fixed, by adjusting the length of the rhombus blocks' sides of meta-atoms "0" and "1" (L1 and L2), we can build up a 2 π distribution of the OAM vortex beam with l =  + 2. The different functions can be realized with the incident of different polarized waves by doing so, as illustrated in Fig. 6a.Fig. 6 Vortex beam generator (a) Under x-polarized and y-polarized incidence at a frequency of 1.234 THz. (b) Reflection amplitude and phase variations with different side lengths of diamond-shaped blocks under x-polarized and y-polarized incidence. (c) Simulated 2D near-field and (d) 3D far-field electric field distributions under x-polarized incidence. (e) Simulated 2D near-field and (f) 3D far-field electric field distributions under y-polarized incidence.

Figure 6b displays the necessary side lengths of the diamond-shaped blocks for the eight sub-wavelength meta-atoms at 1.234 THz. Under x-polarized incidence, the phase distribution remains stable, indicating low sensitivity to changes in the side lengths of the diamond-shaped blocks. Under y-polarized incidence, the phase distribution spans a 2π range, and the reflection amplitude approximates 0.95. Consequently, an OAM metasurface array with l =  + 2 is constructed. Figure 6c–f present the simulated 2D near-field and 3D far-field results over an area of 2400 × 2640 μm2 at z =  + 800 μm under both x-polarized and y-polarized incidences. It is observed that under x-x-polarized incidence, the energy concentrates at the central point and the beam splits into a vertical configuration, as depicted in Fig. 6c and d. Under y-polarized illumination, two voids become apparent at the center of the vortex, aligning with the characteristic profile of a vortex beam, as shown in Fig. 6e. The simulated 3D far-field outcomes in Fig. 6f distinctly reveal voids at the center, confirming that the beam carries an OAM vortex with l =  + 2.

Polarization-multiplexed beam splitting design

Similarly, when ensuring that the other parameters between meta-atom "0" and meta-atom "1" remain constant, the 2 π phase distribution of the desired arranged lens can be realized under x-polarized wave irradiation at 1.551 THz by adjusting the size of meta-atom "0" (r1) and meta-atom "1" (r2), while the phase distribution fails to meet the 2 π distribution under y-polarized wave irradiation. Therefore, different functions can be realized with the incidence of different polarized waves, as demonstrated in Fig. 7a.Fig. 7 Focusing effect. (a) Reflection amplitude and phase of different diamond-shaped blocks with varying side lengths under x-polarized at 1.551 THz. (b) Phase distribution of the two-dimensional focusing lens. (c) Normalized electric field curve in the x-direction and (d) electric field distribution on xoy plane at the z = 800 μm and under x-polarized incidence.

Utilizing this characteristic, a two-dimensional focusing lens under x-polarized incidence was developed based on the phase compensation principle. The phase distribution required for focusing at the plane (z = 0) can be expressed by the following equation51:4 φ1=2πλ((x-xf)2+(y-yf)2+(z-zf)2-zf)+phase0

where, λ represents the designed wavelength, phase0=-π is the initial phase,(xf,yf,zf) denote the coordinates of the focal point, and (x,y,z) denote the coordinates of the lens center. In simulation, the focal distance is set at coordinates 0, 0, 800). This configuration necessitates at least a 20 × 19 meta-atom structure to achieve a 2π phase range simultaneously in both x and y directions. Figure 7b displays the phase distribution of the two-dimensional focusing metasurface lens, while Fig. 7c illustrates the electric field magnitude distribution on the x–y plane, showing pronounced convergence at the focal point. At z =  + 800 mu m, the electric field magnitude distribution at the center (x = 0 μm, y = 0 μm) is markedly higher than at other positions, as shown in Fig. 7d, aligning with the theoretical predictions.

By arranging two meta-atoms that satisfy the 1-bit phase, this study introduces a beam-splitting method that can be controlled by the input polarization states, as depicted in Fig. 8a. Each color patch in Fig. 8b comprises a 3 × 3 array of meta-atoms. The simulated 3D and 2D far-field beam-splitting patterns are illustrated in Fig. 8c–f. Specifically, Fig. 8c and e show the splitting of incident waves into three beams under x-polarized incidence and two beams under y-polarized incidence, respectively. Under normal incidence, the generalized Snell's law is articulated as follows47:5 θ=arcsin(λλΓΓ)

where θ denotes the reflection angle, λ denotes the wavelength of the working frequency in free space, and Γ denotes the period of the coding pattern. The encoding period of the metasurface is arranged according to Fig. 8b, which shows that the periodicity of the arranged metasurface sequence is 2, i.e., meta-atom “0” (L1 = 50 μm, r1 = 44 μm, r2 = 41 μm) and meta-atom “1” (L2 = 36 μm, r3 = 58 μm, r4 = 48 μm ) are repeated at a period of 2, and each meta-atom “0” and “1” consists of 3 × 3 encoding particles. Therefore, it can be calculated that Γ=120×2×3=720 μm. Substituting into formula (5), we can calculate the theoretical deflection angle θ=arcsin(λλΓΓ) = 15.581°. In this case, the phase difference between meta-atom “0” and meta-atom “1” satisfies a phase difference of 180° and their reflection amplitudes are close under y-polarized waves incidence. But, under x-polarized wave incidence, the two units does not satisfy a phase difference of 180°, so that it does not meet the conditions of the coding metasurface. Therefore, three beams are generated under x-polarized wave incidence, and it fails to suppress specular reflection. Figure 8d and f display that the normally incident wave divides into two symmetric reflection beams with angles of (θ,φ)=(15.58∘,0∘) and (θ,φ)=(15.58∘,180∘) defined by theta. Non-ideal phase gradients may lead to a permissible deviation of 0.1° from the generalized Snell’s law, as evidenced in the EM simulations52.Fig. 8 Reflection properties and beam-splitting effects (a) Reflection amplitude and phase of different diamond-shaped blocks with varying side lengths under x-polarized and y-polarized incidence at 1.551 THz. (b) Schematic diagram of the encoding arrangement. (c, d) The far-field scattering pattern under x-polarized incidence. (e, f) The far-field scattering pattern under y-polarized incidence.

Conclusion

In conclusion, we constructed a dual-frequency multifunctional coding metasurface by introducing two meta-atoms. Combined with geometric phase and amplitude variations of meta-atoms, we have designed four different multifunctional metasurface arrays, which achieve reflection imaging, spiral beams, focusing and abnormal reflection respectively. The metasurface 1 enables the control of switchable images through both the incident frequency and reflected polarization. Specifically, under x-polarized incidence at 1.234 THz, the pattern "L" is displayed, while under y-polarized incidence at 1.551 THz, the pattern "7" appears. By integrating a geometric phase distribution within the metasurface meta-atoms, diverse polarization multiplexing functionalities are demonstrated at these frequencies. At 1.234 THz, the metasurface 2 produces perpendicular beams under x-polarized incidence and a vortex beam with an orbital angular momentum l =  + 2 under y-polarized incidence. Meanwhile, at 1.551 THz, the metasurface 4 splits into three beams under x-polarized incidence and two beams under y-polarized incidence. The metasurface 3 develops a two-dimensional focusing lens at 1.551 THz with 2π phase coverage for x-polarization incidence. The innovative and efficient structure proposed herein provides a new paradigm for the design of multifunctional terahertz devices. Additionally, the wavefront coding strategy that synergistically combines polarization, frequency, geometric phase, and amplitude across various functionalities offers enhanced flexibility and integration, thereby broadening the scope of electromagnetic manipulation. This advancement holds significant promise for the future development of advanced meta-materials.

Acknowledgements

The research has been partially supported by the National Natural Science Foundation of China (No.62373136), Key Scientific and Technological Project of Science and Technology Department of Henan Province (No. 242102210154, 242102111171), Innovative Funds Plan of Henan University of Technology (No.2022ZKCJ02) and Key Laboratory of Grain Information Processing and Control (Henan University of Technology), Ministry of Education (No.KFJJ-2023-002).

Author contributions

C.C.: Formal analysis, writing-review & editing. Y.L.: methodology, writing-original draft. Y.Z.: conceptualization, writing-review & editing. M.L.: funding acquisition. Y.Q.: data curation.

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.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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