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Abstract
Due to the limitations of frequency bands and control methods, it is difficult to achieve multi-functional integration and real-time regulation of full-space metasurfaces. In this paper, we proposed a switchable transmissive-reflective mode terahertz metasurface independently depending on the incident wave frequencies and polarizations. The unit cell consists of four metallic layers, which are separated by three silicon dioxide layers. When the x-polarized wave is incident along the ± z-axis, the meta-device achieves focusing function at 1.62 THz. When the y-polarized wave is incident along the ± z-axis, the structure generates the reflective two and four splitting beams at a frequency of 0.82 THz and realizes a focused beam with a topological charge of l=±1 at a frequency of 1.65 THz. The full wave simulation results are in good agreement with the theoretical calculation predictions. The metasurface provides a new idea for the control of terahertz devices, and has a broad application prospect in the field of terahertz systems.
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1. Introduction
Recently, encoded metasurfaces have provided a simple method to control electromagnetic waves, which can realize such as vortex beam [1,2], focusing [3,4], beam splitting [5,6], imaging [7,8] and so on. Generally speaking, coding metasurfaces are mainly divided into two types: reflection mode or transmission mode. For example, in 2020, Jing et al. [9] realized the generation of orbital angular momentum (OAM) beams with different topological charges through a double-layer metasurface (The top layer is composed of bimetallic square bars and the bottom layer is composed of metal square plates and bimetallic square bars with circular grooves). Xin et al. [10] proposed a circular grooves metal pattern and three “C” metal rings with different orientations and radii to achieve the independent regulation of vortex beam in different frequency bands. In 2021, Shabanpour et al. [11] demonstrated a glass-liquid-crystal-gold square sheet-glass structures to produce a switchable vortex beam splitting and vortex focusing functions by external applying bias voltage. In 2022, He et al. [12] presented a stack of photosensitive silicon “C” ring and gold “C” ring hybrid structure to control deflected beam and focused beam by using external laser stimulus. However, the above-mentioned metarsurfaces can only manipulate electromagnetic waves in half space, which limits the use of space resources. In order to improve the utilization rate of information resources, the concept of full space metasurface has been proposed in recent years. In 2020, Li et al. [13] reported a the square cylindrical medium and vanadium dioxide layer sandwiched structure to generate reflection-transmission modes polarization conversion and focusing functions. In 2021, Zhang et al. [14] proposed a coding element composed of four dielectric substrate layers separated by five layers of metal copper structure to achieve the GHz wave beam splitting, double vortex, and deflection. In 2022, Niu et al. [15] designed a double “C” metal rings and vanadium dioxide hybrid structure to produce the bifocal focusing function with both transmission and reflection modes by controlling the phase state of vanadium dioxide. However, these full space metasurfaces (working in GHz region) are with the aid of adjustable materials such as vanadium dioxide, photosensitive silicon, transition metal dichalcogenides (TMDCs), etc. These reported metasurfaces not only have complex requirements for processing technology and control environment, but also are difficult to achieve real-time control. In recent years, dynamic control without the aid of tunable media has become a hot research topic.
In this paper, in order to solve the above problems, we proposed a full space multi-function metasurface by using the multi-layer cascade structure. The unit cell is composed of three silicon dioxide layers and four metallic layers. Without the aid of adjustable materials, the reflection and transmission modes can be freely adjusted by changing the operating frequency and the polarization state of the incident terahertz wave. When x-polarized (x-pol) waves are incident along ± z-axis, the metasurface realizes the focusing function at the frequency 1.62 THz (the focus length are 1060 µm and -1050 µm, respectively). When the y-polarized (y-pol) wave is incident along ± z-axis, the metasurface generates two and four reflection wave beams terahertz at frequency of 0.82 THz, and the vortex beam with topological charge l=±1 at frequency of 1.65 THz. The numerical simulation results are in good agreement with the theoretical prediction. The proposed metasurface provides a new idea for the design of real-time controllable full space multifuctional terahertz devices by using a simple and easy structure.
2. Structure design
Figure 1 depicts the schematics and working principle of the proposed switchable terahertz metasurface, which can manipulate the transmissive-reflective modes terahertz waves independently depending on the incident wave frequencies and polarizations. The unit call consists of four metallic layers which are separated by three silicon dioxide layers (The dielectric constant is 3.75 and the loss angle is 0.0004). As shown in Fig. 1(a), y-polarized wave is incident onto our proposed metasurface along ± z-axis, a reflective mode vortex beam generator with topological charge l=±1 and multi splitting beams can be achieved. Meanwhile, for x-polarized wave incidence along ± z-axis, our designed metasurface works as a transmissive mode plane focusing lens (see Fig. 1(b)). The optimized coding element geometrical parameters are set as: h1 = 9 µm, h2 = 10 µm, P = 100 µm, a = 10 µm, b = 20µm. Our metasurface works with high efficiencies because the coding element is completely reflective for y-polarization incident wave and totally transparent for x-polarization terahertz wave. Our projects not only provide a new method to design compact terahertz beam splitter and vortex beam generator, but also offer a powerful guideline to explore other multifunctional terahertz metasurface-based devices or in other frequency domains functionalities device.
Fig. 1. Schematic diagram of the proposed transmissive-reflective modes switchable terahertz metasurface by polarization wave and operating frequency manipulation and the given unit cell (a) reflection mode, (b) transmission mode, (c) three-dimensional view of unit cell, (b) Top view of top layer metal structure, (c) Top view of middle layer metal structure.
By controlling the corresponding structural parameters, the metasurface can achieve 2π phase coverage for different polarized waves and frequencies for both transmission and reflection modes. Figures 2(a) and 2(b) show the reflection coefficient and phase distribution of the unit cell as a function of d1 under y-polarized wave incidence. Obviously, the reflection coefficient is larger than 0.95 at frequency of 0.82 THz, and reflection phase difference is 180°. Figures 2(c) and 2(d) display the reflection coefficient and phase with different length of the short bar (d2) under y-polarized incidence. The phase difference of the designed eight kinds of unit cells is about 45° at 1.65THz, and their reflection coefficients are larger than 0.88. Figures 2(e) and 2(f) illustrate the transmission coefficient and phase change with various slit length d3 of the intermediate metal layer under the x-polarized wave incidence. The transmission coefficient of the designed unit cell exceeds 0.75 at 1.62 THz, and the phase difference meets 180°. The unit cell meets independently dual-frequency regulation under y-polarized wave incidence and single-frequency regulation under x-polarized wave incidence.
Fig. 2. Transmission, reflection coefficient and phase of the proposed unit cell. (a, b) reflection coefficient and phase (with various value of d1) under y-pol incidence; (c, d) reflection coefficient and phase (with various value of d2) under y-polarized incidence; (e, f) transmission coefficient and phase (with various value of d3) under x-pol incidence.
In order to explain the working mechanism, Figs. 3(a)-(d) display the electric field distribution of the top metal layer and the intermediate metal layer under x-polarized and y-polarized waves incidence along -z-axis. For x-polarized wave incidence, the top layer metal structure has no electric field response at 1.62 THz (see Fig. 3(c)), while there is strong resonance at the square slit of the middle layer metal structure (see Fig. 3(d)). Since the two middle metal layers have the same pattern, the transmission coefficient and phase of x-polarized wave are mainly related to the square slit of the two metal layers. For the y-polarized wave incidence, the strong resonance of the electric field is excited in the middle long metal strip of the top metal structure at 0.82 THz (see Fig. 3(a)). The electric field response is caused in the short metal strip of the top metal structure at 1.65 THz (see Fig. 3(e)). From Figs. 3(b) and 3(d), one can see that there is no electric field response in middle metal layer. It means that the y-polarized incident wave is completely reflected by the layer. Therefore, electric field response of the metal strip in the top layer depends on incident polarizations. The bi-directional incident y-polarized wave is completely reflected by the two middle metal layers.
Fig. 3. Electric field distribution. At 0.82 THz and under y-pol incidence (a) electric field distribution of the first layer, (b) electric field distribution of the second layer. At 1.62 THz and under x-pol incidence (c) electric field distribution of the first layer, (d) electric field distribution of the second layer. At 1.65 THz and under y-pol incidence (e) electric field distribution of the first layer, (f) electric field distribution of the second layer.
3. Simulation results and analysis
Based on the unit cell as above, we design a full space multi-function metasurface to generate focusing, splitting and vortex beams. The metasurface consists of 16 × 16 unit cells, The reflective operating frequencies are set as 0.82 THz and 1.65 THz under y-polarized wave incidence. Similarly, the transmission operating frequency is set as 1.62 THz under x-polarized wave incidence. In order to satisfy the phase of the vortex beam generator, the phase distribution of the (x, y) coding element at different positions of the metasurface can be expressed as
To simplify the design, the metasurface can be divided into N triangular regions, and the phase distribution of each region can be calculated by
Figure 4(a) shows a schematic diagram of the vortex beams metasurface arrangement with topological charge l = 1 (with various value of d1). The whole metasurface area is divided as N = 8 and the wavefront phase are arranged in the counterclockwise direction. The phase coverage range is 0∼2π and the phase difference is π/4. Figure 4(b) and 4(c) give the far-field intensity and phase diagram of the vortex beam generated by the metasurface under y-polarized wave incidence along -z-axis at 1.65 THz. It can be seen from the figure that there is a concave cavity in the vortex center. Since the OAM vortex beam has a phase singularity, the field strength of the beam center approaches 0. In order to evaluate the quality of vortex beam generators, the mode purity concept of OAM is introduced. It is generally believed that the lager is the value of the OAM mode purity, the higher is the corresponding vortex beam quality. The mode purity of OAM vortex beams with different topological charges can be calculated by
Fig. 4. The proposed metasurface arrangement for reflected vortex beam (l = 1), far field, phase, mode purity. (a) reflected vortex beam metasurface arrangement, (b) reflected vortex beam far field, (c) reflected vortex beam far field phase; (d) reflected vortex beam mode purity under y-pol wave incidence along -z-axis at 1.65 THz.
Fig. 5. The proposed metasurface arrangement for reflected vortex beam (l = -1), far field, phase, mode purity. (a) reflected vortex beam metasurface arrangement, (b) reflected vortex beam far field, (c) reflected vortex beam far field phase; (d) reflected vortex beam mode purity under y-pol wave incidence along + z-axis at 1.65 THz.
According to the scattering theory, the far-field scattering function of the proposed digital metasurface can be given by [16]
Fig. 6. The proposed metasurface arrangement for reflected splitting beam, far field, normalized reflected energy amplitude curve. (a) reflected quarter splitting beam metasurface arrangement, (b) reflected quarter splitting beam far field, (c) normalized reflected energy amplitude curve of four splitting beam wave under y-pol wave incidence along -z-axis at 0.82 THz; (d) reflected two splitting beam metasurface arrangement, (e) reflected two splitting beam far field, (f) normalized reflected energy amplitude curve of two splitting beam wave under y-pol wave incidence along + z-axis at 0.82 THz.
In order to realize the transmission mode focusing function, the theoretical transmission phase φ of the unit cell needs to satisfy the following relation [17]
where xi and yj represent the position of the unit cell in the metasurface, and F represents the focal length. Here, the metasurface focal length is set as F = 1000 µm and wavelength λ=185.2 µm. The metasurface arrangement is illustrated in Fig. 7(a) (with various value of d3). When the x-pol wave is incident along -z-axis at the frequency of 1.62THz, the electric field distributions on xoz and xoy planes are shown in Figs. 7(b) and 7(c), respectively. It can be seen from Fig. 7(b) that the focal length of the focal point is -1050 µm, which is close to the theoretical value of 1000 µm. Figure 7(d) shows the lateral electric field intensity distribution curve of the focus at the focal length, where the focus field intensity can reach up to 1.14 V/m. When the x-pol wave is incident along + z-axis at frequency of 1.62 THz, its electric field distributions in the xoz and xoy planes are shown in Figs. 7(e) and 7(f). It can be seen from Fig. 7(e) that the focal length of the focal point is F = 1060 µm, which is close to the theoretical value of 1000 µm. Figure 7(d) shows the lateral electric field intensity distribution curve of the focus at the focal length, whose focus field intensity reaches 1.16 V/m.Fig. 7. The proposed metasurface arrangement for transmitted focused beam, electric field, electric field intensity distribution curve. (a) transmitted focused beam coding metasurface arrangement, (b) transmitted focused beam electric field, (c) transmitted focused beam electric field intensity distribution curve under x-pol wave incidence along -z-axis at 1.62 THz; (b) transmitted focused beam electric field, (c) transmitted focused beam electric field intensity distribution curve under x-pol wave incidence along + z-axis at 1.62 THz.
4. Conclusion
To sum up, we propose a switchable transmissive-reflective modes terahertz metasurface by changing incident wave polarization and operating frequency. It is composed of three dielectric layers and four metal layers. The top and bottom metal layers consist of a single horizontal strip in the center and four vertical strips with different lengths. The middle metal layer is a metal square piece etched with two identical square slits. The full-wave simulation and theoretical calculation results show that the metasurface achieve focusing function at 1.62 THz under x-pol wave incidence along ± z-axis (the focal lengths are 1060 µm and -1050 µm, respectively). When y-pol wave is incident along ± z-axis, the metasurface realizes the reflection of two and four terahertz wave splitting beams at frequency of 0.82THz. At the same time, the structure produces a reflective vortex beam with topological charge l=±1 at frequency of 1.65 THz. The novel switchable transmissive-reflective modes terahertz metasurface by polarizations and operating frequencies manipulation provides a new idea for the design of real-time control of multifunctional terahertz devices.
Funding
National Natural Science Foundation of China (61831012, 61871355, 62271460); Zhejiang Key R & D Project of China (2021C03153, 2022C03166); Fundamental Research Funds for the Provincial Universities of Zhejiang (2022YW87); Natural Science Foundation of Xinjiang Uygur Autonomous Region (2021D01A73).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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