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Abstract
A single metasurface-based device possessing multiple functionalities is highly desirable for terahertz technology system. In this paper, we design a reflective metasurface to generate switchable vortex beams carrying orbital angular momentum (OAM), focusing beams, focusing beams with arbitrary positions, and vortex beams with arbitrary topological charges in the terahertz region. By combining the spin decoupling principle and the phase addition theorem, the superposition states of OAM and focusing beams with arbitrary positions can be independent manipulated under right-handed and left-handed circularly polarized (LCP/RCP) waves illumination. Such a diversified functionalities device provides a promising application in the field of terahertz communication and terahertz super-resolution imaging.
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1. Introduction
Metasurfaces can be flexible used to control the amplitude, frequency and phase of electromagnetic waves through a planar structure less than the operating wavelength. Nowadays, the metasurfaces have been widely used in the fields of electromagnetic wave beam abnormal refraction [1–3], focused beam [4,5] and vortex beam [6–8], etc. Among them, vortex beams are expected to increase wireless communication capacity because of carrying orbital angular momentum [9], and focusing beams provide the possibility for super-resolution imaging [10,11]. However, the metasurface-based device need meet certain phase conditions. In fact, there are two main ways to adjust the phase of the metasurface (e.g. The length of the unit cell causes the propagation phase change under linear polarization wave incidence [12,13]. Under circularly polarized wave incidence, the rotation phase change of the metasurface is geometric phase [14,15]. When the meta-elements arrangement meets the phase distribution of generating a certain functional beam or multiple beams, the metasurface will produce the corresponding functional radiation beam under the different polarization wave incidence. However, the realization of multi-beam regulation is not directly adding or subtracting each functional phase of the metasurface, but by calculating the vector sum of each beam phase in the complex domain [16]. Without considering the coupling between meta-elements, the addition theorem can directly calculate the vector sum of each phase to realize the superposition of multiple functions. The multiple vortex beams and multiple focusing beams are realized easily. Superimposing multiple functions of the proposed metasurface can better meet the needs of modern scene applications, such as miniaturization and integration of electronic devices. One sees that the metasurface phase can be combined with other attributes of the electromagnetic wave, such as frequency, amplitude and polarization, to increase the multiplexing function of metasurface in another dimension [17–23]. For a general dual-frequency metasurface, one can see that the meta-element affects the phase and amplitude in the high-frequency region. While the external structure of the meta-element is related to the phase and amplitude in the low-frequency region of the presented structure [24,25]. When the linear polarization (LP) wave is incident, the metasurface can independently adjust the orthogonal linear polarization wave [26,27]. While the incident wave is changed as circular polarization wave, the geometric phase of LCP/RCP waves is fixed and cannot be adjusted [28]. In order to realize the independent control of the LCP/RCP waves, it is necessary to combine the two phases to complete the conversion from spin angular momentum to orbital angular momentum.
In this paper, we propose a multifunctional metasurface, which combines the geometric phase and propagation phase to realize the independent adjustment of LCP/RCP waves. By using the phase addition theorem, the proposed structure generates the superposition of multiple vortex beams and focusing beams. Three-kind metasurfaces based on the proposed meta-elements are designed to realize the different functions including switchable vortex beam, focusing beam, four focusing beams with different positions, and four vortex beams with different topological charges. Furthermore, different functions can also be switched by changing the polarization state of the incident wave. The simulated near-field and far-field radiation patterns are consistent with the theoretical calculation predictions. The designed metasurfaces provides a method to increase manipulation freedom degree of terahertz wave in both polarization and phase.
2. Structure design and theoretical analysis
The functions schematic diagram of the proposed metasurface to independently manipulate LCP/RCP incident wave are illustrated in Fig. 1. For RCP wave incidence, the metasurface (M1) produces a focusing beam with a focal length of 2000 µm. For the LCP wave incidence, the metasurface (M1) realizes a vortex beam with a topological charge of l = 2. Similarly, for RCP wave incidence, the metasurface (M2) generates two focusing beams with position coordinates of (x=±700µm, z = 1200µm) on xoz plane. For LCP incidence, the metasurface (M2) appears two focusing beams with position coordinates of (y=±700µm, z = 1200µm) on yoz plane. Likewise, under RCP wave incidence, the metasurface (M3) achieves two vortex beams carrying topological charges of l=-1 and l = 2. For LCP wave incidence, the metasurface (M3) attains two vortex beams with topological charges l = 1 and l=-2. Among them, each vortex beam or focusing beam is determined by pre-designed phase distribution of the metasurface. A matrix method is given to decouple the LCP/RCP waves and to derive requirement of the geometric phase and propagation phase. When the incident wave is irradiated perpendicularly on the metasurface, the electric field of the corresponding reflected wave can be described by a matrix [28,29]
From the formula (2), it can be concluded that φL=φx−2α and φR=φx+2α. The relationship between the geometric phase rotation angle α and LCP/RCP wave phases (φR and φL) is α=(φR−φL)/4. The relationship between the propagation phase (φx, φy) and the phase of LCP/RCP wave is described as: φx = (φL +φR)/2 and φy = (φR+φL)/2-180°. Formula (3) reveals the general design of the unit cell when the amplitude of the linear x-polarized (y-polarized) wave equals 1 (Rx = Ry = 1) and the phase difference is 180° (φx-φy = 180°). By adjusting the parameters α, φx and φy, we can independently control the phase of LCP/RCP waves.
Figure 2 displays the designed meta-particle consisting of five layers structure. From the top layer to the bottom layer, the meta-particle is composed of two metal pattern layers and two polyimide layers alternately superimposed on the metal plate substrate. The structure is beneficial to reduce the crosstalk between the phase change (φx) in x direction and the phase change (φy) in y direction. The multi-layer structure effectively increases the phase variation range. The thickness of metal and polyimide layer are of 35 µm and 1 µm, respectively. The period of the meta-particle is 150 µm and the radius of hollow metal circle is 70 µm. The width of the metal strip is 20 µm. The arm length of the cross is marked as x and y, respectively. The proposed structure is simulated by using finite element method, a commercial software CST Microwave Studio. The simulation model and boundary conditions are illustrated in Fig. 2(c). Figure 3(a) shows the amplitude spectra and phase of the proposed meta-particle. By adjusting the arm length and rotation angle of the crossing, the reflected amplitude is over 0.8, and phase difference between φxx and φyy is about 180°. Figure 3(b) shows the phase variation range of φxx as the length x increases from 20µm to 150µm (Here, the length y is set to be 80µm and 120µm, respectively). After optimized calculation by using formula (3), 15 kinds of meta-particles cover 2π phase with a step size of 22.5°, as shown in Fig. 3(c). From Fig. 3(d), one can see that the polarization conversion amplitude of 15 kinds of meta-particles is around 0.9 at 0.6THz under the incident of left circularly polarized wave. In order to meet the phase requirements, the phase of RCP/LCP waves incidence covers 360° range. The 15 meta-particles were rotated with 22.5° interval angle to form a 64 meta-particles library, as shown in Figure (4). Based on the meta-particle library, three kinds metasurfaces composed of 24×24 meta-particles are designed to generate multi-function including switchable vortex beam, focusing beam, multiple superimposed focusing beams and multiple superimposed vortex beams.
Fig. 2. (a) Three-dimensional diagram of the designed meta-particle, (b) Top view of the top and middle metals layer, (c) Simulation model
Fig. 3. (a) Simulated reflective amplitude and phase of the proposed meta-particle, (b) Amplitude spectra and phase of the proposed meta-particle with different x length, (c) 15 kinds of the meta-particles cover 2π phase range with 22.5° interval under the linearly polarized waves incidence, and (d) the polarization conversion reflection amplitudes from 0.4THz to 0.87THz under the incidence of left circularly polarized waves.
3. Dual-function metasurface for switching between focusing beam and vortex beam
Firstly, a bifunctional metasurface is proposed to produce switchable focusing beam and vortex beam, as shown in Fig. 5 (a). Under the right-handed circular polarization (RCP) wave incidence, the metasurface generates a focusing beam with focal length of 1200µm. A vortex beam with topological charge of l = 2 is generated on the same metasurface under the left-handed circular polarization (LCP) wave incidence. The phase distribution of the proposed metasurface can be given by the following relation
Fig. 5. Schematic illustration of the first metasurface to independently manipulate cross-polarized reflective terahertz wave, (a) Schematic diagram of vortex beam and focusing beam under RCP/LCP incidence, (b) Preset coding phase of the focusing beam and vortex beam, (c) Difference between the calculated phase and the simulated phase of the focusing beam.
Among them, φR and φL are the phase distribution under RCP and LCP wave incidence, respectively. λ is the operating wavelength, f is focal length, and l is topological charge. The coded phase distribution of the focusing beam with focal length of 2000µm and the vortex beam with topological charge value of l = 2 is shown in Fig. 5 (b). The simulated results are consistent with the calculated phase value, as shown in Fig. 5 (c).
Here, we simulated the electric field distribution and phase of the proposed metasurface by using CST Microwave Studio. Figure 6 (a-c) reveals that the near-field focusing intensity distribution of the metasurface under right-handed circular polarization wave under normal incidence (along the z-axis) at frequency of 0.6THz. The focal spot locates at 2000µm on the top of the metasurface (in xoz plane). One can see that the electric field energy is mainly concentrated in xoz plane center, and the energy scattering around is less. The full width at half peak (FWHM) is about 0.414 mm (i.e. 0.828λ). The designed structure shows good focusing characteristics. In addition, Figs. 6 (d-f) demonstrate the phase and electric field intensity distribution generated by the vertical incidence of left-handed circular polarization wave at frequency of 0.6THz. It can be seen that the designed structure produces a vortex beam with topological charge value l = 2, and the mode purity is 0.75.
Fig. 6. Electric field distribution of vortex beam and focusing beam generated by the first metasurface under RCP/LCP incidence. (a) Three-dimensional electric field energy distribution of the focusing beam, (b) Axial electric field intensity of the focusing beam, and (c) Focal plane electric field intensity of the focusing beam, (d-f) Electric field intensity and phase of the vortex beam, (f) Mode purity of the vortex beam.
4. Switchable metasurface for superimposing multiple focusing beam
Secondly, we design the second kind of meta-atoms array to generate multiple focusing beams at different positions for incident terahertz waves, as shown in Fig. 7 (a). Under the right-handed circular polarization wave incidence, the designed metasurface produces two symmetrical reflected focused beams along x-axis. But, for the incidence of left-handed circular polarization wave, the designed metasurface realizes two symmetrical reflected focusing beams along y-axis. Figure 7 (b) displays the discretized coding phase under the right-handed circular polarization wave incidence. Figure 7 (c) shows the comparison between the theoretical calculation phase and the simulated coding phase. It can be seen from Fig. 7(c) that the difference between the calculated and the simulated coded phase is tiny. According to the addition theorem, the required phase distribution for generating double focusing beams can be calculated by
Fig. 7. Schematic illustration of the second metasurface to independently manipulate cross-polarized reflective terahertz wave, (a) Schematic diagram of vertical (horizontal) dual-focusing beam under RCP/LCP incidence, (b) Preset coding phase of the horizontal dual-focus beam, (c) Difference between the calculated phase and the simulated phase of the horizontal dual-focus beam.
Figure 8 (a) describes the electric field intensity and normalized value in xoz plane under incidence of right circularly polarized wave. From the figure, it can be clearly seen that two focus points locates on the preset position (x=-700µm, z = 1200µm). The full width at half maximum (FWHM) of the two focused beams are of 354µm and 351µm, respectively. The results show that the designed metasurface has subwavelength focusing ability. Figure 8 (b) shows the focal points of the two focusing beams is located on the focal plane (z = 1200µm, xoy plane). Figures 8 (c-d) display the electric field intensity and normalized intensity in yoz plane under left-handed circularly polarized wave incidence. It can be clearly seen from the figure that there are two focus points at z = 1200 µm and the FWHM at the focal plane are 347µm and 324µm, respectively. When linearly polarized wave is incident, the designed metasurface produces four focusing beams, as shown in Fig. 8(e). At z = 1200µm, four focal points can be clearly found at the focal plane. It indicates that the proposed metasurface can generate multiple focused beams.
Fig. 8. Electric field distribution of vortex beam and focusing beam under three kinds of polarized waves incidence. (a-b) and (c-d) are the axial and transverse electric fields of double-focusing beam under RCP/LCP incidence, respectively. (e) Electric field intensity of the four focusing beams under LP incidence.
5. Switchable metasurface for superimposing multiple vortex beam
Here, we design the third metasurface to genetrate four vortex beams with different topological charges under RCP/LCP incidence, as shown in Fig. 9(a). One can see that the designed metasurface produces two off-axis vortex beams, which are located on positive axis of y-axis(x-axis) and negative axis of x-axis(y-axis). The functional beams meet the following phase distribution
Fig. 9. Schematic illustration of the third metasurface to independently manipulate cross-polarized reflective terahertz wave, (a) Schematic diagram of two off-axis vortex beams with topological charge of l = 1(l=-1) and l=-2(l = 2) under RCP/LCP incidence. (b) Preset coding phase of vortex beam under RCP incidence, (c) The simulated phase and calculated phase of the proposed metasurface.
Fig. 10. Far-field of vortex beam generated by the third metasurface under different polarized waves incidence, (a-b) and (c-d) are far-field phase and far-field radiation of vortex beam (topological charge l = 1, 2) under RCP and LCP incidence, respectively, (e) Far-field radiation of vortex beam under LP incidence.
Fig. 11. The purity of the OAM mode with different topological charges of l = 1 and l = 2 under RCP/LCP
Table 1. Performance comparison of our proposed metasurface with some previous literature reported works
6. Conclusion
To sum up, we demonstrate a novel metasurface to generate switchable superposition functions by changing RCP/LCP incident waves. The proposed metasurface realizes various functionalities including switchable vortex beam and focusing beam, double focusing beam along x- and y-axis, and vortex beam with four different topological charges. Multiple vortex beam and focusing beam are generated under three kinds of polarization waves incidence. One can manipulate the superposition of vortex and focusing beams by controlling the polarization states of the incidence wave. The simulation results are consistent with the theory predictions. Our work shows the proposed devices has potential applications in multi-channel communication and imaging. Different from the previous works [33,34], our proposed metasurface can make multiple phase functions simultaneously to generate independent control circular polarization. Furthermore, in this work, the proposed metasurface produces multiple vortex beams carrying different topological charge values.
Funding
National Natural Science Foundation of China (61831012, 61871355); Talent Project of the Science and Technology Department of Zhejiang Province (2018R52043); Zhejiang Key R & D Project of China (2021C03153, 2022C03166); Research Funds for the Provincial Universities of Zhejiang (2020YW20, 2021YW86).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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