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Abstract
We propose a terahertz metasurface that can independently regulate linearly circularly polarized waves. It consists of the top layer “O-O” metal pattern, polyimide layer, middle layer “I” shaped metal pattern, polyimide layer, and metal substrate from top to bottom. By using the phase principle of Pancharatnam Berry (PB) for encoding and arrangement, the metasurface generates vortex beams with different topological charges under circularly polarized terahertz wave incidence, and achieves focusing shift at different positions. Combining the convolution theorem for encoding arrangement, the metasurface can achieve focused vortex function under circularly polarized terahertz wave incidence. The designed metasurface can also generate Airy beam under linearly polarized terahertz wave incidence. The simulation results indicate that under different polarization (linear/circular polarization) terahertz wave incidence, the metasurface can achieve different functions, which provides a new approach for flexible control of terahertz waves.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces are composed of two-dimensional subwavelength artificial structures with periodic structures, which have strong capabilities in regulating the amplitude, phase, and polarization of electromagnetic waves, providing convenience for device integration and miniaturization [1–3]. In 2014, Cui et al. [4] proposed that digital encoded metasurfaces provide great degrees of freedom for controlling electromagnetic waves. The reported digital encoded metasurface devices include planar polarizers [5–7], focusing lenses [8], holography [9,10], and vortices [11–14]. In 2021, Fan et al. [15] used the PB phase principle to design a multi bit digital encoding element and performed metasurface array compensation with different encoding sequences, achieving free control of the scattering angle of reflected electromagnetic waves. In 2023, Chen [16] introduced a diagonal cross shaped graphene structure into metasurfaces to achieve vortex beams with tunable topological charges under linearly polarized wave incidence. The above-mentioned metasurfaces can only respond to linearly polarized terahertz waves or circularly polarized terahertz waves separately. Recently, linear and circular polarization wavefront manipulation has attracted attention [17–25]. To achieve multi-degree of freedom control of terahertz waves, it is necessary to design a metasurface with simultaneously regulating both linearly polarized and circularly polarized waves.
In this article, we design a terahertz metasurface with independent modulation of linear-circular polarization wave by using “O-O” metal pattern. From top to bottom, the proposed metasurface consists of a top layer “O-O” metal pattern, a polyimide layer, an intermediate layer “I” shaped metal pattern, a polyimide layer, and a metal substrate. By independently changing the rotation angle of the top metal structure and the size of the middle metal structure, independent control of circularly polarized and linearly polarized terahertz waves can be achieved. Simulation results are consistent with theoretical predictions. The designed metasurface provides a polarization and phase control method for terahertz waves, greatly improving the degree of freedom and efficiency of terahertz wave control.
2. Structure design
Figure 1 shows a schematic diagram and coding element of the proposed terahertz wave metasurface with independent control of circular and linear polarization. The metasurface structure consists of a top layer “O-O” metal pattern, a polyimide layer, an intermediate layer “I” shaped metal pattern, a polyimide layer, and a metal substrate from top to bottom. Relative dielectric constant of polyimide is ɛ= 3.6 with a thickness of 39 µm. The top layer “O-O” metal pattern, the middle layer “I” shaped metal pattern, and the bottom metal material are all made of gold, with a thickness of 1 µm. The optimized encoding element parameters are: P = 100 µm, l = 48 µm, w = 20 µm, and g = 30 µm. We employed CST simulation software to optimize the coding element. In the numerical simulation of the coding elements, both x-axis and y-axis are set as the periodic boundary condition. +z direction is set as floquet port, and terahertz wave incidence along -z direction. Under circularly polarized terahertz wave incidence, eight kinds of encoding elements can be obtained by rotating the top metal structure according to the PB phase principle. The designed 3-bit encoding elements and related parameters are shown in Table 1. The amplitude and phase response curves of eight kinds of encoding elements under circularly polarized terahertz wave incidence are shown in Fig. 2. The reflection amplitude of terahertz wave is greater than 0.8, and the reflection phase difference between adjacent encoding elements is about 45°. Figure 3 shows the amplitude and phase response curves of the designed encoding elements under linearly polarized terahertz wave incidence. At frequency of 1.7 THz, by adjusting the rotation angle β, which can meet the reflection phase requirements of 0° or 180°.
Fig. 1. Schematic diagram of independent modulation of terahertz metasurface function by linear-circular polarization, (a) three-dimensional diagram of encoding element, (b) schematic diagram of top layer metal structure, (c) intermediate layer metal structure.
Fig. 2. Amplitude and phase response curves of the designed metasurface under circularly polarized terahertz wave incidence.
Fig. 3. Amplitude and phase response curves of the designed metasurface under linearly polarized terahertz wave incidence.
Table 1. Schematic diagram and related parameters of 3-bit encoding element
3. Results analysis
3.1 Vortex beam
The phase distribution of different topological charges can be used to design vortex metasurfaces. To meet the phase requirement exp(ilφ) of vortex beams, the phase distribution of each position (x, y) of the encoding element can be calculated by
where l is the topological charge of the vortex beam. To simplify the design, the proposed metasurface can be divided into N triangular regions, and the phase distribution of each region can be obtained byFig. 4. Metasurface phase and encoding element layout corresponding to vortex beams with different topological charges, (a-d) phase distribution, (e-f) encoding element layout.
Using electromagnetic simulation software CST, we perform electromagnetic simulation calculations on the four designed metasurfaces. We assume that a right-handed circularly polarized (RCP) terahertz beam is vertically incident on the metasurface. Figure 5 displays the three-dimensional far-field, phase distribution, and normalized electric field intensity of vortex beams generated by metasurfaces with different topological charges (l=−2, −1, 1, 2) under right circularly polarized terahertz wave incidence at frequency of 1THz. From Fig. 5(a-d), it can be clearly seen that the vortex beam generated by the metasurface has a donut shaped contour and amplitude at the center of different topological charges, satisfying the far-field characteristics of the OAM vortex beam. The center of the far-field intensity distribution forms a concave cavity, which is consistent with the typical characteristic of a hollow amplitude in the OAM vortex beam in space. This is due to the phase singularity of the OAM vortex beam, which causes the intensity in the middle of the beam to be zero. In addition, it can be noted that the radius of the cavity in the middle of the far-field intensity also increases as the topological charge l increases. This is due to the inherent divergence of the orbital angular momentum vortex beam. The electric field distribution at reflection direction 2000µm distance from metasurface is shown in Fig. 5(e-h). It can be clearly seen from the figure that the amplitude of the electric field at the center of the vortex beam is 0. It can also be more intuitively observed that as the topological charge increases, the radius of the central dark ring in the reflection field donut shape also increases.
Fig. 5. Three dimensional far-field modes and normalized amplitudes of vortex beams with different topological charges, (a-d) three-dimensional far-field intensity and phase, (e-h) normalized electric field intensity.
To evaluate the quality of the vortex beam generator, OAM mode purity is introduced. It is generally believed that the larger the purity of OAM mode, the higher the quality of its corresponding vortex beam. Based on Fourier transform, the mode purity and azimuth of OAM vortex beams with different topological charges can be calculated. Φ is a periodic function, and the corresponding Fourier conjugate is the vortex beam spectrum, which can be expressed as
3.2 Focusing offset
The encoding metasurface for achieving focus shift needs to meet the following phase distribution
where a factor of $\xi $=500 µm is introduced in the x and y directions is used to generate off axis focus, with a focal length set to ${z_f}$=2000µm. The metasurface contains 24 × 24 encoding elements. The phase distribution of metasurfaces, that can produce left-right up and down shift focusing effects, is shown in Fig. 7(a-d). Figure 7(e-f) displays the two-dimensional electric field generated by the metasurface with left-right offset focused beams under the incidence of RCP terahertz waves at frequency of 1 THz. The electric field deviates ±500µm along the x-axis. The position has a significant focusing effect. Corresponding to x = 500µm, the distribution of electric field in the y-z section is shown in Fig. 7(i-j). From the figure, it can be observed that a noticeable focusing effect is at position of zf = 2000µm. Figure 7(g-h) gives the two-dimensional electric field generated by the metasurface with up and down offset focused beams under the incidence of RCP terahertz waves at frequency of 1 THz. The electric field deviates ±500 µm along the y-axis. The position has a significant focusing effect. The distribution of electric field in the x-z section at y = 500 µm is shown in Fig. 7(k-l). There is a noticeable focusing effect at position zf = 2000µm. As shown in Fig. 7, the designed metasurface can generate focused beams with different offset directions in the horizontal and vertical directions, which is consistent with the preset results.Fig. 7. Focusing offset, (a-d) phase arrangement of left, right, up, and down focusing offset metasurfaces, (e-h) two-dimensional electric field in the x-z section, (i-l) two-dimensional electric field in the y-z section.
3.3 Focused vortex beam
The phase arrangement process of the focused vortex metasurface is obtained by superimposing the phase of the focusing lens and the phase of the vortex beam, as shown in Fig. 8. The phase distribution of the focused vortex beam metasurface can be calculated by
Fig. 8. Phase distribution process of focused vortex metasurface, (a) phase distribution of focused metasurface, (b) phase distribution of vortex beam metasurface, (c) phase distribution of focused vortex beam metasurface.
Fig. 9. (a-d) The phase arrangement of the focused vortex beam metasurface (l=± 1, l=± 2), (e-h) Spiral phase of the focused vortex beam, (i-l) Normalized electric field intensity of the focused vortex beam, and (m-p) Two-dimensional electric field of the focused vortex beam.
3.4 Airy beam
Airy beams are the non-diffracting waves in one-dimensional planar systems. In addition to their non diffracting characteristics, the propagation of Airy beams exhibits unique self-bending and self-healing behaviors in the absence of any external potential. The phase distribution and amplitude distribution of the one-dimensional Airy beam generator can be expressed as
The designed metasurface has one-dimensional amplitude and phase distribution characteristics along x-direction and y-axis. The amplitude and phase distribution along the x-direction of the designed encoding elements are shown in Figs. 10(a) and 10(b), respectively. Numerical simulations were conducted by using electromagnetic simulation software CST, and periodic and open boundary conditions were applied in the y and x directions, respectively. Figure 10(c) shows the electric field intensity of the Airy beam at frequency of 1.7 THz, from which the non-diffraction and self-bending characteristics can be clearly observed. By placing a size of 400µm × 400 µm rectangular PEC obstacle in front of the center of the main lobe (−210 µm, 1000 µm), we studied the unique self-healing characteristics of Airy beams. Figure 10(d) represents the electric field distribution of PEC barrier at frequency of 0.8 THz. The results indicate that due to the diffraction effect, the introduced obstacles can locally modify the contour of the beam, but the interfered beam contour can be automatically corrected after passing through the obstacles. One can see that an Airy beam generator has been implemented using the proposed metasurface structure with phase and amplitude modulation.
Fig. 10. Airy beams generated by metasurfaces. (a) The arrangement of Airy beam metasurface, (b-c) Amplitude and phase of encoding elements, (d-e) Airy beam electric field distribution with and without rectangular PEC obstacles.
4. Conclusion
To sum up, we design a terahertz metasurface that can independently control linearly/circularly polarized waves. Under the incidence of circularly polarized waves, the designed metasurface generates vortex beams with different topological charges, focusing offset beams at different positions, and focusing vortex beams with different topological charges. A comparison with other similar articles can be seen in Table 2, one can see that the designed metasurface has relatively good performance and multi-function. Under the incidence of linearly polarized waves, the designed metasurface produces Airy beam. By independently regulating linearly/circularly polarized waves, the metasurface design concept provides a new approach for flexible control of terahertz waves with high degrees of freedom.
Table 2. Performance comparison of our work with some previous works.
Funding
Natural Science Foundation of Zhejiang Province (LZ24F050005); National Natural Science Foundation of China (62271460).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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