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Reconfigurable three multi-mode terahertz metasurface

Jiu-Sheng Li, Jia-Hui Ren, and Ri-Hui Xiong

Open Access Open Access

Abstract

We designed a three reconfigurable multi-mode terahertz metasurface based on a concentric elliptical ring structure. The proposed unit cell is a concentric elliptical ring composed of copper, vanadium oxide and photosensitive silicon from the inside ring to the outside ring. The conductivity of photosensitive silicon and vanadium oxide can be adjusted by changing the external operating temperature and pump light intensity. The same unit cell can reconstruct three kinds of states with different properties, and they have completely different transmission characteristics in various terahertz bands. By encoding the arrangement, through changing external stimulus and operating frequencies, the reconfigurable terahertz metasurface can achieve multiple functions including terahertz focusing with adjustable focal length, vortex beam with different topological charge, and near-field imaging with different patterns. It provides what we believe to be a new idea for the field of information security and the design of multifunctional and multifrequency terahertz devices.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Metasurface is a planar subwavelength topological array, which has the characteristics of simple structure, easy processing, convenient integration, and flexible manipulating wavefront capability [1,2]. In recent years, metasurface-based devices by tailoring the amplitude, phase, and polarization of electromagnetic wave have realized various compact terahertz components such as filters [3,4], absorbers [5,6], focusing lenses [7,8], orbital angular momentum generator [9–12], wavefront processing [13] and so on. Among these devices, multifunctional devices have attracted great attention due to their great potential for future terahertz frequency division multiplexing communication system with small miniaturization, high integration and light weights [14–16]. For example, in 2019, Wang et al. [17] proposed a metasurface combining dual C-slots with elliptical resonators to achieve independent phase and amplitude modulation at two terahertz frequencies by rotating the pattern orientation and changing its size. Tang et al. [18] designed a diagonal unit cell combined with vanadium oxide metasurface, which can control the terahertz wave absorption from 20% to 90% in two frequency bands by changing the external temperature. In 2022, Shang et al. [19] utilized a metal resonator and a grating layer to form a hybrid metasurface to generate four holographic images with independent reflection directions at two operating frequencies. Liu et al. [20] presented a metasurface based on three resonators to produce vortex beams at three different terahertz frequencies. However, in order to achieve multifunctional characteristics, current existing metasurfaces are mostly required the design of multiple different unit cells for array layout, hindering their application, especially in highly miniaturized and integrated devices. Hence, multi-mode and multifrequency devices using a single reconfigurable structure regulated flexibly through external stimulus are especially desirable.

To address this challenge, in this article, we propose a concentric elliptical ring metasurface unit cell composed of copper, vanadium oxide and photosensitive silicon materials, respectively. By changing the external working conditions, the same coding atom has three different coding states. By utilizing this feature for metasurface phase arrangement, multi-mode functions have been achieved including terahertz focusing with adjustable focal length, vortex beam with different topological charge, and terahertz imaging with variable pattern. Moreover, three functions within the three operating frequency bands do not affect each other. In Ref. [21–23], the reported multifunctional metasurfaces operate at a single frequency, or a dual channel metasurface works a single function, or a three functional metasurfaces operates in three frequencies, but each function is not adjustable. The existing reconfigurable metasurfaces are either multifunctional or frequency switchable. In addition, the reported near-field imaging metasurfaces have the problem of being unable to change the imaging pattern. In this article, the proposed reconfigurable multi-mode metasurface can achieve versatility and adjustable operating frequency and can switch the imaging pattern by changing the operating frequency. The designed metasurface provides a new perspective for terahertz imaging, terahertz focusing, information security, and terahertz wireless communication systems.

2. Device design and theoretical analysis

Figure 1 shows the schematic illustration of the proposed metasurface, that enables an incident terahertz beam with specific polarization to be terahertz focusing with adjustable focal length, frequency switching vortex beam, and terahertz imaging with variable pattern. The top layer is made of three concentric elliptical rings, which is composed of copper, vanadium dioxide (VO2) and photosensitive silicon from the inside ring to the outside ring. Firstly, we conducted parameter optimization scanning on the long and short axes a and b of the elliptical metal structure, and the results are shown in Fig. 2(a). The reflection curve shows a red shift with changes in a and b. When a = 10µm and b = 20µm, the terahertz wave reflectivity is the highest. Secondly, the parameter scanning results of the VO2 elliptical ring width w1 are displayed in Fig. 2(b). As w1 increases, the terahertz wave reflection curve undergoes a red shift. When w1 = 10µm, the peak reflection of terahertz waves is maximum. Finally, the width w2 of the photosensitive silicon was scanned, and the terahertz reflection curve produced a red shift as w2 increased, as shown in Fig. 2(c). When w2 = 14µm, the peak reflection coefficient at terahertz is the highest. Based on the above analysis, this article has selected the optimized values for elliptical parameters as follows: The major axis a of the copper sheet is 20µm, and the minor axis b is 10µm. The width of VO2 and photosensitive silicon ring are w1 = 10µm and w2 = 14µm. The intermediate layer is silica with the height of 20µm. The thicknesses of VO2 and photosensitive silicon are 0.2µm. The bottom layer is 0.2µm thick metal plate. The period of the unit cell is P = 100µm. The device can be fabricated as following steps: (a) Prepare a double-sided polished silica wafer; (b) Copper layers are deposited on both sides of the silica wafer; (c) Photoresist is spin coated and deposited on one of the copper layer by using photolithography; (d) Metal oval pattern is formed by using electron beam lithography; (e) The metal pattern is protected by a thin film, and then we apply a layer of photoresist and using magneton sputtered technique to create a vanadium dioxide elliptical pattern; (f) Using the same method, we finally produced an elliptical pattern of photosensitive silicon. (g) At last, the structure is obtained by lift-off process. When both the VO2 and photosensitive silicon are in the medium states, the designed unit cell is defined as state 1. When the VO2 is in the metal state, the unit cell works as state 2. While both the VO2 and photosensitive silicon are in the metal state, the unit cell operates as state 3. The details parameters and corresponding modes of unit cell working in different phase states are shown in Table 1.

 figure: Fig. 1.

Fig. 1. (a) Function schematic diagram of the proposed metasurface. (b) Three-dimensional view of the unit cell, (c) its structure parameters.

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 figure: Fig. 2.

Fig. 2. Parameters optimization scanning of the proposed unit cell.

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Tables Icon

Table 1. Detailed parameters and corresponding modes of the proposed unit cell in different phase states.

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For the Pancharatnam-Berry (PB) type phase metasurface, the rotation angle can be regarded as the rotation of the two-dimensional coordinate system. The axes of the rotated local coordinate system are u and v, respectively. The rotation angle is γ. The modulation effect of the unit cell can be expressed by the Jones matrix [24]

$$R = \left[ {\begin{array}{cc} {{R_{uu}}}&{{R_{uv}}}\\ {{R_{vu}}}&{{R_{vv}}} \end{array}} \right]$$

For anisotropic metasurface, Ruu≠Rvv, and Ruv = Rvu = 0. Then the reflection matrix can be expressed by

$${\textrm{R}_{ret}} = T({ - \gamma } )\cdot \left[ {\begin{array}{cc} {{R_{uu}}}&0\\ 0&{{R_{vv}}} \end{array}} \right] \cdot T(\gamma )= \left[ {\begin{array}{cc} {{R_{uu}}{{\cos }^2}\gamma + {R_{vv}}{{\sin }^2}\gamma }&{({R_{uu}} - {R_{vv}})\cos \gamma \sin \gamma }\\ {({R_{uu}} - {R_{vv}})\cos \gamma \sin \gamma }&{{R_{uu}}{{\sin }^2}\gamma + {R_{vv}}{{\cos }^2}\gamma } \end{array}} \right]$$

Under the circularly polarized wave incidence, the reflected wave can be derived as

$$\left[ \begin{array}{@{}l@{}} {E_{xout}}\\ {E_{yout}} \end{array} \right] = {\textrm{R}_{ret}}\left[ \begin{array}{@{}l@{}} {E_{xin}}\\ {E_{yin}} \end{array} \right] = \frac{{{\textrm{R}_{ret}}}}{{\sqrt 2 }}\left[ \begin{array}{@{}c@{}} 1\\ j\sigma \end{array} \right] = \frac{1}{{2\sqrt 2 }}\left( {({{R_{uu}} + {R_{vv}}} )\left[ \begin{array}{@{}c@{}} 1\\ j\sigma \end{array} \right] + ({{R_{uu}} - {R_{vv}}} ){e^{2j\sigma \gamma }}\left[ \begin{array}{@{}c@{}} 1\\ - j\sigma \end{array} \right]} \right)$$
where σ=±1, -1 denotes left circularly polarized (LCP) incidence, and +1 denotes right circularly polarized (RCP) incidence. According to Eq. (3), the reflected wave has both co-polarization and cross-polarization components under circularly polarized incidence. Due to the change of the propagation direction of the reflected wave, the polarization direction of the reflected waves is different from that of incident waves. The first term of formula (3) is cross-polarized reflection, and the second term is co-polarized reflection, which carries an additional PB phase α= ± 2 γ. Figure 3(a) shows the reflection coefficients of the proposed reconfigurable-multimode unit cell with different rotation angles in three frequency bands, and the reflection amplitudes of the unit cells are above 0.9. The corresponding phase differences of the reconfigurable-multimode unit cell are illustrated in Fig. 3(b).

 figure: Fig. 3.

Fig. 3. (a) Reflection amplitude, (b) corresponding phase with different rotation angles of unit cells in three states.

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3. Results and discussions

3.1 Reflective mode focus

The metasurface planar lens is designed by using a hyperboloid phase profile theory. The phase shift φ(x, y) of each unit cell position must satisfies the following relation [25]

$$\varphi ({x,y} )= \frac{{2\pi }}{\lambda }\left( {\sqrt {({{x^2} + {y^2}} )+ {f_L}^2} - {f_L}} \right)$$
where λ is the wavelength in free space, fL is defined as the focal length of the lens. The geometric center of the metasurface is defined as (0, 0). The width of the unit cell is set to be 100µm. Since the proposed unit cell has eight phase states, each unit cell can be calculated by
$${\delta _{mn}} = \left\{ {\begin{array}{ll} 0&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{0,\pi /8} ]\cup [{15\pi /8,2\pi } ]\\ {\pi / 4}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{\pi /8,3\pi /8} ]\\ {\pi / 2}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{3\pi /8,5\pi /8} ]\\ {{3\pi } / 4}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{5\pi /8,7\pi /8} ]\\ \pi &\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{7\pi /8,9\pi /8} ]\\ {{5\pi } / 4}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{5\pi /4,11\pi /8} ]\\ {{3\pi } / 2}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{11\pi /8,13\pi /8} ]\\ {{7\pi } / 4}&\textrm{for}\textrm{ }\Delta {\varphi_{mn}} - 2\pi n \in [{13\pi /8,15\pi /8} ] \end{array}} \right.$$
where n = 0, 1, 2… From Fig. 3, it can be seen that the reflection amplitudes of the reconfigurable unit cell are larger than 0.9 at frequency points 0.88THz, 1.35THz, and 1.86THz. By rotating the reconfigurable unit cell, the coverage range of the wavefront phase is 0 to 2 π, which meets the coding requirements of the focusing lens. Figure 4 displays the unit cell array arrangement of the focusing lens and its corresponding phase distribution.

Figure 5 displays the focusing function schematic diagram of the reconfigurable terahertz metasurface. From Fig. 5(a), it can be seen that the reconfigurable metasurface has good focusing effect, and the focus is all located on the central axis of the xoy plane. The lens composed of the unit cell in state 1 (see in Fig. 4(a)) produces a focusing effect at 0.88 THz with a focal length of 1050µm. The lens made of the unit cell in state 2 (see in Fig. 4(b)) generates a focusing effect at 1.35THz with a focal length of 1200µm. The lens composed of the unit cell in state 3 (see in Fig. 4(c)) achieves a focusing effect at 1.35THz with a focal length of 1200µm.

 figure: Fig. 4.

Fig. 4. (a-c)#The metasurface lens array arrangement diagram, (d-f) corresponding phase distribution diagram.

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 figure: Fig. 5.

Fig. 5. (a) Focusing function schematic diagram under RCP wave incidence, (b) The lens of Fig. 3(a) produces a focusing effect at 0.88 THz with a focal length of 1050µm, (c) The lens of Fig. 3(b) produces a focusing effect at 1.35THz with a focal length of 1200µm, (d) The lens of Fig. 3(c) produces a focusing effect at 1.86THz with a focal length of 1300µm.

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3.2 Vortex beam regulation

According to the unit structure in the three states designed, the metasurface arrangement can be designed by the phase distribution of different topological charges. To satisfy the exp(ilφ) phase of the vortex beam, the phase distribution of each metasurface position (x, y) should meet [26].

$$\varphi ({x,y} )= l \cdot {tan ^{ - 1}}\left( {\frac{y}{x}} \right)$$
where l is the topological charge of 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 calculated by
$$\varphi ({x,y} )= \frac{{2\pi }}{N}\left[ {\frac{{l\,{{tan }^{ - 1}}({y/x} )}}{{2\pi /N}} + 1} \right]$$
where N is the number of the evenly separated regions on the metasurface. Here, the topological charge is set as l = 1 and l = 2, respectively. Figure 6(a) shows the phase distribution of the vortex beam metasurface with topological charge of l = 1. The metasurfaces obtained from the array arrangement of the proposed unit cell in three states are shown in Figs. 6(b-d). Figure 6(e) represents the phase distribution of the vortex beam metasurface with the topological charge of l = 2. The corresponding metasurfaces obtained from the array arrangement of the proposed unit cell in three states are illustrated in Fig. 6(f-h).

 figure: Fig. 6.

Fig. 6. Phase distribution and structural arrangement of vortex beam metasurface. (a) Phase distribution with topological charge of l = 1, (b-d) corresponding metasurfaces obtained from the array arrangement of the proposed unit cell in three states; (e) Phase distribution with topological charge of l = 2, (f-h) corresponding metasurfaces obtained from the array arrangement of the proposed unit cell in three states.

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When the topological charge is l = 1, under the incidence of RCP waves, the metasurface generates the vortex beams in three states. Figure 7 illustrate the far-field intensity, far-field phase, electric field amplitude and electric field phase of the vortex beam at frequencies of 0.88THz, 1.35THz, and 1.86THz. The distribution of hollow ring amplitude and 2π helix phase in the figure indicates that the topological charge of vortex beam generated by the designed metasurface equals 1.

 figure: Fig. 7.

Fig. 7. Far-field intensity, far-field phase, electric field amplitude, and phase diagram of vortex beam with topological charge of l = 1 at different frequencies, (a) metasurface composed of unit cell in state 1 at 0.88THz, (b) metasurface composed of unit cell in state 2 at 1.35THz, (c) metasurface composed of unit cell in state 3 at 1.86THz.

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Generally, the mode purity can characterize the quality of the generated vortex beam, which can be defined as the ratio of the main mode power to the total power of all modes. According to the Discrete Fourier transform algorithm, the Fourier relationship between OAM spectrum Al and the corresponding sampling phase α(φ) can be described as [27]

$$\left\{ {\begin{array}{c} {\alpha (\varphi )= \sum \nolimits^{ + \infty }_{l ={-} \infty }{A_l}exp (il\varphi )}\\ {{A_l} = \frac{1}{{2\pi }}\smallint\nolimits^{\pi}_{ - \pi }d\varphi \alpha (\varphi )exp (il\varphi )} \end{array}} \right.$$
where α(φ) is the sampling of phase and exp(ilφ) is the spiral harmonic, Al represents the spectral mode weight of topological charge l. The mode purity of the vortex beam with topological charge of l = 1 is shown in Fig. 8. One can see that the mode purity of vortex beam at 0.88THz, 1.35THz and 1.86THz are 91.1%, 89.7% and 81.5%, respectively.

 figure: Fig. 8.

Fig. 8. The mode purity of the vortex beam with topological charge of l = 1 at different frequencies, (a) metasurface composed of unit cell in state 1 at 0.88THz, (b) metasurface composed of unit cell in state 2 at 1.35THz, (c) metasurface composed of unit cell in state 3 at 1.86THz.

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When the topological charge becomes l = 2, under the incidence of RCP waves, the metasurface composed of unit cell in three states generates the corresponding vortex beams. Figure 9 displays the far-field intensity, far-field phase, electric field amplitude and electric field phase of the vortex beam at frequencies of 0.88THz, 1.35THz, and 1.86THz. The distribution of hollow ring amplitude and 4π helix phase in the figure manifests that the topological charge of vortex beam equals 2, which is consistent with the theoretical design. The mode purity of vortex beam with topological charge of l = 2 is shown in Fig. 10. The mode purity of vortex beam at 0.88THz, 1.35THz and 1.86THz are 93.9%, 92.5% and 87.3%, respectively.

 figure: Fig. 9.

Fig. 9. Far-field intensity, far-field phase, electric field amplitude, and phase diagram of vortex beam with topological charge of l = 2 at different frequencies, (a) 0.88THz, (b) 1.35THz, (c) 1.86THz.

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 figure: Fig. 10.

Fig. 10. The mode purity of the vortex beam with topological charge of l = 2 at different frequencies, (a) 0.88THz, (b) 1.35THz, (c) 1.86THz.

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2.3 Near-field imaging

To achieve near-field imaging by utilizing metasurfaces, the encoding unit cells usually needs to have a large reflection amplitude difference. From Fig. 11, it can be seen that the reflection amplitude of the proposed unit cell in state 1 is close to 0.90, and the reflection amplitudes of the proposed unit cell in states 2 and 3 are below 0.15 under the terahertz wave normal incidence at 0.88 THz, indicating a significant difference in reflection amplitude. Similarly, at 1.35THz, the reflection amplitude of the proposed unit cell in state 2 is near to 0.95, while the reflection amplitudes of the proposed unit cell in state 1 and 3 are less than 0.25, indicating a significant difference in reflection amplitude. In addition, at 1.87THz, the reflection amplitude of the proposed unit cell in states 3 is close to 1, but the reflection amplitudes of the proposed unit cell in states 1 and 2 are both less than 0.4, indicating a significant difference in reflection amplitude. The results indicate that the proposed unit cell in three states meets the coding imaging requirements at several discrete frequencies. To achieve near-field imaging, the ‘Taiji’ pattern array arrangement of the imaging metasurface is displayed in Fig. 12 (a). The ‘Yang fish’ and ‘Yin fish’s eye’ in the ‘Taiji’ pattern are distributed by using the unit cell in state 1. The ‘Yang fish’s eye’ in ‘Taiji’ pattern is distributed by utilizing the proposed unit cell in state 2. The ‘Yin fish’ in the ‘Taiji’ pattern is distributed by employing the proposed unit cell in state 3. When the frequency of the incident terahertz wave is 0.88THz, the designed metasurface array presents a complete ‘Taiji’ pattern diagram, in which the part arranged unit cell in state 1 displays red, and the rest displays blue, as shown in Fig. 12(b). Similarly, as the incident terahertz wave frequency becomes 1.35THz, only the ‘Yang fish’s eye’ arranged by unit cell in state 2 can be find, as illustrated in Fig. 12(c). Furthermore, while the frequency of the incident terahertz wave is 1.86THz, we can see that the positions of ‘Yin and Yang fish’ are reversed and the ‘Yin fish’s eye’ disappears, as shown in Fig. 12(d). It can be assumed that the state of the unit cells can be continuously adjustable through external conditions, the designed structure can also achieve more patterns, providing a new development direction for information coding security.

 figure: Fig. 11.

Fig. 11. Reflection amplitudes of the proposed unit cell in three states at several terahertz frequency bands.

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 figure: Fig. 12.

Fig. 12. (a) Arrays distribution of the imaging metasurface (Yang fish and Yin fish’s eye in ‘Taiji’ pattern are distributed by using the proposed unit cell in state 1; Yang fish’s eye in ‘Taiji’ pattern is distributed by using the proposed unit cell in state 2; Yin fish in ‘Taiji’ pattern is distributed by using the proposed unit cell in state 3.). Imaging renderings at different frequencies of (b) 0.88THz, (c) 1.35THz, (d) 1.86THz.

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4. Conclusion

To sum up, we proposed a three reconfigurable multi-mode metasurface based on VO2 and photosensitive silicon. To our knowledge, reconfigurable metasurfaces have been reported for the first time. The metasurface can realize three modes such as focusing, vortex beam and imaging by varying external stimulus. Among them, the reconfigurable multimode terahertz metasurface becomes the focusing lens with different focal lengths, the vortex beam generator with different topological charges, and the near-field imaging with different patterns at three operating terahertz regions. Furthermore, by changing the corresponding geometric parameters of the unit cell, the proposed metasurface can be extended to the microwave and optical region. The presented metasurface lays the foundation for further development of terahertz information encryption and wavefront regulation.

Funding

National Natural Science Foundation of China (61831012, 62271460); Key Research and Development Program of Zhejiang Province (2021C03153, 2022C03166).

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.

References

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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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Figures (12)
Fig. 1.
Fig. 1. (a) Function schematic diagram of the proposed metasurface. (b) Three-dimensional view of the unit cell, (c) its structure parameters.

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Fig. 2.
Fig. 2. Parameters optimization scanning of the proposed unit cell.

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Fig. 3.
Fig. 3. (a) Reflection amplitude, (b) corresponding phase with different rotation angles of unit cells in three states.

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Fig. 4.
Fig. 4. (a-c)#The metasurface lens array arrangement diagram, (d-f) corresponding phase distribution diagram.

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Fig. 5.
Fig. 5. (a) Focusing function schematic diagram under RCP wave incidence, (b) The lens of Fig. 3(a) produces a focusing effect at 0.88 THz with a focal length of 1050µm, (c) The lens of Fig. 3(b) produces a focusing effect at 1.35THz with a focal length of 1200µm, (d) The lens of Fig. 3(c) produces a focusing effect at 1.86THz with a focal length of 1300µm.

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Fig. 6.
Fig. 6. Phase distribution and structural arrangement of vortex beam metasurface. (a) Phase distribution with topological charge of l = 1, (b-d) corresponding metasurfaces obtained from the array arrangement of the proposed unit cell in three states; (e) Phase distribution with topological charge of l = 2, (f-h) corresponding metasurfaces obtained from the array arrangement of the proposed unit cell in three states.

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Fig. 7.
Fig. 7. Far-field intensity, far-field phase, electric field amplitude, and phase diagram of vortex beam with topological charge of l = 1 at different frequencies, (a) metasurface composed of unit cell in state 1 at 0.88THz, (b) metasurface composed of unit cell in state 2 at 1.35THz, (c) metasurface composed of unit cell in state 3 at 1.86THz.

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Fig. 8.
Fig. 8. The mode purity of the vortex beam with topological charge of l = 1 at different frequencies, (a) metasurface composed of unit cell in state 1 at 0.88THz, (b) metasurface composed of unit cell in state 2 at 1.35THz, (c) metasurface composed of unit cell in state 3 at 1.86THz.

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Fig. 9.
Fig. 9. Far-field intensity, far-field phase, electric field amplitude, and phase diagram of vortex beam with topological charge of l = 2 at different frequencies, (a) 0.88THz, (b) 1.35THz, (c) 1.86THz.

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Fig. 10.
Fig. 10. The mode purity of the vortex beam with topological charge of l = 2 at different frequencies, (a) 0.88THz, (b) 1.35THz, (c) 1.86THz.

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Fig. 11.
Fig. 11. Reflection amplitudes of the proposed unit cell in three states at several terahertz frequency bands.

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Fig. 12.
Fig. 12. (a) Arrays distribution of the imaging metasurface (Yang fish and Yin fish’s eye in ‘Taiji’ pattern are distributed by using the proposed unit cell in state 1; Yang fish’s eye in ‘Taiji’ pattern is distributed by using the proposed unit cell in state 2; Yin fish in ‘Taiji’ pattern is distributed by using the proposed unit cell in state 3.). Imaging renderings at different frequencies of (b) 0.88THz, (c) 1.35THz, (d) 1.86THz.

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Tables (1)

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Table 1. Detailed parameters and corresponding modes of the proposed unit cell in different phase states.

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Equations (8)

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R = [ R u u R u v R v u R v v ]
R r e t = T ( − γ ) ⋅ [ R u u 0 0 R v v ] ⋅ T ( γ ) = [ R u u cos 2 γ + R v v sin 2 γ ( R u u − R v v ) cos ⁡ γ sin ⁡ γ ( R u u − R v v ) cos ⁡ γ sin ⁡ γ R u u sin 2 γ + R v v cos 2 γ ]
[ E x o u t E y o u t ] = R r e t [ E x i n E y i n ] = R r e t 2 [ 1 j σ ] = 1 2 2 ( ( R u u + R v v ) [ 1 j σ ] + ( R u u − R v v ) e 2 j σ γ [ 1 − j σ ] )
φ ( x , y ) = 2 π λ ( ( x 2 + y 2 ) + f L 2 − f L )
δ m n = { 0 for   Δ φ m n − 2 π n ∈ [ 0 , π / 8 ] ∪ [ 15 π / 8 , 2 π ] π / 4 for   Δ φ m n − 2 π n ∈ [ π / 8 , 3 π / 8 ] π / 2 for   Δ φ m n − 2 π n ∈ [ 3 π / 8 , 5 π / 8 ] 3 π / 4 for   Δ φ m n − 2 π n ∈ [ 5 π / 8 , 7 π / 8 ] π for   Δ φ m n − 2 π n ∈ [ 7 π / 8 , 9 π / 8 ] 5 π / 4 for   Δ φ m n − 2 π n ∈ [ 5 π / 4 , 11 π / 8 ] 3 π / 2 for   Δ φ m n − 2 π n ∈ [ 11 π / 8 , 13 π / 8 ] 7 π / 4 for   Δ φ m n − 2 π n ∈ [ 13 π / 8 , 15 π / 8 ]
φ ( x , y ) = l ⋅ t a n − 1 ( y x )
φ ( x , y ) = 2 π N [ l t a n − 1 ( y / x ) 2 π / N + 1 ]
{ α ( φ ) = ∑ l = − ∞ + ∞ A l e x p ( i l φ ) A l = 1 2 π ∫ − π π d φ α ( φ ) e x p ( i l φ )
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