Terahertz reconfigurable dielectric metasurface hybridized with vanadium dioxide for two-dimensional multichannel multiplexing

The metasurface hybridized with vanadium dioxide (VO₂) can be dynamically tuned, which has attracted enormous attention in recent years and orbital angular momentum (OAM) multiplexing based on metasurfaces has shown promising prospects in terahertz communications. However, existing research on VO₂ metasurface focuses on the metallic metasurface. The dielectric VO₂ metasurface used for OAM multiplexing is rarely reported to the present. This paper proposed a terahertz reconfigurable dielectric metasurface hybridized with VO₂ for two-dimensional multichannel multiplexing combing with spatial and frequency domains. The metasurface works in both reflection and transmission modes and simultaneously the polarization control and operating frequency band regulation can be realized by switching the VO₂ from the metallic state to the insulator state. For the reflective or transmissive metasurface, when 4×M-channel (M is a positive integer) off-axis plane waves are incident on the metasurface, the co-polarization reflected or cross-polarization transmitted waves are transformed into 4×M-channel orthogonal on-axis beams with topological or frequency orthogonality. A metasurface composed of 14 × 14 unit cells is designed for verification. The simulated result shows that two-dimensional 12-channel multiplexing combing with OAM and frequency by the designed metasurface can be realized on the reflection and transmission modes in two different frequency bands. The proposed metasurface has great potential in terahertz communications.

Introduction

The metasurface [1], as the two-dimensional metamaterial, can effectively manipulate the phase, amplitude, and polarization of electromagnetic (EM) waves and considerable effort has been devoted to investigating the metasurface. The metasurface hybridized with dynamically tunable materials, such as graphene [2], liquid crystals [3], and PIN diode [4], is called reconfigurable metasurface [5]. Compared with the fixed metasurface without active materials, EM properties of the reconfigurable metasurface can be dynamically tuned by controlling the active devices, which has attracted enormous attention in recent years. The phase-change material vanadium dioxide (VO₂) offers excellent switching behavior from insulator state to metallic state around 68°C driven by temperature, electric fields, and laser pumping in the terahertz region [6, 7]. Therefore, it is an efficient method to incorporate VO₂ into the metasurface to realize the terahertz reconfigurable metasurface. Besides, according to the primary category of materials constituting metasurface, metasurfaces can be divided into metallic and dielectric metasurfaces. The dielectric metasurface has advantages of low Ohmic loss, low cost, ultrahigh transmission efficiency, etc., compared with metallic metasurface [8]. But the existing research on VO₂ reconfigurable metasurface has been focused on the metallic metasurface. Therefore, the reconfigurable dielectric metasurface hybridized with VO₂ is worthy of being further studied.

In general, five physical domains, including time, polarization, frequency, quadrature, and space, can be used for beam multiplexing to improve the data rate and capacity of communication systems [9]. The vortex beam carrying orbital angular momentum (OAM) is characterized by the doughnut-shaped intensity profile and helical phase front. Besides, OAM beams with various topological charges are orthogonal with each other and are available for spatial multiplexing [10]. Therefore, generating the OAM beam [11–15], achieving OAM multiplexing [13, 16–23], and further realizing two-dimensional or multi-dimensional multiplexing combined with OAM and other four physical domains by metasurface [24–28], have shown promising prospects in high-speed and huge-capacity communication systems, especially in terahertz communications. However, existing VO₂ reconfigurable metasurfaces are mainly concentrated on achieving active manipulation of the transmission coefficient [29], reflection coefficient [30], planar-chiral response [31], and Mie resonant [32], or realizing dynamic polarization converter [33, 34], metalens [35], absorber [36, 37], beam splitter [38, 39], OAM generator [40], and meta-holography [41]. The VO₂ metasurface used for OAM multiplexing [42] is rarely reported to the present.

A terahertz reconfigurable dielectric metasurface embedded with VO₂ for two-dimensional multichannel multiplexing combing with spatial and frequency domains is presented in this paper. The metasurface can simultaneously realize reflection-transmission mode switching and polarization regulation and the working frequency is controlled by easily tuning the state of VO₂ without physically changing the structure. The unit cell of the metasurface comprises a top silicon elliptical pillar and a silicon-VO₂ substrate. When the circularly polarized wave is perpendicular to the unit cell with VO₂ in the metallic and insulator states respectively, the simulation result shows that both the 3 dB bandwidth of the co-polarization reflection coefficient and the cross-polarization transmission coefficient is about 0.1 THz. Operating frequency bands are about 0.18–0.28 THz and 0.25–0.35 THz respectively. The metasurface is designed based on the method of two-dimensional multichannel multiplexing combing with spatial and frequency domains [27] and the Pancharatnam Berry (PB) phase (geometric phase) principle [43, 44]. The simulated results show that the designed metasurface can work in both reflection and transmission modes with the working frequency range of 0.18–0.28 THz and 0.25–0.35 THz respectively. By switching the state of VO₂, 12-channel orthogonal on-axis co-polarization reflected beams and cross-polarization transmitted beams with topological or frequency orthogonality are generated, when 12-channel off-axis plane waves are incident onto the dielectric metasurface. That is, two-dimensional multichannel multiplexing combing spatial and frequency domains can be achieved in both reflection and transmission mode by the proposed metasurface. The proposed metasurface has great potential in terahertz communications.

Operating principle

Figure 1 shows the schematic diagram for two-dimensional multichannel multiplexing combing spatial and frequency domains by the terahertz reconfigurable dielectric metasurface which can work in both reflection and transmission modes by tuning the VO2.

FIGURE 1

FIGURE 1. The schematic diagram for two-dimensional multichannel multiplexing combing with spatial and frequency domains is achieved by the reconfigurable dielectric metasurface which can work in both reflection and transmission modes (A) For reflective metasurface, 4×M-channel off-axis RCP plane waves with the frequency f_m and angle of incidence θ_i (f_m) (m = 1, … , M) are incident on the metasurface from the negative z-axis along negative x and y directions, and positive x and y directions respectively, RCP reflected waves are transformed into 4×M-channel orthogonal on-axis OAM beams with different topological charges (l = l₁, l₂, l₃, and l₄) or frequencies (f = f₁ to f_M) (B) Similarly, for the transmissive metasurface, 4×M-channel off-axis LCP plane waves are incident on the transmissive metasurface from the positive z-axis along with negative x and y directions, and positive x and y directions respectively, RCP transmitted waves are transformed into 4×M-channel orthogonal on-axis OAM beams with topological or frequency orthogonality.

As shown in Figure 1A, the designed metasurface works in the reflection mode. For the group 1 (channels C₁₁ to C_1M), M-channel right-handed circularly polarized (RCP) plane wave with frequency f_m and angle of incidence θ_i (f_m) (m = 1, … , M) obliquely illuminate the reflective metasurface from the negative z-axis along the -x direction, in the direction perpendicular to the metasurface, the co-polarization reflected waves (RCP reflected wave) are transformed into on-axis OAM beams with l₁. Because frequencies of channels C₁₁ to C_1M are different, the generated M-channel on-axis OAM beams are orthogonal with each other. In the same way, for the group 2 (channels C₂₁ to C_2M), the group 3 (channels C₃₁ to C_3M), and the group 4 (channels C₄₁ to C_4M), the RCP plane wave with frequency f_m and the angle of incidence θ_i (f_m) obliquely illuminate on the reflective metasurface from the negative z-axis along negative y, positive x, and positive y directions respectively, in the direction perpendicular to the metasurface, RCP reflected waves are transformed into M-channel orthogonal on-axis OAM beams with l₂, l₃, and l₄ respectively. Besides, the topological charges of these four groups of OAM beams are different from each other. Thus, it can be seen that 4×M-channel orthogonal on-axis beams with topological or frequency orthogonality are realized, and two-dimensional multichannel multiplexing combing with spatial and frequency domains by the reflective metasurface is achieved.

As shown in Figure 1B, the designed metasurface works in the transmission mode. Similarly, for the group 1 to group 4, 4×M-channel left-handed circularly polarized (LCP) plane waves with frequency f_m and angle of incidence θ_i (f_m) (m = 1, … , M) obliquely illuminate on the transmissive metasurface from the positive z-axis along negative x and y directions, as well as positive x and y directions respectively, in the direction perpendicular to the metasurface, the cross-polarization transmitted waves (RCP transmitted wave) are transformed into 4×M-channel orthogonal on-axis OAM beams with topological or frequency orthogonality. Thus, two-dimensional multichannel multiplexing combing with spatial and frequency domains by the transmissive metasurface can be realized.

First, to generate the OAM beam with topological charge l, the phase profile φ_l of the metasurface should satisfy Eq. 1:

${\phi }_l\left(x,y\right)=l\bullet \arctan \frac{y}{x},l=0,\pm 1,\pm 2,\cdots (1)$

where (x, y) represents the arbitrary coordinate position on the metasurface and l represents the topological charge. It is worth noting that the topological charge of the plane wave is 0.

Then, according to the generalized laws of reflection and refraction [45], set the phase-gradient metasurface as the interface between the media one and 2. When the EM wave is incident on the metasurface from media one along the negative z-axis, the incidence angle α_i and reflected angle α_r should satisfy Eq. 2, and when the EM wave is incident on the metasurface from media two along the positive z-axis, the incidence angle α_i and refracted angle α_t should satisfy Eq. 3:

$\sin \left({\alpha }_{\mathrm{r}}\right)-\sin \left({\alpha }_{\mathrm{i}}\right)=\frac{{\lambda }_0}{2\pi n_{\mathrm{i}}}\frac{d{\phi }_{\mathrm{d}}\left(x\right)}{dx}\text{or}\sin \left({\alpha }_{\mathrm{r}}\right)-\sin \left({\alpha }_{\mathrm{i}}\right)=\frac{{\lambda }_0}{2\pi n_{\mathrm{i}}}\frac{d{\phi }_{\mathrm{d}}\left(y\right)}{dy}(2)$

$\sin \left({\alpha }_{\mathrm{t}}\right)n_{\mathrm{t}}-\sin \left({\alpha }_{\mathrm{i}}\right)n_{\mathrm{i}}=\frac{{\lambda }_0}{2\pi }\frac{d{\phi }_{\mathrm{d}}\left(x\right)}{dx}\text{or}\sin \left({\alpha }_{\mathrm{t}}\right)n_{\mathrm{t}}-\sin \left({\alpha }_{\mathrm{i}}\right)n_{\mathrm{i}}=\frac{{\lambda }_0}{2\pi }\frac{d{\phi }_{\mathrm{d}}\left(y\right)}{dy}(3)$

where n_i and n_t are refractive indices of the media. (dφ_d/dx) and (dφ_d/dy) are constant gradients of phase discontinuity along the metasurface. If n_i = 1, n_t = 1, and α_i = 0°, the phase profile φ_d of the phase-gradient metasurface can be expressed as Eq. 4:

${\phi }_{\mathrm{d}}\left(x\right)=\pm \frac{2\pi }{D}\bullet x\text{or}{\phi }_{\mathrm{d}}\left(y\right)=\pm \frac{2\pi }{D}\bullet y(4)$

where D = M · P is the super unit cell period along the phase gradient direction, P is the period of the unit cell, and M is the number of units constituting the super unit cell. α_r and α_t can be expressed as Eqs. 5,6:

${\alpha }_{\mathrm{r}}\left(f\right)=\arcsin \left(\frac{C}{\mathit{2}\pi f}\bullet \frac{d{\phi }_{\mathrm{d}}\left(x\right)}{dx}\right)\text{or}{\alpha }_{\mathrm{r}}\left(f\right)=\arcsin \left(\frac{C}{\mathit{2}\pi f}\bullet \frac{d{\phi }_{\mathrm{d}}\left(y\right)}{dy}\right)(5)$

${\alpha }_{\mathrm{t}}\left(f\right)=\arcsin \left(\frac{C}{\mathit{2}\pi f}\bullet \frac{d{\phi }_{\mathrm{d}}\left(x\right)}{dx}\right)\text{or}{\alpha }_{\mathrm{t}}\left(f\right)=\arcsin \left(\frac{C}{\mathit{2}\pi f}\bullet \frac{d{\phi }_{\mathrm{d}}\left(y\right)}{dy}\right)(6)$

where f is the incident wave frequency and C represents the EM wave velocity in the free space. α_r and α_t are related to f.

Therefore, according to Eqs. 1,4, when a plane wave with f is vertically incident on a reflective or transmissive metasurface, to generate four-channel off-axis beams deflected along ± x and ± y directions with α_r or α_t and different topological charges, the transfer function t of the metasurface should satisfy Eq. 7:

$t={\displaystyle \sum }_{m=\mathit{1}}^{\mathit{4}}{e}^{j\left({\phi }_{l_m}+{\phi }_{{\mathrm{d}}_m}\right)}(7)$

Next, according to Eq. 7, if four-channel off-axis plane beams are incident on the reflective metasurface from the negative z-direction or on the transmissive metasurface from the positive z-direction with f and the angle of incidence θ_i (f), the phase profile ϕ of the metasurface can be expressed as Eq. 8 [25, 44]. It is worth noting that for the reflective and transmissive metasurfaces, θ_i should satisfy Eqs. 5,6 respectively.

$\varphi \left(x,y\right)=\text{angle}\left(t\right)=\text{angle}\left({\displaystyle \sum }_{m=\mathit{1}}^{\mathit{4}}{e}^{j\left({\phi }_{l_m}+{\phi }_{{\mathrm{d}}_m}\right)}\right)(8)$

Therefore, if the designed metasurface satisfies Eq. 8, the two-dimensional multichannel multiplexing can be achieved by this metasurface working in reflection or transmission mode.

Then, according to the PB phase principle (geometric phase principle) [43], when the unit cell rotates φ_rot clockwise, for the reflective unit cell, there is a phase shift (PB phase) which is as twice the rotation angle 2φ_rot between the RCP reflective wave and RCP wave incident from above the unit cell. For the transmissive unit cell, there is a PB phase 2φ_rot between the RCP transmitted wave and LCP wave incident from the back of the unit cell. Therefore, the 0–2π phase shift can be covered by rotating the unit cell from 0 to π and the proposed metasurface can be designed by the geometric phase principle. The rotation angle profile of the metasurface can be expressed as follows:

${\phi }_{\text{rot}}\left(x,y\right)=\frac{\varphi \left(x,y\right)}{\mathit{2}}(9)$

Moreover, in the THz region, according to the Drude model, the permittivity ε of VO₂ varying with angular frequency ω can be expressed as follows [37, 41]:

$\epsilon \left(\omega \right)={\epsilon }_{\infty }-\frac{{\omega }_p^{\mathit{2}}\left(\sigma \right)}{{\omega }^{\mathit{2}}+i\gamma \omega }(10)$

${\omega }_p^{\mathit{2}}\left(\sigma \right)=\frac{\sigma }{{\sigma }_{\mathit{0}}}{\omega }_p^{\mathit{2}}\left({\sigma }_{\mathit{0}}\right)(11)$

where ε_∞ = 12 is the high frequency permittivity, ${\omega }_p^2\left(\sigma \right)$ is plasma frequency depending on the conductivity σ of VO₂, γ = 5.75 × 10¹³ rad/s is the collision frequency, ω_p (σ₀) = 1.4 × 10¹⁵ rad/s with σ₀ = 3 × 10³ Ω⁻¹cm⁻¹, and σ = 2 × 10³ s/cm or 2 s/cm with VO₂ in the metallic or insulator state respectively.

In summary, the required metasurface working in both reflection and transmission modes for two-dimensional multichannel multiplexing can be designed by Eq. 8, PB phase principle, and VO₂.

Unit cell

Figure 2 depicts the unit cell of the proposed reconfigurable dielectric metasurface. As shown in Figures 2A,B, the unit cell comprises top silicon (ε = 11.9) elliptical pillar and Si-VO₂ substrate. It is worth noting that to distinguish the Si pillar and the Si substrate, the different colors are used. The period of the unit cell is p = 550 μm, the height of the Si pillar is t_p = 900 μm, the thickness of the Si-VO₂ substrate is t_s = 5 μm and t_v = 0.2 μm, and the minor and major axes of the ellipse are a = 54 μm and b = 520 μm respectively. The angle between the major axis and positive x-axis is φ_rot. As shown in Figures 2C,D, the unit cell can work in reflection and transmission modes by switching the VO₂ from the metallic state to the insulator state.

FIGURE 2

FIGURE 2. Schematic diagram of the unit cell composed of the top Si elliptical pillar and Si-VO₂ substrate (A) Stereoscopic view (B) Vertical view (C) Reflective unit cell (D) Transmissive unit cell. p = 550 μm, t_p = 900 μm, t_s = 5 μm, t_v = 0.2 μm, a = 54 μm, and b = 520 μm.

CST Microwave Studio is applied to investigate the unit cell numerically. Periodic boundaries and Floquet ports are employed along with the x-y and z directions. For the reflective and transmissive unit cell with VO₂ in metallic and insulator state, RCP and LCP waves are normally incident onto the unit cell along -z and +z directions, respectively. VO₂ is modeled by the Drude model by Eqs. 10,11. Besides, φ_rot changes from 0° to 180°. Figure 3 shows the simulated phase and amplitude of the co-polarization reflection coefficient R_RR and the cross-polarization transmission coefficient T_RL versus frequency with φ_rot = 0°, 30°, 65°, 105°, and 155°, respectively (Si substrate is hidden in the schematic diagram of the unit cell). The maximum amplitude of R_RR and T_RL are about 0.87 and 0.98. Therefore, the 3 dB bandwidth of the R_RR and T_RL are about 0.1 THz, and the operating frequency band is about 0.18–0.28 THz (The relative bandwidth is about 43.5%) and 0.25–0.35 THz (The relative bandwidth is about 36.7%) respectively. Besides, the phase shift is near-parallel and can cover 0–2π by rotating the unit cell from 0 to π in the operating frequency band. It is worth noting that based on the PB principle, the required phase shift can also be satisfied under the oblique incident wave.

FIGURE 3

FIGURE 3. The simulated phase and amplitude versus frequency of the unit cell with φ_rot = 0°, 30°, 65°, 105°, and 155° respectively (A) The co-polarization reflection coefficient R_RR with the RCP wave normally incident along the negative z-direction (B) The cross-polarization transmission coefficient T_RL with the LCP wave normally incident along the positive z-direction.

Metasurface

A reconfigurable dielectric metasurface consist of 14 × 14 unit cells with M = 5, l₁ = 0, l₂ = +2, l₃ = -2, and l₄ = +4 is designed for verification. The phase profile ϕ (x, y) and rotation angle profile φ_rot (x, y) of the designed metasurface can be obtained by Equations 8, 9, respectively. The phase profile and structure diagram are shown in Figure 4.

FIGURE 4

FIGURE 4. (A) The phase profile (B) The structure diagram.

When the metasurface works in the reflection mode with VO₂ in the metallic state, take f₁ = 0.18 THz, f₂ = 0.23 THz, and f₃ = 0.28 THz for example, the corresponding angle of incidences are θ_i (f₁) ≈ 37.5°, θ_i (f₂) ≈ 28.5°, and θ_i (f₃) ≈ 23.1° respectively, calculated based on Eq. 5. While the metasurface works in the transmissive mode with VO₂ in the insulator state, take f₁ = 0.25 THz, f₂ = 0.3 THz, and f₃ = 0.35 THz with θ_i (f₁) ≈ 26°, θ_i (f₂) ≈ 21.4°, and θ_i (f₃) ≈ 18.3° respectively for examples, obtained based on Eq. 6. According to Figure 1, the schematic diagram for two-dimensional 12-channel multiplexing combing with OAM and frequency realized by the designed metasurface (Si substrate is hidden) is shown in Figure 5.

FIGURE 5

FIGURE 5. The schematic diagram for two-dimensional 12-channel multiplexing combing with OAM and frequency realized by the designed metasurface (A) Reflective metasurface (B) Transmissive metasurface.

When the designed metasurface works in the reflection mode, simulated far-field patterns of the RCP reflected wave are shown in Figure 6. As shown in Figure 6A, for the channel C₁₁, the off-axis RCP plane wave is incident on the metasurface with f₁ and θ_i (f₁) along the negative x-axis, and an RCP reflected beam with a solid intensity profile and unchanged phase front is generated in the direction perpendicular to the metasurface. Therefore, the incident wave is transformed into a beam with f₁ and l₁ = 0. Similarly, for channel C₁₂ or C₁₃, the incident wave is transformed into a beam with f₂ or f₃ and l₁ = 0. Therefore, the generated 3-channel on-axis beams of group 1 are orthogonal with each other. As shown in Figure 6B, For group 2, when the incident RCP plane wave with f_m and θ_i (f_m) (m = 1, 2, and 3) obliquely illuminates on the metasurface along the negative y-direction, an RCP reflected beam is generated in the direction perpendicular to the metasurface. Besides, the intensity profile is doughnut-shaped and the phase front changes 4π clockwise observing along the +z direction. Therefore, incident waves are transformed into 3-channel orthogonal on-axis beams with different frequencies (f₁, f₂, and f₃) and l₂ = +2 respectively. In the same way, for group 3 or group 4, when off-axis incident RCP plane waves with f_m and θ_i (f_m) illuminate on the metasurface along + x or + y directions respectively, in the direction perpendicular to the metasurface, RCP reflected waves are transformed into 3-channel orthogonal on-axis OAM beams with topological charge l₃ = -2 or l₄ = +4 (The intensity profile is doughnut-shaped and the phase front changes -4π or +8π clockwise along the +z direction). Besides, the topological charges of the four groups of beams are different from each other. Therefore, the 12-channel orthogonal on-axis beams with topological or frequency orthogonality can be achieved, and two-dimensional 12-channel multiplexing combing with spatial and frequency domains by the reflective metasurface can be realized. It is worth noting that there are strong sidelobes in the far field patterns resulting from the angle-multiplexed metasurface design principle [42], which will affect the overall efficiency of the metasurface. In addition, according to the far field pattern, the maximum intensity of the generated beam is available. Take group 1 for example, the maximum value is about -4.26, 2.8, and 3.41 dB respectively.

FIGURE 6

FIGURE 6. Simulated far field patterns of the RCP reflected wave. RCP reflected waves are transformed into 3-channel orthogonal on-axis beams with different frequencies (f₁ = 0.18 THz, f₂ = 0.23 THz, and f₃ = 0.28 THz) and the same topological charge (A) l₁ = 0 (B) l₂ = +2 (C) l₃ = -2 (D) l₄ = +4. Therefore, 12-channel orthogonal on-axis beams with topological or frequency orthogonality can be achieved.

When the designed metasurface works in the transmission mode, simulated far-field patterns of the RCP transmitted wave are shown in Figure 7. For group 1 to group 4, when 12-channel LCP plane waves with f_n and θ_i (f_n) obliquely illuminate on the metasurface from the positive z-axis along negative x and y directions, and positive x and y directions respectively, RCP transmitted wave are transformed into 12-channel orthogonal on-axis beams with topological orthogonality (l₁ = 0, l₂ = +2, l₃ = -2, and l₄ = +4) or frequency orthogonality (f₁ = 0.25 THz, f₂ = 0.3 THz, and f₃ = 0.35 THz). Therefore, two-dimensional 12-channel multiplexing combing with spatial and frequency domains by the transmissive metasurface can be realized. Similarly, take group 1 for example, the maximum intensity of the generated beam is about 2.56, 7.01, and 5.47 dB respectively.

FIGURE 7

FIGURE 7. Simulated far field patterns of the RCP transmitted wave. RCP transmitted waves are transformed into 3-channel orthogonal on-axis beams with different frequencies (f₁ = 0.25 THz, f₂ = 0.3 THz, and f₃ = 0.35 THz) and the same topological charge (A) l₁ = 0 (B) l₂ = +2 (C) l₃ = -2 (D) l₄ = +4. Therefore, the 12-channel orthogonal on-axis beams with topological or frequency orthogonality can be achieved.

In addition, the phase gradient method [46] can be used to measure the purity of the generated OAM mode based on the simulated far field phase. For the reflective metasurface, take channel C₂₃ for example. The far field phase of the RCP reflected wave is sampled at a pitch angle of 5° and an interval of 1° in the spherical coordinate system. For the transmissive metasurface, take channel C₄₃ for example. The far field phase of the RCP transmitted wave is sampled at a pitch angle of 10° and an interval of 0.5°. Table 1 shows the calculated variances σ² for different OAM modes. It can be seen that for channel C₂₃, when the topological charge l is set as +2 during calculation, the variance is the smallest and the purity is the highest. Therefore, the topological charge of the generated OAM beam is +2. Similarly, for channel C₄₃, when l = +4, the variance is the smallest and the purity is the highest. Therefore, the topological charge of the generated OAM beam is +4.

TABLE 1

TABLE 1. The calculated variances σ² for different OAM modes.

Based on the above results, two-dimensional 12-channel multiplexing combing with spatial and frequency domains by the reconfigurable dielectric metasurface is realized. Besides, the metasurface works in both reflection mode and transmission mode with the operating frequency band switching from 0.18–0.28 THz to 0.25–0.35 THz by tuning the VO₂.

Conclusion

A terahertz reconfigurable dielectric metasurface embedded with VO₂ for two-dimensional multichannel multiplexing combing with spatial and frequency domains is presented in this paper. The metasurface works in both reflection mode and transmission mode by switching the VO₂ from the metallic state to the insulator state. For reflective metasurface, 4×M-channel off-axis RCP plane wave with f_m and angle of incidence θ_i (f_m) (m = 1, … , M) illuminate on the metasurface from the negative z-axis along with negative x and y directions, and positive x and y directions respectively, in the direction perpendicular to the metasurface, RCP reflected waves are transformed into 4×M-channel orthogonal on-axis beams with topological orthogonality (l = l₁, l₂, l₃, and l₄) or frequency orthogonality (f = f₁ to f_M). For transmissive metasurface, 4×M-channel off-axis LCP plane waves are incident on the metasurface from the positive z-axis along with negative x and y directions, and positive x and y directions respectively, in the direction perpendicular to the metasurface, RCP transmitted waves are transformed into 4×M-channel orthogonal on-axis beams with topological or frequency orthogonality. A metasurface composed of 14 × 14 unit cells with l₁ = 0, l₂ = +2, l₃ = -2, and l₄ = +4 is designed for verification. The metasurface works in both reflection and transmission modes with the operating frequency band switching from 0.18–0.28 THz to 0.25–0.35 THz by tuning the state of VO₂. When the metasurface works in the reflection or transmissive mode, take f₁ = 0.18 THz, f₂ = 0.23 THz, and f₃ = 0.28 THz, or f₁ = 0.25 THz, f₂ = 0.3 THz, and f₃ = 0.35 THz for examples. The simulation results show that two-dimensional 12-channel multiplexing combing with spatial and frequency domains by the metasurface is realized. The proposed metasurface has great potential in terahertz communications.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.

Author contributions

LW, YY, and LD conceived the work and suggested the outline of the article. LW, FG, ST, ZT, XZ, and JL carried out investigations and wrote the article.

Funding

This research was funded in part by the Natural Science Foundation of Hunan Province, grant number 2022JJ40114 and in part by the Research Foundation of Education Bureau of Hunan Province, grant number 21C0831.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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