1. Introduction

Phase change materials, including germanium antimony telluride (GST) and vanadium dioxide (VO₂), as an enabling technology for tunable metadevices have been extensively investigated during the past few years due to their extreme flexibility in controlling electromagnetic waves [1–12]. Compared with GST, which can switch between an amorphous state and a crystalline state, VO₂ undergoes an insulator-to-metal transition (IMT) around room temperature (T_IMT∼67 °C) and possesses a significant change in material properties over a broad spectral range. In particular, during the phase transition, VO₂ experiences a ∼10³ times increase in THz electrical conductivity (σ₁), which has attracted increasing attention in the development of VO₂ based THz metadevices [13–28]. At THz frequencies, GST, in both amorphous and crystalline phases, should be treated as a lossy dielectric material. A recent review paper has provided a comprehensive description of the development of this research field [29]. In most of these reported studies, VO₂ has been introduced into metallic resonators, in the form of thin films or non-resonant structures, to create metal/VO₂ hybrid systems in which VO₂ provides the tunable dielectric environment. Strong modulations of THz radiation have been demonstrated in a variety of hybrid metal/VO₂ systems, indicating the capability of VO₂ for enabling active THz devices. However, from the standpoint of device fabrication, these hybrid systems generally involve challenges of growing VO₂ on amorphous (metallic) substrates and/or a complex patterning process. A close inspection shows that THz conductivity of VO₂ in its metallic state is just one order of magnitude lower than that of gold, leading to the fact that VO₂ micro-structures can support strong THz resonances [20]. Having a single patterning process, Wen and coworkers have demonstrated a THz metasurface consisting of an array of VO₂ cut-wires for thermally tunable transmission [16]. Nevertheless, compared with their hybrid counterpart, THz metasurfaces based on pure VO₂ resonators remain rare. Given the fact that thicker VO₂ films are necessary for strong resonance, simple designs that create versatile THz systems are highly desired. We note that, although the growth of thick VO₂ films is challenging, the lack of information about pure VO₂-based THz metasurfaces is mainly due to the fact that researchers have only just recently recognized the potential of VO₂ for realizing metadevices in the THz spectral regime.

Besides the intensity (transmission/reflection) control of electromagnetic waves, metasurfaces can also be used to realize a spatial-dependent phase control [30]. Among many approaches for obtaining phase discontinuity, the geometric phase (Pancharatnam–Berry phase or P-B phase) metasurfaces, which require circularly polarized (CP) incident light, are particularly attractive because of their two unique characteristics [31]: (1) a phase gradient arises from the in-plane relative rotation of meta-atoms, and (2) they are dispersionless. In other words, broadband geometric metasurfaces can be created by simply utilizing identical subwavelength antennas that possess spatially varying orientations, which significantly reduces the device fabrication challenges and simplifies arbitrary phase control of CP waves. The geometric phase approach has enabled a variety of interesting phenomena, including metasurface-based beam steering, holograms, vortex beam generation, etc. [31–35]. In addition, the circular-polarization dependent phase discontinuity of geometric metasurfaces makes them a natural candidate for optical spin Hall effect (SHE). The spin Hall effect was originally used to describes the spin-orbit coupling of electrons, which leads to spin polarization-dependent transverse currents. As an analog of electronic SHE, an optical SHE is referred to as an optical phenomenon where spin-polarized photons can be laterally separated by their interaction with inhomogeneous media. For instance, for left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) incident waves, the corresponding transmitted waves of the opposite circular polarization (known as the anomalous beams) propagate in different directions determined by the orientational rotation of the meta-atoms. Though phase-change material enabled reconfigurable phase discontinuities have been studied [5], geometric THz metasurfaces based on VO₂ resonators have so far not been reported in the literature.

Here in this work, we explore the possibility of applying VO₂ dipole micro-antennas as the subwavelength building blocks of geometric metasurfaces for tunable THz SHE. By performing full-wave simulations (CST Microwave Studio), we first show that the interaction between CP THz radiation and a metasurface consisting of an array of VO₂ dipole micro-antennas can result in a phase gradient determined by the orientation of the resonators. We further demonstrate that the corresponding beam steering effect is strongly related to the THz electrical conductivity (σ₁) of VO₂. In particular, the intensity of the anomalous beam dramatically varies as VO₂ undergoes a phase transition, indicating the close dependence of the efficiency of THz SHE on σ₁. Furthermore, based on the same phase discontinuity control mechanism, we show that VO₂ THz metasurfaces composed of two sets of spin components can be used to realize a 45° polarization rotation of an incident linearly polarized wave. The intensity of the corresponding transmission component decreases with decreasing σ₁, further confirming the potential of VO₂ resonator based geometric metasurfaces as a versatile platform for sophisticated manipulation of THz radiation. The proposed metasurfaces in our work which show potential for active manipulations of both wavefront and polarization of THz radiation significantly broaden the scope of research in VO₂ enabled THz metadevices.

2. Numerical simulations and discussions

In the geometric phase approach, the capability of adding an abrupt phase shift varying from 0 to 2π arises from the polarization-change induced phase acquisition during the scattering process. Consequently, this phase shift is intrinsically dispersionless, while the corresponding conversion efficiency which describes the power of the opposite polarization (e.g., RCP) relative to the incident polarization (e.g., LCP) is determined by the scattering strength of the subwavelength scatters. On the other hand, it has been shown that VO₂ micro-structures can support THz resonances. More importantly, at THz frequencies, the permittivity of VO₂ can be described by a Drude model, $\varepsilon (\omega )= \; {\varepsilon _\infty } - \omega _\textrm{p}^2({{\sigma_1}} )/({{\omega^2} + i\gamma \omega } )$, where ${\varepsilon _\infty }$ is the permittivity at high frequency, $\gamma $ is the collision frequency, ${\omega _\textrm{p}}({{\sigma_1}} )$ is the conductivity dependent plasmon frequency that satisfies the relation $\omega _\textrm{p}^2({{\sigma_1}^{\prime}} )= ({\sigma_1^{\prime}/{\sigma_1}} )\; \omega _\textrm{p}^2({{\sigma_1}} )$ [20]. The parameters in this Drude model can be obtained from a fitting of the measured material properties of VO₂ in its metallic phase [14], i.e., ${\varepsilon _\infty }$ = 12, ${\omega _\textrm{p}}$ = 1.40 × 10¹⁵ rad/s (σ₁= 3 × 10³ Ω⁻¹cm⁻¹), and $\gamma $ = 5.75 × 10¹³ rad/s. In contrast, VO₂ in its insulator phase can be treated as a low loss dielectric (σ₁= 10 Ω⁻¹cm⁻¹). In our simulations, these Drude model parameters were used to describe the permittivity of VO₂, while the sapphire is assumed to have a constant permittivity of 11.7. This significant variation in σ₁ indicates the remarkably large tunable scattering strength of VO₂ resonators during the IMT and suggests an inherent tuning capability of VO₂ micro-structure based geometric metasurfaces.

Figure 1(a) illustrates a geometric metasurface consisting of an array of VO₂ dipole micro-antennas. In particular, with the same geometries, the VO₂ micro-antennas are designed to repeat in the y direction and have spatially different orientations along the x direction in a periodic manner [28]. As the schematic illustrated in Fig. 1(a) shows, when VO₂ is in its metallic phase, a CP (e.g., LCP) incident wave may split into two beams after transmitting through the metasurface, i.e., an anomalous beam of the opposite spin (e.g., RCP) representing the geometric phase and the (e.g., RCP) ordinary beam dominated by the conventional Snell’s law [27,28]. In sharp contrast, when VO₂ is in its insulator phase, the ordinary beam will be largely dominant in the transmission [Fig. 1(d)], while the anomalous beam is essentially negligible due to the corresponding low conversion efficiency. Unit-cell based simulations were first performed to study the transmission of a uniform metasurface under normal incidence of a CP wave at 0.8 THz. The dependence of the co-polarized and cross-polarized transmission on the width (w) and length (L) of the VO₂ structure are shown in Figs. 1(b) and 1(c), respectively. Clearly, for a fixed square lattice constant of 80 µm, more power in the CP incident wave will convert into a CP wave of the opposite handedness when wider and longer antennas are used. To avoid the small gaps in the following metasurface design, w = 28 µm and L = 70 µm are adopted for the remainder of our study. The transmission when VO₂ is in its insulating phase is shown in Figs. 1(e) and 1(f), indicating that almost no power is converted into the cross-polarized transmitted wave upon scattering from the VO₂ micro-antennas. It should be noted that the conversion efficiency is also influenced by the thickness of the VO₂ resonators [33]. Although it has been shown that thicker VO₂ can in general support a stronger THz resonance due to the limited σ₁ in the metallic phase, 1-µm-thick VO₂ structures are used in our study when taking into consideration the potential fabrication challenges [26]. We note that, compared with the reported THz metasurfaces based on pure VO₂ microstructures [16], the fabrication of the proposed geometric metasurface does not required extra processes. The potential fabrication can include the following procedures [16]: (1) deposition of the VO₂ film on a sapphire substrate by reactive magnetron sputtering in an argon–oxygen atmosphere; and (2) CF₄/O₂ plasma etching of the VO₂ film to obtain the designed metasurface pattern.

 

Fig. 1. Active THz spin Hall effect based on VO₂ geometric metasurfaces. (a) Schematic of the proposed metasurface consisting of an array of metallic-phase VO₂ micro-antennas located on top of a sapphire substrate. The orientation of the VO₂ micro-antennas is rotated in a periodic manner. The unit cell is arranged in a two-dimensional square lattice with a lattice constant of 80 µm. Transmission of a CP THz wave forms two beams, i.e., the anomalous beam of the opposite spin and the ordinary beam of the incident polarization. Because the local phase shift satisfies Φ = ±2φ, where φ is the antenna’s orientation rotation angle relative to the x-axis and the sign is determined by the handedness of the incident wave, the propagation direction of the anomalous beam for LCP and RCP incident waves varies. The dependence of (b) co-polarized and (c) cross-polarized transmission at 0.8 THz for a uniform metasurface with a width (w) and length (L) of the VO₂ micro-antennas. (d) Schematic of the proposed metasurface when VO₂ is in its insulator phase. The corresponding simulated (e) co-polarized and (f) cross-polarized transmissions. Periodic boundary conditions were employed in the unit cell simulations.

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The anomalous refraction of geometric metasurfaces varies with the antenna’s spatial-dependent rotation angle φ as well as the handedness of the incident CP waves. Figure 2 illustrates the anomalous refraction behavior of the VO₂ geometric metasurfaces. Figures 2(a)–2(c) show the phase distributions of a system based on 10-unit-cell supercells (φ = 18°) under illumination of a normally incident LCP THz wave at 0.6 THz, 0.8 THz, and 1.0 THz, respectively. Note that the phase distributions of the incident wave are plotted in the z < 0 region of space, while those of the anomalous refracted wave are plotted in the z > 0 region. The frequency-dependent off-normal propagation of the anomalous beams indicates the existence of a dispersionless phase gradient arising from the geometric phase. A close inspection shows that the refraction angle identified from the phase distribution mappings agrees well with that determined by the general Snell’s law, i.e., ${n_\textrm{t}}\textrm{sin}{\theta _\textrm{t}} - {n_\textrm{i}}\textrm{sin}{\theta _\textrm{i}} = \left( {\frac{\lambda }{{2\mathrm{\pi }}}} \right)\left( {\frac{{d\mathrm{\Phi }}}{{dx}}} \right)$ [30,31]. On the other hand, without carrying geometric phase, the ordinary transmitted waves (not shown) propagate along the z direction upon normal incidence. Furthermore, Figs. 2(d)–2(f) show that, for normal incidence (θ_i = 0), the sign of the refraction angle flips when the handedness of the incident polarization switches. Moreover, the resulting sets shown in Figs. 2(g)–2(j), which correspond to metasurfaces based on 5- and 15-unit-cell supercells (φ = 36° and 12°), reveal that the anomalous refraction of the proposed metasurface can be easily tuned by varying the local phase discontinuity.

 

Fig. 2. Anomalous refraction by VO₂ geometric phase THz metasurfaces. Simulated phase distributions upon illumination by normally incident (a)–(c) LCP and (d)–(f) RCP waves at 0.6 THz, 0.8 THz, and 1.0 THz corresponding to a rotation angle of φ = 18°. To clearly show the refraction behavior, phase distributions of the incident wave are plotted in the z < 0 region of space, while those of the anomalous refracted waves are plotted in the z > 0 region. Phase distributions at 0.8 THz for a rotation angle of φ = 36° are shown in (g)–(h), while those of φ = 12° are shown in (i)–(j). In all simulations, the THz conductivity of VO₂ (σ₁) is assumed to be 2 × 10³ Ω⁻¹ cm⁻¹. Periodic boundary conditions were employed in the supercell simulations.

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Given the fact that the electromagnetic response of the VO₂ micro-structures is strongly dependent on the THz electrical properties of the material, IMT enabled changes in σ₁ can lead to dramatic response variations of the VO₂ geometric metasurfaces. In Fig. 3, we show the tunable anomalous refraction of a system based on a 10-unit-cell supercell (φ = 18°). It can be seen from Fig. 3(b) that the power peak of anomalous refraction is found at a larger observation angle with smaller absolute value when the frequency decreases, and, for the considered scenario (i.e., θ_i = 0°), the power peaks corresponding to LCP and RCP illuminations are located symmetrically with respect to the observation angle of 0°. Figures 3(c) and 3(d) present a complete picture of the anomalous refraction behavior of the metasurface considered here. More importantly, Figs. 3(e)–3(g) show the anomalous refraction behavior at 0.6 THz, 0.8 THz, and 1.05 THz for a series of VO₂ conductivity values, which unambiguously reveals the influence of the phase transition of VO₂ on the response of the metasurface. Particularly, normalized to the maximum value in each plot, the peak power of the anomalous beam identified in Figs. 3(e)–3(g) decreases with decreasing σ₁, while the anomalous refraction effect becomes negligible when VO₂ is in its insulator phase. Figure 3(h) summarizes the peak power of anomalous refraction at a few frequencies of interest as a function of σ₁, which reveals the wide tuning capability of the VO₂ geometric metasurfaces in terms of both their magnitude and bandwidth. We note that, compared with the reported geometric metasurfaces based on metal-VO₂ hybrid structures [24], the proposed metasurface has a simpler structure and more pronounced tuning capability.

 

Fig. 3. Tunable anomalous refraction. (a) Schematic of the refraction behavior of the anomalous and ordinary beams when the metasurface (φ = 18°) is illuminated by a CP incident wave. (b) Normalized transmitted power of anomalous refracted wave at a series of frequencies as a function of the observation angle in the far-field when θ_i = 0°. The frequency dependence of the anomalous refraction of the metasurface upon illumination by normally incident (c) RCP and (d) LCP waves. (e)–(g) Transmitted power of anomalous refracted wave at three different frequencies for a series of VO₂ conductivity (σ₁) values. In (e)–(g), the power in each plot was normalized to the peak value corresponding to σ₁ = 2 × 10³ Ω⁻¹ cm⁻¹. (h) The peak power of the anomalous beam at a series of frequencies as a function of σ₁. Periodic boundary conditions were employed in the supercell simulations.

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To further exploit the opportunity offered by VO₂ geometric metasurfaces as a versatile platform for manipulation of THz radiation, we next study a system which can realize linear polarization rotation as well as its tunability. Figure 4(a) illustrates the schematic of the proposed metasurface inspired by the gap–plasmon metasurfaces for reflection-mode photonic SHE [36]. In particular, each supercell of our design includes two rows (in the y direction) of the VO₂ micro-antennas with the opposite spatial-dependent rotation, while the two rows are shifted for two unit cells with respect to each other along the x direction. This design is primarily based on three characteristics of geometric metasurfaces at normal incidence: (1) with the fixed phase gradient dΦ/dx, anomalous refraction of LCP and RCP incident waves propagate symmetrically with respect to the surface normal (see Fig. 3); (2) for an incident CP wave of a certain handedness the sign of the phase gradient is determined by the local rotation direction of the antennas; and (3) each unit cell is a subwavelength scatterer, while the anomalous refraction in the far-field is consequently determined by a superposition of scattering from all unit cells. The spatial shift between the two rows in each supercell provides a phase delay of 90° between RCP and LCP incident waves. Therefore, for a linearly polarized incident wave, there are two anomalous refraction beams whose maximum intensity occurs at ${\theta _\textrm{t}} ={\pm} \textrm{asin}({\lambda /P} )$, which undergoes a polarization rotation of 45°. Furthermore, independent of the initial phase of the incident wave, this polarization rotation effect is found to be invariant over the polarization angle [defined as ϕ shown in Fig. 4(a)] of the incident wave [36].

 

Fig. 4. VO₂ geometric metasurfaces for tunable polarization rotation. (a) Schematic of the metasurface for polarization rotation. This design was inspired by the plasmonic metasurface for reflection-mode photonic SHE [36]. Each supercell includes two rows (in the y direction) of VO₂ micro-antennas with the opposite spatial-dependent rotation, while the two rows are shifted for two unit cells with respect each other along the x direction. The anomalously refracted wave experiences a 45° polarization rotation relative to the polarization of the linearly polarized incident wave. (b)–(d) P_+45°/P_tot spectra for a series of VO₂ conductivity (σ₁) values when the polarization angle of the incident wave is ϕ = 0°, 45°, 90°, and 135°, respectively. P_−45°/P_tot representing the orthogonal polarization component is shown in the inset of (b)–(d). Normalized P_+45°/P_tot at a series of frequencies as a function of σ₁ when (e) ϕ = 0° and (f) ϕ = 135°, respectively. Periodic boundary conditions were employed in the supercell simulations.

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Figures 4(b)–4(d) illustrate the polarization state results obtained at the observation angles ${\theta _\textrm{t}} ={\pm} \textrm{asin}({\lambda /P} )$ corresponding to ϕ = 0°, 45°, 90°, and 135°, respectively. It should be noted that the total transmission power (P_tot) of the anomalous beams and the transmission power evaluated at a polarization angle at ϕ + 45° (P_+45°) are calculated to obtain the power ratio (i.e., P_+45°/P_tot) which can be used to evaluate the polarization rotation effect. The transmission power evaluated at the polarization angle of ϕ − 45° (P_−45°) represents the component at the orthogonal polarization state. When VO₂ is in its metallic phase (σ₁ = 2 × 10³ Ω⁻¹ cm⁻¹), within the frequency range of interest, P_+45°/P_tot with near-unity values is found for all four incident polarization states, indicating a near-complete polarization rotation effect. Furthermore, besides the slight change observed at frequencies around 0.7 THz, the decrease in VO₂’s conductivity only causes negligible variation in the power ratio, which is attributed to the insensitivity of the phase gradient to the resonance strength of the antennas. In other words, the ability of the metasurface to support polarization rotation could be well preserved when VO₂ undergoes IMT. However, as the conversion efficiency (total power of anomalous refraction) drops with decreasing σ₁ [Fig. 3(h)], the anomalous beams that carry the phase gradient information of the metasurface vanish when VO₂ approaches its insulator phase. This can be clearly seen from the dependence of the normalized P_+45°/P_tot on σ₁ shown in Fig. 4(e) when ϕ = 0° and in Fig. 4(f) when ϕ = 135°, respectively. Results shown in Fig. 4 reveal the potential of the VO₂ geometric metasurfaces to enable broadband polarization manipulations of THz radiation with tunable power levels.

3. Conclusion

In summary, we have numerically validated that geometric metasurfaces based on VO₂ dipole antennas can be used to realize tunable wavefront and polarization manipulation of THz radiation. Supporting THz electromagnetic resonances, a metallic-phase VO₂ micro-structure can realize strong scattering of circularly polarized THz incident waves and impart an additional phase to the scattered wave of the opposite handedness. Though the phase discontinuity of geometric metasurfaces is primarily determined by the local spatial-dependent orientation of the resonators, the power of the anomalous refraction beams is closely dependent on the scattering strength of the meta-atoms. Accordingly, we show that the efficiency of the THz SHE in the proposed metasurfaces can be largely tuned by the THz electrical conductivity of VO₂. Our findings reveal that geometric metasurfaces based on VO₂ micro-structures can enable a variety of tunable THz metadevices as platforms for active THz optics based on the insulator-to-metal transition of VO₂. For instance, the active beam steering and polarization rotation enabled by the proposed VO₂ geometric metasurfaces could be utilized for highly tunable THz power distributors and modulators.