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Abstract
We propose a switchable broadband and wide-angular terahertz asymmetric transmission based on a spiral metasurface composed of metal and VO2 hybrid structures. Results show that asymmetric transmission reaching up to 15% can be switched on or off for circularly polarized terahertz waves when the phase of VO2 transits from the insulting state to the conducting state or reversely. Strikingly, we find that relatively high asymmetric transmission above 10% can be maintained over a broad bandwidth of 2.6–4.0 THz and also over a large incident angular range of 0°–45°. We further discover that as the incident angle increases, the dominant chirality of the proposed metasurface with VO2 in the conducting state can shift from intrinsic to extrinsic chirality. We expect this work will advance the engineering of switchable chiral metasurfaces and promote terahertz applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical chirality has attracted increasing attention due to its promising applications in polarized optoelectronic devices [1], ultrafast information transmission [2], and biomolecule detection [3]. Amongst the chiro-optical effects including circular dichroism and optical activity [4,5], asymmetric transmission manifests itself as a difference in the total transmission between forward and backward propagation for polarized waves [6]. This interesting phenomenon resembles the non-reciprocal Faraday effect in magnetic media, but takes place in absence of magnetic field [7].
Since the idea of chiral metamaterials, the unit cells of which lack mirror symmetry, was first proposed by Tretyakov et al. [8], research efforts have been focused on two directions [9]: non-planar three-dimensional (3D) chiral metamaterials and planar chiral metamaterials, i.e., chiral metasurfaces. After the first experimental demonstration by Menzel et al. [10], various 3D chiral metamaterials, most of which are composed of multilayered structures, have been developed for achieving asymmetric transmission [11–19]. By further integrating 3D metamaterials with silicon, Chowdhury et al. [20] demonstrated a dynamically reconfigurable terahertz metamaterial, and Zhou et al. [21] demonstrated dynamically tunable optical activity in the terahertz regime. By adopting phase transition materials such as vanadium dioxide (VO$_2$), Liu et al. [22] demonstrated for the first time nonlinear metamaterial responses through the phase transition. Wang et al. [23] numerically investigated dynamic tuning of terahertz polarization control. Lv et al. [24], Liu et al. [25], and Li et al. [26] respectively demonstrated temperature-controlled terahertz asymmetric transmission for linearly polarized waves. Recently, Dai et al. [27,28] also designed 3D metamaterials made of Dirac semimetals for achieving tunable and broadband terahertz asymmetric transmission.
Meanwhile, planar chiral metasurfaces have been extensively investigated, since they can also exhibit strong chirality and they are relatively easier to fabricate compared to the nonplanar metamaterials [29]. Fedotov et al. reported asymmetric propagation of electromagnetic waves first in the microwave regime [30] and then in the visible and the near-infrared regimes [31] bt using planar chiral structures. Later, Singh et al. [7] demonstrated terahertz asymmetric transmission of circularly polarized wave incident on a metasurface composed of coupled metal split-ring resonators. Quite recently, Liu et al. [32] proposed a chiral metasurface in a spiral shape and showed coexistence of circular asymmetric transmission and circular dichroism in the terahertz regime.
Over the years, tunable asymmetric transmission based on graphene metasurfaces have also been widely investigated. Zhou et al. [33] proposed a graphene-loaded metal grating and showed that asymmetric propagation of terahertz waves can be tuned by adjusting either the extrinsic magnetic field or the Fermi level of graphene. Li et al. [34] and Huang et al. [35] respectively proposed graphene chiral metasurfaces and numerically showed tunable asymmetric transmission for circularly polarized terahertz waves. However, the modulation ranges are relatively small, only 3.5%-5.2% in [34] or 0.05%-3.5% in [35] by changing the Fermi energy of graphene. Even worse, the operation bandwith is very narrow [33–35], restricting the applications of these graphene chiral metasurfaces. To our knowledge, tunable asymmetric transmission with broad operation bands and based on VO$_2$ has not been reported for metasurfaces yet, although there are many reports on broadband asymmetric transmission for 3D metameterials [6,16,18] and many tunable 3D metameterials with asymmetric transmission are based on VO$_2$ [23,25,26].
In this work, we propose a novel chiral metasurface composed of metal and VO$_2$ hybrid structures with switchable broadband and wide-angular asymmetric transmission for circularly polarized terahertz waves. We will show that the asymmetric transmission effect can be switched on or off by changing the phase of VO$_{2}$ from the insulating state to the conducting state or reversely, which can be realized electrically, thermally or optically [36]. Strikingly, we will show that the asymmetric transmission can reach 15%, which is 5 times of the literature on dynamically tunable asymmetric transmission metasurfaces, and that asymmetric transmission above 10% holds over a very broad bandwidth of 2.4–4.2 THz for normal incidence, or over 2.6–4.0 THz for a wide incident angular range of 0$^{\circ }$–45$^{\circ }$. We will also discover that as the incident angle increases the dominant chirality can transit from intrinsic to extrinsic chirality for the proposed metasurface with VO$_2$ in the conducting state. The underlying physics will also be clarified.
2. Design and simulation setup
Figure 1 illustrates the proposed chiral metasurface of spiral G shape, which is composed of U-shaped gold stripes and L-shaped VO$_2$ stripes standing on a quartz substrate. All the stripes have width of $W=4~\mu$m and thickness of 200 nm, and the gold stripes have length of $L = 24~\mu$m. The unit has periods of $\Lambda =28~\mu$m in both $x$ and $y$ directions. The vertical VO$_2$ stripe locates at the center of the unit. The proposed metasurface can be fabricated using state-of-the-art micro-fabrication processes: a thin film of VO$_2$ is first deposited on the quartz substrate, followed by spin coating of photoresist, photolithography, etching, and photoresist removal, and then the U-shape gold stripes are patterned by the standard lift-off process.
Fig. 1. Schematic diagrams of transmission of the proposed hybrid gold-VO$_{2}$ metasurface. (a) At room temperature VO$_{2}$ is in the insulating state (shown in blue), the chirality in form of asymmetric transmission is turned off. (b) At 87$^{\circ }$C VO$_{2}$ is in the conducting state (shown in red), thus the chirality in form of asymmetric transmission is turned on.
The metasurface is illuminated by terahertz plane wave with right-hand circular polarization (RCP), and unless otherwise specified we consider normal incidence. The transmission efficiencies for the RCP and the left-hand circularly polarized (LCP) waves are represented by $T_{++}$ and $T_{-+}$, respectively. Here $T_{++}$ is the direct transmission, and $T_{-+}$ is the circular polarization conversion transmission from the RCP to the LCP. The arrows on top of $T$ indicate the directions of the incidence, that is, $\overrightarrow {T}$ and $\overleftarrow {T}$ mean that the terahertz wave impinges from the left (superstrate) side and from the right (substrate) side, respectively.
The operation principle of the proposed metasurface is as follows. At room temperature, VO$_2$ is in the insulating state, as illustrated in blue in Fig. 1(a), thus the VO$_2$ stripes would have little influences on the interactions between terahertz waves and the U-shape gold stripes. As a result, we expect no intrinsic chirality in form of asymmetric transmission for the metasurface due to mirror symmetry of the gold stripes: $\overrightarrow {T}_{-+}=\overleftarrow {T}_{-+}$ and $\overrightarrow {T}_{++}=\overleftarrow {T}_{++}$, as illustrated by Fig. 1(a). At 87$^{\circ }$C, however, the conductivity of VO$_2$ increases dramatically such that it is in the conducting state, as illustrated in red in Fig. 1(b), the metasurface acts as a spiral G-shaped metallic structure. According to our previous work [32], relatively large asymmetric transmission with $\overrightarrow {T}_{-+}\neq \overleftarrow {T}_{-+}$ and $\overrightarrow {T}_{++}=\overleftarrow {T}_{++}$ can be expected, as illustrated by Fig. 1(b). Therefore, by adjusting the phase of VO$_2$ from the insulating state to the conducting state or reversely, we expect that asymmetric transmission can be turned on or off.
Note that $\overrightarrow {T}_{++}=\overleftarrow {T}_{++}$ for the RCP incidence, as well as $\overrightarrow {T}_{--}=\overleftarrow {T}_{--}$ for the LCP incidence, is guaranteed by non-C4 symmetry of our chiral metasurface, of which the direct transmissions are insensitive to the polarization or the propagation directions [37]. The asymmetric transmission $\Delta T$ is defined as the difference between $\overrightarrow {T}_{-+}$ and $\overleftarrow {T}_{-+}$,
Here $\Delta T^{+}$ and $\Delta T^{-}$ are the asymmetric transmissions for the RCP and the LCP incidences, respectively.According to reciprocity theorem, we have $\overleftarrow {T}_{-+}=\overrightarrow {T}_{+-}$, where $T_{+-}$ is the circular polarization conversion transmission from the LCP to the RCP. Thus hereafter we only consider incidence from the left (superstrate) side and omit the right arrow “$\rightarrow$” on top of $T$ for convenience. Since $\Delta T^{+}=\Delta T^{-}$, we only consider $\Delta T^{-}$, which can be written as
CST Microwave Studio was employed to numerically calculate the transmission spectra for both the LCP and the RCP incidences. Unit cell boundary conditions were applied in $x$ and $y$ directions, open and space conditions were adopted in $z$ direction. Frequency domain solver with tetrahedral mesh type was used. In our simulations, we took the conductivity of gold to be $\sigma =5.8\times 10^{7}$ S/m, and the permittivity of quartz substrate to be 2.25 [38]. We adopted the Drude model to describe the frequency-dependent dielectric property of VO$_{2}$ in the terahertz range,3. Results and discussion
3.1 Conductivity of VO$_2$
In order to determine the conductivity of VO$_2$, we fabricated ten batches of $\sim 230$ nm VO$_2$ films on 500 $\mu$m-thick high resistive float-zone silicon wafer coated with a 200 nm Si$_{3}$N$_{4}$ layer by reactive RF magnetron sputtering. In the optimal deposition process, a vanadium target (99.99%, ZhongNuo Advanced Material Co. Ltd) was sputtered onto the wafer with an RF-power density of 4.17 W/cm$^2$ in [Ar:O$_2=50:1$] gas mixtures under operating pressure of 0.3 Pa. During deposition, the wafer was heated to the temperature of 540$^{\circ }$C. After deposition, the sample was annealed at 500$^{\circ }$C for one hour.
The conductivity of the as-deposited VO$_2$ films was measured by the standard four-point probe method with temperature finely controlled ($\pm 1^{\circ }$C) by a heater. Figure 2(a) shows that at room temperature, the as-deposited VO$_2$ films have low conductivities of 10–200 S/m, corresponding to the insulating state. At 87$^\circ$C, the conductivities of the as-deposited VO$_2$ films are between $4\times 10^3$–$6\times 10^4$ S/m, indicating that VO$_2$ is in the conducting state. We note that relatively higher or lower conductivities can be obtained on demand via properly adjusting the deposition conditions.
Fig. 2. (a) Measured conductivities of ten batches of as-deposited VO$_2$ samples in the insulating state at room temperature (blue bars) and in the conducting state at 87$^{\circ }$C (red bars). (b) Measured conductivity as a function of temperature for the as-deposited VO$_2$ film of Batch No. 4. The red and blue curves are for the heating up and cooling down processes, respectively.
Figure 2(b) shows the temperature dependent conductivity for the as-fabricated VO$_2$ film of Batch No. 4. Results show that the phase transition temperature is around 68$^\circ$C, consistent with the literature [22], and that the conductivities are $\sigma =20$ S/m at room temperature and $\sigma =2\times 10^4$ S/m at 87$^\circ$C. Therefore, in simulations we took $\sigma =20$ S/m for VO$_2$ in the insulating state at room temperature and $\sigma =2\times 10^4$ S/m for VO$_2$ in the conducting state at 87$^\circ$C.
3.2 Switching of asymmetric transmission
Figures 3(a) and (b) show the transmission spectra for the proposed metasurface at room temperature. It is clear that the direct transmission spectra for the LCP and the RCP incidences are identical in 0.1–5 THz range, that is $T_{++}=T_{--}$, while the circular polarization conversion transmission spectra are also identical, that is $T_{-+}= T_{+-}$. In other words, the metasurface does not exhibit asymmetric transmission in this scenario. This is because at room temperature VO$_{2}$ has low conductivity of $\sigma =20$ S/m and is in the insulating state, thus the interactions between the VO$_{2}$ stripes and the terahertz waves can be negligible and the metasurface can be effectively treated as a U-shaped metallic split-ring resonator (SRR) only. For such a mirror-symmetric structure under normal incidence, it is known that it does not have intrinsic or extrinsic chirality. Note that intrinsic chirality arises from the geometric characteristics of the man-made structures, whereas extrinsic chirality relies on external illumination conditions [40].
Fig. 3. Transmission spectra of the proposed hybrid gold-VO$_{2}$ metasurface with (a)(b) $\sigma =20$ S/m at room temperature and (c)(d) $\sigma =2\times 10^4$ S/m at 87$^\circ$C.
At 87$^{\circ }$C the conductivity of VO$_{2}$ increases to $\sigma =2\times 10^4$ S/m such that VO$_{2}$ is in the conducting state. Figure 3(c) shows that $T_{++}$ and $T_{--}$ overlap well with each other, suggesting the absence of circular dichroism. For the circular polarization conversion transmission spectra, Fig. 3(d) shows there are two transmission peaks for both $T_{+-}$ and $T_{+-}$ around $f_1=2.75$ THz and $f_2=4.25$ THz, and that there are evident differences between $T_{+-}$ and $T_{-+}$ over a broad spectral range of $1.2-4.6$ THz. In other words, after the phase of VO$_{2}$ transits from the insulating state to the conducting state, the proposed metasurface now presents strong and broadband asymmetric transmission. Remarkably, the asymmetric transmission reaches up to $\Delta T^- =14\%$ at $f_{1}$, and reaches $\Delta T^- =9\%$ at $f_{2}$. The maximum asymmetric transmission can even reach 15% at 3.1 THz, which is more than 5 times of that of graphene-based tunable metamaterials [35]. Therefore, comparing Figs. 3(b) and (d) we find switching off or on of broadband terahertz asymmetric transmission by adjusting the phase of VO$_2$ in the proposed metasurface.
We further explored the relationship between the circular polarization conversion transmission spectra and the conductivity of VO$_{2}$. Figures 4(a) and (b) show that, for low conductivity of $\sigma =20$ S/m $T_{+-}$ (black solid curve) and $T_{-+}$ (black dashed curve) are identical, corresponding to negligible $\Delta T^-$ ($<10^{-4}$). For the conductivity of $\sigma =20$ S/m and $2\times 10^2$ S/m, $T_{+-}$ (red solid curve) holds the values for $\sigma =20$ S/m while $T_{-+}$ (red dashed curve) slightly decreases, corresponding to small $\Delta T^-$. As the conductivity increases to $\sigma =2\times 10^3$ S/m, $T_{+-}$ (blue solid curve) decreases slightly, whereas $T_{-+}$ (blue dashed curve) decreases dramatically, leading to asymmetric transmission with maximum value of 7%. For conductivity of $\sigma =2\times 10^4$ S/m, $T_{+-}$ (green solid curve) further decreases slightly, whereas $T_{-+}$ (green dashed curve) becomes very small. This corresponds to a large and broadband asymmetric transmission $\Delta T^-$. If the conductivity further increases to $\sigma =2\times 10^5$ S/m, $T_{-+}$ becomes large again, and there are two transmission peaks for both $T_{+-}$ and $T_{-+}$. Compared with $\sigma =2\times 10^4$ S/m, however, the maximum asymmetric transmission is decreased by half, to less than 8%. Therefore, we show that there exists an optimal conductivity for VO$_2$ to achieve the best asymmetric transmission performance.
Fig. 4. (a) Circular polarization conversion transmission spectra ($T_{+-}$ in solid curves and $T_{-+}$ in dashed curves) and (b) the corresponding asymmetric transmission spectra $\Delta T^-$ for different conductivities of VO$_{2}$. Note that the black solid and dashed curves overlap well with each other.
3.3 Broadband and wide-angular performance
We now investigate the incident angular performance of the proposed chiral metasurface. Figures 5(a) and (b) show the circular polarization conversion transmission spectra for incident angles of $\theta =0^{\circ }$, 30$^{\circ }$, 45$^{\circ }$ and 60$^{\circ }$ with $\sigma =20$ S/m at room temperature and $2\times 10^4$ S/m at 87$^{\circ }$C, respectively. Results show that at room temperature, the spectra of $T_{+-}$ and $T_{-+}$ are almost identical, indicating negligible asymmetric transmission regardless of the incident angle and the operation wavelength. This is consistent with the work by Plum et al. on 2D extrinsic chirality mechanism [41], the U-shaped structure will not present asymmetric transmission under oblique incidences.
Fig. 5. (a)(b) Conversion transmission spectra for different incident angles when VO$_2$ has (a) $\sigma =20$ S/m at rooms temperature and (b) $\sigma =20000$ S/m at 87$^{\circ }$C. (c) Asymmetric transmission as a function of incident angle and operation frequency at 87$^{\circ }$C.
At 87$^{\circ }$C, however, Fig. 5(c) shows that as the incident angle increases from 0$^{\circ }$ to 60$^{\circ }$, the maximum value of $T_{+-}$ decreases slightly whereas $T_{-+}$ experiences a large increase for $\theta >45^{\circ }$. For all these incident angles, the asymmetric transmission of $T_{+-}>T_{-+}$ remains pronounced over a broad operation bands of 2.4–4.2 THz. For oblique incident angle of 60$^{\circ }$, another asymmetric transmission window of $T_{-+}>T_{+-}$ appears for the spectral range of 1.5-2.0 THz. Since this window only exists for large incident angles, we can attribute it to extrinsic chirality.
Figure 5(c) further shows $\Delta T^-$ as functions of the incident angle $\theta$ and the operation frequency. Results show that large asymmetric transmission with $\Delta T^->10\%$ can be observed over a broad spectral band of 2.6–4.0 THz and meanwhile over a large incident angular range of $\theta =0^{\circ }$–$45^{\circ }$, as outlined by the black dashed box. As the incident angle further increases, the bandwidth for $\Delta T^->10\%$ gradually decreases, and $\Delta T^-<10\%$ for $\theta >70^{\circ }$. Meanwhile, we also discover $\Delta T^-$ shifts from positive to negative at around 1.5 THz. We thus surmise that the asymmetric transmission with negative $\Delta T^-$, as indicated by the deep blue region, should originate from the extrinsic chirality. In other words, as the incident angle increases, the dominant chirality of the proposed metasurface with VO$_2$ in the conducting state shifts from intrinsic to extrinsic. More specifically, in terms of asymmetric transmission, the spectral range for positive $\Delta T^-$ gradually decreases while that for negative values gradually increases after $\theta >45^{\circ }$.
Therefore, our results show that the proposed hybrid metal-VO$_2$ metasurface can present strong terahertz asymmetric transmission over a broad spectral band and meanwhile over a large incident angular range. This striking performance makes the proposed structure appealing in practical applications.
3.4 Near-field distributions
In order to understand the asymmetric transmission performance of the proposed metasurface, we plot the simulated surface current distributions on the top surface of the proposed metasuface at 1.5 THz. Here 1.5 THz is chosen because at this frequency $\Delta T^-$ changes from positive to negative as the incident angle increases from 0$^\circ$ (normal incidence) to 70$^\circ$ (large oblique incidence), as shown by Fig. 5(c), and thus one can determine the contributions from the intrinsic chirality and from the extrinsic chirality. When VO$_{2}$ is in the insulating state with $\sigma =20$ S/m, Figs. 6(a) and (b) show that the surface currents excited by the LCP or the RCP waves are mainly distributed along the U-shaped gold stripes, whereas those along the L-shaped VO$_2$ stripes are negligible. In other words, in this scenario the proposed metasurface can be equivalently treated as a U-shaped metallic metasurface, which does not have intrinsic or extrinsic chirality [41]. Therefore, the asymmetric transmission is negligible, consistent with our expectation.
Fig. 6. Simulated surface current distributions at the top surface of the proposed metasuface at 1.5 THz for VO$_2$ with (a)(b) $\sigma =20$ S/m at room temperature under normal incidence, and (c)–(f) $\sigma =2\times 10^4$ S/m at 87$^{\circ }$C under (c)(d) normal incidence and (e)(f) oblique incidence of $\theta =60^{\circ }$. The top and the bottom panel are under the excitation of the RCP and the LCP incidences, respectively.
When VO$_{2}$ is in the conducting state with $\sigma =2\times 10^4$ S/m and under normal incidence, Figs. 6(c) and (d) show that the surface currents along the L-shaped VO$_2$ stripes are so strong that they are comparable to those along the U-shaped gold stripes. In this scenario, the proposed metasurface composed of U-shaped gold stripes and L-shaped conducting VO$_{2}$ stripes can be approximately treated as a spiral G-shaped metallic metasurface, which was shown to have large intrinsic chirality under normal incidence [35]. The asymmetric transmission in such a spiral G-shaped metallic metasurface can be explained with a coupling model of electric and magnetic dipoles as illustrated by Fig. 7. We take Fig. 6(d) as the example, the uneven vortex-like surface current distribution can be decomposed into a magnetic dipole $\bf {m}$ that is perpendicular to the surface and an electric dipole $\bf {d}$ on the surface. The coupling between the magnetic and the electric dipoles under the condition $\bf {m}\times \bf {d}\neq 0$ results in asymmetric transmission [32].
Fig. 7. Schematic diagram of the mechanism of intrinsic chirality (asymmetric transmission). Uneven vortex-like surface current distribution (the magnitude is indicated by the length of the red arrows) can be decomposed into a magnetic dipole $\bf {m}$, which is perpendicular to the surface and is induced by circular currents, and an electric dipole $\bf {d}$ on the surface. The coupling between the magnetic and the electric dipoles results in asymmetric transmission.
Under oblique incidence of $\theta =60^{\circ }$, Figs. 6(e) and (f) show that the proposed metasurface can also be approximately treated as a spiral G-shaped metallic metasurface, the differences lie on the relative strength of the surface currents under the excitation of the LCP and the RCP incidences. Under normal incidence, Figs. 6(c) and (d) show that the surface currents for the LCP incidence are stronger than those for the RCP incidence, resulting in $T_{+-}>T_{-+}$. Under oblique incidence of $\theta =60^{\circ }$, however, Figs. 6(e) and (f) show that the surface currents for the LCP incidence are weaker than those for the RCP incidence, resulting in $T_{+-}<T_{-+}$.
4. Conclusions
In conclusions, we have proposed a chiral metasurface composed of hybrid gold-VO$_{2}$ structures, and have achieved switching on or off asymmetric transmission through adjusting the phase of VO$_2$ from the insulating state to the conducting state or reversely. Results have shown that asymmetric transmission of $\Delta T^- > 10\%$ can be achieved over a broad spectral band of 2.6–4.0 THz and meanwhile over a wide angular range of 0$^{\circ }$–45$^{\circ }$. We have also discovered that as the incident angle increases, the asymmetric transmission at 1.5 THz shifts from positive $\Delta T^-$ to negative values when VO$_2$ in the metasurface is in the conducting state. In other words, the dominant chirality changes from intrinsic to extrinsic . We expect the proposed hybrid metal-VO$_2$ metasurface with switchable broadband and wide-angular asymmetric transmission performance will advance the engineering of tunable chiral metasurface, and will find applications in dynamically tunable polarization-dependent photonic devices, especially those used in reconfigurable communication networks.
Funding
Shenzhen Research Foundation (JCYJ20180507182444250); National Natural Science Foundation of China (11774288, 11974279, 62065005); State Key Laboratory of Advanced Optical Communication Systems and Networks, China (2019GZKF2); Natural Science Foundation of Guangxi Province (2018GXNSFAA050043, 2019JJD110007).
Disclosures
The authors declare no conflicts of interest.
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