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Multiband switchable terahertz vanadium dioxide-GeTe hybrid metasurface

Jiu Sheng Li and Rou-Lan Wu

Open Access Open Access

Abstract

We proposed a multi-band switchable terahertz metasurface based on vanadium dioxide (VO2) and the chalcogen phase change material (GeTe). By controlling the phase transition of VO2 and GeTe, the operation function of the metasurface can be switched among linear-to-linear polarization converter, linear-to-circular polarization converter, and bandstop filter. The results show that the metasurface works in linear-to-linear polarization conversion mode as the VO2 is in insulating state (at 25°C). The polarization conversion rate (PCR) is more than 90% within 3.50-3.55 THz and 3.81-4.29 THz. When the VO2 is in the metallic state, it becomes a linear-to-circular polarization conversion mode. The normalized ellipticity is -1 in the range of 2.65-3.60 THz. While the GeTe is transitioned to the crystalline state, the structure operates as terahertz bandstop filter with 3 dB band-stop bandwidth of 355 GHz. Furthermore, the working principle of the proposed metasurface is analyzed by electric field distribution. Based on these characteristics, the proposed metasurface is expected to be used in various terahertz systems.

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

1. Introduction

Metasurfaces have garnered increasing attention due to its exceptional flexibility in controlling electromagnetic waves and easy integration [1–5]. Generally, the regulation function of electromagnetic wave is fixed and immutable after the metasurface structure is determined. In order to manipulate terahertz waves more flexibly and effectively, researchers often utilize tunable dielectric such as graphene [6,7], VO2 [8,9], and photosensitive silicon [10,11] integrated in metasurface to realize controllable manipulation of various electromagnetic wave physical properties, such as phase [12,13], amplitude [14,15], and polarization [16], etc. Terahertz filters are essential functional devices in terahertz systems such as communication, imaging, and detection. For example, in 2020, Wang et al. [17] proposed VO2 embedded in the open square ring metasurface to control terahertz wave transmission and absorption by varying the phase state of VO2. In 2021, Liu et al. [18] designed VO2 hybrid metasurface to modify the terahertz wave transmission rate from 80% to 0 within 0.72-0.75 THz. Polarization is also an important physical property of terahertz waves. The magnetophotometry of detecting the hall effect and studying the chiral structure of proteins and DNA require effective terahertz polarization conversion devices [19]. For example, in 2022, Yu et al. [20] demonstrated a VO2 metasurface to change PCR from 90% to 0 in the range of 2.22-5.42 THz. Additionally, the chalcogenide material (GeTe) has attracted many attentions due to its phase transition regulated by temperature [21]. In 2022, Shi et al. [22] used Ge2Sb2Te5 (GST) to design circular dichroism to achieve frequency tunable metasurfaces as GST switching between amorphous and crystalline states. Chen et al. [23] created a metasurface by combining GST with metal rods to produce linear-to-linear polarization conversion and broadband absorption. The above mentioned results are focus on adjustable single-function devices, which hinder the application and development of terahertz wave, resulting in imperfect research on terahertz functional devices.

In this study, we design a tunable metasurface using the phase transition properties of VO2 and GeTe, in which the functions can be regulated by temperature. When VO2 is in the insulating state, the metasurface behaves a linear-to-linear polarization converter within 3.50-3.55 THz and 3.81-4.29 THz with the PCR higher than 90%. When VO2 is in the metallic state, the metasurface becomes a linear-to-circular polarization converter. The ellipticity χ equals -1 in the range of 2.65-3.60 THz. As GeTe changes from amorphous state to crystalline state, the proposed metasurface becomes terahertz bandstop filter with 3 dB band-stop bandwidth of 355 GHz. It can be noted that the metasurface can achieve three different functions with temperature changes, which provides a new idea for the design of multifunctional switching terahertz devices.

2. Structure design

The structure diagram and parameters definition of the proposed terahertz metasurface based on VO2 and GeTe is illustrated in Fig. 1. From top to bottom, the metasurface consists of the patterned GeTe/metal layer, polyethylene cyclic olefin copolymer (TOPAS) layer, VO2 layer, TOPAS layer, and patterned GeTe/metal layer. The permittivity and conductivity of the amorphous GeTe are 63 and 10 S/m, whereas those of the crystalline GeTe are 1 and 4.1 × 105 S/m [24]. According to Drude model, the effective dielectric permittivity of VO2 in the terahertz range can be given by [25]

$$\varepsilon \left( \omega \right) = {\varepsilon _\infty } - \frac{{\omega _p^2\left( \sigma \right)}}{{{\omega ^2} + i\gamma \omega }}$$
where ɛ∞=12, the collision frequency γ=5.75 × 1013 rad/m, ωp represents the plasma frequency. The conductivity variation of VO2 is 10 to 3 × 105 S/m [26]. The optimum geometric parameters of the proposed metasurface are as follows: P = 50 µm, r1 = 20 µm, r2 = 2 µm, r3 = 15 µm and r4 = 8 µm. The thickness of the pattern GeTe/metal layer and VO2 layer are 0.17 µm and 2 µm, respectively. The dielectric substrate is made of TOPAS with the thickness of 13.9 µm and the relative permittivity of 2.35 [27]. In this article, simulation computations are performed using the finite-difference frequency-domain approach in the CST Microwave Studio program. The ± x and ± y directions are set to periodic boundary conditions, whereas the z direction is arranged in open boundary conditions.

 figure: Fig. 1.

Fig. 1. 3D sketch map of the metasurface structure based on VO2/GeTe composite dielectric. (a) 3D structure of the unit cell, (b) linear-to-linear polarization converter at 25°C, (c) linear-to-circular polarization converter at 68°C, (d) bandstop filter at 160°C, (e) Top view of the unit cell, (f) bottom view of the unit cell.

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3. Results and discussions

3.1 Linear-to-linear polarization converter

Since the designed unit structure is symmetrical along the diagonal direction, the electromagnetic response to x-polarized waves and y-polarized waves are consistent. Here, we can only take account the y-polarized wave incidence into the calculation procedure. The reflected electric field under the incident y-polarized terahertz wave can be represented as [28]

$${E_r} = {E_{xr}}{e_x} + {E_{yr}}{e_y} = {r_{xy}}\exp \left( {j{\varphi _{xy}}} \right){E_{yi}}{e_x} + {r_{yy}}\exp \left( {j{\varphi _{yy}}} \right){E_{yi}}{e_y}$$
where x and y denote the polarization direction of the electromagnetic wave, i and r represent the incident and reflected terahertz waves, respectively. The cross-polarization transmission coefficient (txy) denotes as txy=|Etx|/|Eiy|, and the co-polarization transmission coefficient (tyy) is defined as tyy=|Ety|/|Eiy|. The φxy and φyy are the corresponding phases of rxy and ryy, respectively. The PCR of the terahertz wave orthogonal linear polarization converter is calculated by [29]
$$\textrm{PCR}y = \frac{{r_{xy}^2}}{{r_{xy}^2 + r_{yy}^2 + t_{xy}^2 + t_{yy}^2}}$$

At 25°C (i.e. VO2 is in insulating state and GeTe is in amorphous state.), the electromagnetic response curve and PCR curve under normal incidence of y-polarized terahertz wave are shown in Fig. 2. Figure 2(a) demonstrates that the cross-polarization transmission coefficient txy is zero in the frequency range of 3.50-3.55 THz and 3.81-4.29 THz. While the cross-polarization reflection coefficient rxy equals 0.92, 0.95, 0.97 at the resonance frequencies of 3.53 THz, 3.89 THz, and 4.24 THz, respectively. At this time, the values of tyy≈ryy are 0.14, 0.03 and 0.04, respectively. According to analysis as above, the incident linearly polarized terahertz wave is entirely transformed into the cross-polarized terahertz wave. From Fig. 2(b), one can see that the PCR of the normal incident y-polarized terahertz wave are 95.70%, 99.84%, and 99.66%, respectively. These PCR are larger than 90% in the frequency ranges of 3.50-3.55 THz and 3.81-4.29 THz, demonstrating that the designed structure has high polarization conversion efficiency.

 figure: Fig. 2.

Fig. 2. (a) Electromagnetic response curve, (b) PCR curve of metasurface at 25°C.

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Figure 3 shows the pattern of the top and bottom current distributions of the proposed metasurface at frequency of 3.53 THz, 3.89 THz, and 4.24 THz. It can be seen from Fig. 3(a) that the currents on the outer and lower sides of the top and bottom eight-sided metal rings have the same direction at 3.53 THz. Additionally, the electric dipole moments of p1 and p2 are excited to generate induced electric fields of E1 and E2. The current in the inner ring of the eight-sided metal ring at the bottom is divided into currents along the -y direction and the x direction, which results in two electric dipole moments of p3 and p4. There forms induced electric fields of E3 and E4. The induced electric fields of E1 and E3 are perpendicular to the magnetic field of the incident wave, and produce a coupling effect at 3.53 THz. In addition, the induced electric fields of E2 and E4 are parallel to the incident wave magnetic field and have no effect on the polarization conversion at 3.53 THz. Figure 3(b) shows the inner ring current in the bottom eight-sided metal ring at 3.89 THz. It can be decomposed into currents along the -y and x directions. The top eight-sided metal ring current flows along the x direction, which excites electric dipole moment of p1 to produce induced electric field of E1, and electric dipole moment of p2 to produce induced electric field of E2. Since the induced electric field of E1 is perpendicular to the incident wave magnetic field, the cross-coupling between the incident wave magnetic field of H and the induced electric field of E1 results in polarization conversion. The induced electric field of E2 is parallel to the incident wave magnetic field, thus the cross-coupling is unable to generate and the polarization conversion is unaffected. Figure 3(c) shows the inner ring current of the upper eight-sided metal ring at 4.24 THz, which is divided into currents along the y and x directions. We can find that the current in the y direction is the opposite of the current in the bottom inner ring, which generates a magnetic dipole moment of m1. It results in an induced magnetic field of H1 perpendicular to the incident magnetic field of H. Thus, they cannot create cross-coupling. The electric dipole moments of p1 and p2 excite to create the induced electric fields of E1 and E2. A coupling effect is produced because the generated electric field of E1 is perpendicular to the incident wave magnetic field of H. In addition, the induced electric field of E2 is parallel to the the incident wave magnetic field of H, there are no electromagnetic cross-coupling occurring. As a result, E1 is the primary factor in producing the orthogonal polarization conversion.

 figure: Fig. 3.

Fig. 3. Current distribution diagram of the top and bottom metal layers under different frequencies, (a) 3.53 THz, (b) 3.89 THz, (c) 4.24 THz.

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3.2 Linear-to-circular polarization converter

At 68°C (i.e.VO2 is in metallic state and GeTe is in amorphous state), the VO2 layer transforms into a metallic layer, and the proposed composite metasurface operates as the linear-to-circular polarization converter. The cross-polarization and co-polarization reflection coefficient (rxy and ryy) under the y-polarized terahertz wave perpendicular incidence are shown in Fig. 4(a). It can be find that rxy≈ryy in 2.65-3.60 THz. Figure 4(b) shows the phase differences Δφ (corresponding to rxy and ryy equals to -π/2 or 3π/2, respectively). It indicates that the y-component exceeds the x-component by 90°, fully satisfying the realization conditions of the linear-to-circular polarization [30]. The Stoke parameter is used to verify whether the reflected wave is the left-handed circularly polarized wave (LHCP) or the right-handed circularly polarized wave (RHCP) [31].

 figure: Fig. 4.

Fig. 4. (a) Reflection coefficient of y-polarized terahertz wave under normal incidence, (b) Phase φyy, φxy and phase difference Δφ corresponding to ryy and rxy.

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$${S_0} = |{r_{yy}}{|^2} + |{r_{xy}}{|^2}$$
$${S_1} = |{r_{yy}}{|^2} - |{r_{xy}}{|^2}$$
$${S_2} = 2|{r_{xy}}||{r_{yy}}|\cos \left( {{\varphi _{xy}} - {\varphi _{yy}}} \right)$$
$${S_3} = 2|{r_{xy}}||{r_{yy}}|\sin \left( {{\varphi _{xy}} - {\varphi _{yy}}} \right)$$

The normalized ellipticity e and axial ratio AR can be defined as

$$e = \frac{{{S_3}}}{{{S_0}}} = \frac{{2|{r_{xy}}||{r_{yy}}|\sin \left( {{\varphi _{xy}} - {\varphi _{yy}}} \right)}}{{|{r_{yy}}{|^2} + |{r_{xy}}{|^2}}}$$
$$AR = \sqrt {\frac{{{S_0} + \sqrt a }}{{{S_0} - \sqrt a }}}$$
$$a = |{r_{xy}}{|^4} + |{r_{yy}}{|^4} + 2|{r_{xy}}{|^2}|{r_{xy}}{|^2}\cos \left( {2{\varphi _{xy}} - {\varphi _{yy}}} \right)$$
where S0, S1, S2, and S3 stand for the intensity of the reflected terahertz wave, y-polarized component, 45° linearly polarized component, and circularly polarized component, respectively. The normalized ellipticity χ can be used to evaluate the efficacy of the polarization converter. When χ=±1, the reflected terahertz waves are RHCP and LHCP, respectively. The axial ratio AR is used to measure the circular polarization features of the reflected wave, indicating the purity of the circular polarization.

The normalized ellipticity curve is illustrated in Fig. 5(a). The ellipticity in the range of 2.65–3.60 THz is -1, indicating that the reflected wave is transform into LHCP wave with the relative bandwidth of 30.4%. The linear-to-circular polarization conversion rate is more than 85%. Figure 5(b) displays the axial ratio curve calculated according to the axial ratio formula. In 2.65-3.60 THz, the axial ratio is less than 3 dB, indicating that the designed metasurface can convert the y-polarized terahertz waves into left-handed circularly polarized terahertz waves.

 figure: Fig. 5.

Fig. 5. (a) Normalized ellipticity and linear-circular polarization conversion efficiency, (b) axial ratio of the designed metasurface structure.

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Figure 6(a) and 6(b) show the variation of e and AR with the incident angle of y-polarized waves under the oblique incidence, respectively. When the incident angle changes from 0° to 50°, the ellipticity χ is less than -0.95, and the AR is below 3 dB. When the incident angle increases, the electromagnetic field component along the y-axis direction gradually weakens, and finally the electromagnetic resonance is no longer excited.

 figure: Fig. 6.

Fig. 6. Under incidence of y-polarized terahertz wave, (a) ellipticity e, (b) axial ratio AR as a function of incident angle.

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3.3 Terahertz bandstop filter

At 160°C (i.e. VO2 is in metallic state and GeTe is in crystalline state), the terahertz reflection characteristics of the designed metasurface are shown in Fig. 7. At frequency of 5.03 THz, the attenuation depth reaches -34.864 dB and the -3 dB band-stop bandwidth is 0.355 THz, which behaves as a terahertz band-stop filter. The falling edge slope of the filter is 161.830 dB/THz, and the rising edge slope is 178.128 dB/THz.

 figure: Fig. 7.

Fig. 7. At 160 °C, the reflection coefficient under y-polarized wave normal incidence.

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The electric field distribution of the proposed metasurface at 5.03 THz is depicted in Fig. 8. The charge energy concentrates in the three elliptical corners at the upper and lower ends, showing strong coupling. The charge inside the ring is concentrated at the upper and lower elliptical corners, which excites electric dipole resonance. The top GeTe/metal composite pattern has the same positive and negative charge distribution as the VO2 layer, which excites the electric dipole resonance. The resonance of multiple pairs of electric dipoles manifests as electric field absorption loss, which produces the characteristics of a terahertz band-stop filter. A comparison of our work with previous work is shown in Table 1.

 figure: Fig. 8.

Fig. 8. Electric field distribution at 5.03 THz, (a) GeTe/metal combination pattern, (b) VO2 layer.

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Tables Icon

Table 1. Comparison between references and our work

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4. Conclusion

To sum up, we designed and analyzed a multi-band switchable terahertz metasurface based on VO2 and GeTe, which can realize the switching of linear-to-linear polarization converter, linear-to-circular polarization converter and terahertz bandstop filter by dynamically adjusting the operating temperature. When the temperature is 25°C, the designed metasurface achieves dual-band linear-to-linear polarization conversion mode in the region of 3.50-3.55 THz and 3.81-4.29 THz. At the temperature of 68°C, the structure works as linear-to-circular polarization conversion mode the frequency range of 2.65-3.60 THz. In addition, when the temperature rise to 160°C, the proposed metasurface operates as a band-stop filter in the range of 4.60-5.40 THz. The proposed absorber based on VO2 and GeTe has some potential applications in various terahertz detection and communication system.

Funding

National Natural Science Foundation of China (61831012, 62271460); Zhejiang Key R & D Project of China (2021C03153, 2022C03166); Research Funds for the Provincial Universities of Zhejiang (2022YW87, 2020YW20).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Figures (8)
Fig. 1.
Fig. 1. 3D sketch map of the metasurface structure based on VO2/GeTe composite dielectric. (a) 3D structure of the unit cell, (b) linear-to-linear polarization converter at 25°C, (c) linear-to-circular polarization converter at 68°C, (d) bandstop filter at 160°C, (e) Top view of the unit cell, (f) bottom view of the unit cell.

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Fig. 2.
Fig. 2. (a) Electromagnetic response curve, (b) PCR curve of metasurface at 25°C.

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Fig. 3.
Fig. 3. Current distribution diagram of the top and bottom metal layers under different frequencies, (a) 3.53 THz, (b) 3.89 THz, (c) 4.24 THz.

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Fig. 4.
Fig. 4. (a) Reflection coefficient of y-polarized terahertz wave under normal incidence, (b) Phase φyy, φxy and phase difference Δφ corresponding to ryy and rxy.

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Fig. 5.
Fig. 5. (a) Normalized ellipticity and linear-circular polarization conversion efficiency, (b) axial ratio of the designed metasurface structure.

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Fig. 6.
Fig. 6. Under incidence of y-polarized terahertz wave, (a) ellipticity e, (b) axial ratio AR as a function of incident angle.

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Fig. 7.
Fig. 7. At 160 °C, the reflection coefficient under y-polarized wave normal incidence.

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Fig. 8.
Fig. 8. Electric field distribution at 5.03 THz, (a) GeTe/metal combination pattern, (b) VO2 layer.

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Tables (1)

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Table 1. Comparison between references and our work

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Equations (10)

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ε ( ω ) = ε ∞ − ω p 2 ( σ ) ω 2 + i γ ω
E r = E x r e x + E y r e y = r x y exp ⁡ ( j φ x y ) E y i e x + r y y exp ⁡ ( j φ y y ) E y i e y
PCR y = r x y 2 r x y 2 + r y y 2 + t x y 2 + t y y 2
S 0 = | r y y | 2 + | r x y | 2
S 1 = | r y y | 2 − | r x y | 2
S 2 = 2 | r x y | | r y y | cos ⁡ ( φ x y − φ y y )
S 3 = 2 | r x y | | r y y | sin ⁡ ( φ x y − φ y y )
e = S 3 S 0 = 2 | r x y | | r y y | sin ⁡ ( φ x y − φ y y ) | r y y | 2 + | r x y | 2
A R = S 0 + a S 0 − a
a = | r x y | 4 + | r y y | 4 + 2 | r x y | 2 | r x y | 2 cos ⁡ ( 2 φ x y − φ y y )
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