## Abstract

We present the bifunctional design of a broadband absorber and a broadband polarization converter based on a switchable metasurface through the insulator-to-metal phase transition of vanadium dioxide. When vanadium dioxide is metal, the designed switchable metasurface behaves as a broadband absorber. This absorber is composed of a vanadium dioxide square, silica spacer, and vanadium dioxide film. Calculated results show that in the frequency range of 0.52-1.2 THz, the designed system can absorb more than 90% of the energy, and the bandwidth ratio is 79%. It is insensitive to polarization due to the symmetry, and can still work well even at large incident angles. When vanadium dioxide is an insulator, a terahertz polarizer is realized by a simple anisotropic metasurface. Numerical calculation shows that efficient conversion between two orthogonal linear polarizations can be achieved. Reflectance of a cross-polarized wave can reach 90% from 0.42 THz to 1.04 THz, and the corresponding bandwidth ratio is 85%. This cross-polarized converter has the advantages of wide angle, broad bandwidth, and high efficiency. So our design can realize bifunctionality of broadband absorption and polarization conversion between 0.52 THz and 1.04 THz. This architecture could provide one new way to develop switchable photonic devices and functional components in phase change materials.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Metamaterials, artificially designed electromagnetic composite materials, have aroused great interests in the scientific community because of its potential applications in super-lens [1–3], perfect absorber [4–6], and polarization rotator [7–9]. Typical metamaterials often consist of metal or dielectric element whose size is much smaller than the working wavelength. The behaviors of previous metamaterials are not easy to change once they are fabricated. Recently, a lot of efforts have focused on the manufacture of active metamaterials at microwave, terahertz, and optical frequencies. It is of great significance to develop tunable metamaterials for modulating amplitude, phase, or polarization so as to obtain active devices, such as filter [10,11], modulator [12,13], and sensor [14,15]. One possible way is to integrate metamaterial system with suitable materials like phase change material, because phase change material can be used as thermally or electronically switchable photonic devices. Vanadium dioxide (VO_{2}) as one of phase change materials is an excellent functional material [16], which is a typical Mott material. Its optical and electrical properties will change dramatically during phase transition. This is mainly caused by the transformation of the structure phase from an insulating monoclinic phase (low temperature) to a metallic tetragonal phase (high temperature) around $68{\;^\circ}C$. The dielectric permittivity varies greatly during the phase transition from insulator to metal. VO_{2} has been extensively studied in recent years due to the large change of dielectric permittivity in the process of phase transition [17]. When thermal heating, external electrical field, or optical stimulus is applied, phase transition of VO_{2} can occur at an ultra-fast time scale (∼100 fs) [18–20]. It shows strong dependence on temperature or electric field, and will have some possibilities for smart design and construction of switchable metamaterial devices. Combining metamaterial system with the large dielectric permittivity change of VO_{2}, it can be used to make new photonic devices. Different applications using VO_{2} phase transition have been explored, such as metasurface (2D version of metamaterial) [21–25], optical memory device [26], nano-antenna [27], temperature sensor [28], and rewritable device [29].

Most of these designs are usually designed for a single functionality. In 2015, A. Tittl et al. presented the first experimental demonstration of a mid-infrared absorber with multispectral thermal imaging capability [30]. Their design has very high absorption performance insensitive to incident angle and polarization. It can be integrated on absorption pixels less than 10 $\mu m$, which is of great significance for mid-infrared near diffraction-limited imaging. In 2018, C.R. de Galarreta et al. successfully demonstrated how to combine phase change material with plasmonic metasurface to create a new, nonvolatile, reconfigurable near-infrared beam control and beam shaping devices [31]. When phase-change layer is in the crystalline state, the device reflects incident light in the way of specular reflection, while phase-change layer is in the amorphous state, the device reflects abnormally at a predesigned angle. In 2019, S.G.C. Carrillo et al. combined the structure of chalcogenide phase change material and absorber to create a novel type of tunable optoelectronic color system [32]. Using phase-change layer of crystalline phase, the resonant absorber can be tuned to selectively absorb red, green, and blue bands of visible spectrum, thus producing vivid cyan, magenta, and yellow pixels. When phase-change layer changes to the amorphous phase, resonant absorption is suppressed, resulting in a pseudo white reflection. So it is very desirable to promote the integration of various functionalities into a single device. In this work, a switchable terahertz metasurface based on VO_{2} is presented, and it can be switched from a broadband absorber to a reflective brandband linear polarization converter in the same frequency band. When VO_{2} is metal, high absorptance >90% from 0.52 THz to 1.2 THz is achieved with an optimized geometry. Once VO_{2} is insulator, the design becomes a broadband linear polarization converter with reflectance of 90% from 0.42 THz to 1.04 THz. This VO_{2}-based switchable metasurface exhibits a couple of advantages, such as bifunctionities and ease of scaling to other frequency band.

## 2. Design and method

As shown in Fig. 1, the basic unit cell of the designed switchable metasurface consists of six layers, which from top to bottom are as follows: VO_{2} squared patch, (silica) SiO_{2} spacer, gold strip, VO_{2} film, SiO_{2} spacer, and the bottom gold substrate. The optical permittivity of VO_{2} is described by Drude model $\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }}$ in the terahertz range, where ${\varepsilon _\infty } = 12$ is dielectric permittivity at high frequency, ${\omega _p}(\sigma )$ is the plasma frequency dependent on conductivity and $\gamma$ is the collision frequency [33–37]. Besides, $\omega _p^2(\sigma )$ and $\sigma$ are proportional to free carrier density. The plasma frequency at $\sigma$ can be approximately described by $\omega _p^2(\sigma ) = \frac{\sigma }{{{\sigma _0}}}\omega _p^2({\sigma _0})$ with ${\sigma _0} = 3 \times {10^3}\;{\Omega ^{ - 1}}c{m^{ - 1}}$, ${\omega _p}({\sigma _0}) = 1.4 \times {10^{15}}\;rad/s$, and $\gamma = 5.75 \times {10^{13}}\;rad/s$ which is independent of $\sigma$. The phase-transition process of VO_{2} is accompanied by significant changes in both conductivity and dielectric permittivity. In the process of calculation, different permittivities are used in different phase states of VO_{2}. In our simulation, it is assumed that the conductivity of VO_{2} is $2 \times {10^5}$ S/m (0 S/m) when it is in the metallic (insulating) state. The relative dielectric permittivity of the insulating VO_{2} is set as 12. These two assumptions can mimic phase-transition process of VO_{2}. The relative permittivity of gold is described by a Drude model ${\varepsilon _{Au}} = 1 - \omega _p^2/\omega (\omega + i\Gamma )$ with plasma frequency ${\omega _p} = 1.37 \times {10^{16}}\;rad/s$ and collision frequency $\Gamma = 1.2 \times {10^{14}}\;rad/s$ [38]. The dielectric constant of SiO_{2} is 3.8 with negligible loss at terahertz frequencies [39,40]. With these material parameters, full-wave electromagnetic simulations are carried out using finite-element-method. Unit cell boundary conditions are applied in the x and y directions to mimic the infinite arrays, and open boundaries are set in the z direction. The whole structure is illuminated by a linearly polarized plane wave propagating along the z direction. The simulation mesh is accurately controlled to ensure the conversed results. After some carefully calculations, the optimal geometrical parameters are obtained. The chosen period, width of VO_{2} square, width of gold strip, thickness of the top SiO_{2}, and thickness of the bottom SiO_{2} are $P = 150\;\mu m$, ${w_1} = 90\;\mu m$, ${w_2} = 60\;\mu m$, ${t_1} = 41\;\mu m$, and ${t_2} = 40\;\mu m$. The thicknesses of VO_{2} square, gold strip, and the bottom gold substrate are $0.08\;\mu m$, $0.5\;\mu m$, and $0.5\;\mu m$, respectively.

## 3. Results and discussions

#### 3.1 Designed switchable metasurface behaves as a broadband absorber when $V{O_2}$ is metal

As shown in Fig. 1, the designed switchable metasurface performs as a typical structure of absorber when VO_{2} is metal. It consists of the top VO_{2} patch, middle SiO_{2} layer, and the bottom VO_{2} film. Using finite element method, structure parameters marked in Fig. 1 are optimized to obtain a broadband absorption. In simulation, the complex frequency-dependent *S* parameters (${S_{11}}$ and ${S_{21}}$) can be obtained. Absorptance (A) of the structure can be written as $A = 1 - R - T = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$, where $R = {|{{S_{11}}} |^2}$ ($T = {|{{S_{21}}} |^2}$) is the reflectance (transmittance). Transmission ($|{{S_{21}}} |$) is nearly zero in the interesting frequency range since the thickness of VO_{2} film is $1\;\mu m$ which is thicker than the penetration depth. So absorptance can be directly obtained by A=1-R. Figure 2 shows the calculated absorptance of the designed structure with the conductivity $2 \times {10^5}$ S/m of VO_{2}. It clearly tells that two distinct absorption peaks are observed around 0.61 THz and 1.14 THz. In the frequency range of 0.52-1.2 THz, the designed system can absorb more than 90% of the energy, and the bandwidth ratio $({f_{\max }} - {f_{\min }})/[({f_{\max }} + {f_{\min }})/2]$ is 79%. Absorptance larger than 50% can be maintained within the range of 0.408-1.25 THz, and its bandwidth ratio is 102%. To understand the functionality of the composite structure used here, Fig. 2 numerically compares absorptance with (red) and without (blue) VO_{2} patch. For the VO_{2} patterned design, the wave attenuation capability is significantly improved in both bandwidth and efficiency.

Figure 3 shows the retrieved physical parameters (permittivity, permeability, refractive index, impedance) [41]. The effective optical path is ${\mathop{\rm Re}\nolimits} (n) \times {t_1} = 2.96 \times 41 = 121.36\;\mu m$ at 0.6 THz. It will give rise to a quarter-wavelength mode at the wavelength of $4{\mathop{\rm Re}\nolimits} (n) \times {t_1} = 485.44\;\mu m$. This value is almost equal to the first peak wavelength $500\;\mu m$ (0.6 THz). So the first absorption peak can be attributed to a lowest Fabry-Perot-type resonance. Similarly, at 1.14 THz, the absorption peak is a higher order Fabry-Perot-type resonance. The real and imaginary parts of the effective impedance ${Z_{eff}} = \sqrt {\frac{{{\mu _{eff}}}}{{{\varepsilon _{eff}}}}} = \sqrt {\frac{{{{(1 + {S_{11}})}^2} - S_{21}^2}}{{{{(1 - {S_{11}})}^2} - S_{21}^2}}}$ in Fig. 3(d) are close to one and zero at the frequencies of absorption peak, respectively. At the absorption peaks, the effective impedance of absorber becomes nearly matched with that of free space, which results in near zero reflection and therefore maximum absorption. So this absorption is caused by the impedance adaptation between the effective impedance of metamaterial structure and that of free space. This is achieved by carefully tailoring geometrical parameters and optical properties of materials, which leads to changes in the effective dielectric permittivity and effective permeability.

To better understand the performance of absorber, the influences of geometrical parameters (${t_1}$ and ${w_1}$) are investigated, and the results are plotted in Fig. 4. In Fig. 4(a), it is found that the intensity of absorptance firstly increases with the increasing of ${t_1}$, and then absorptance narrows when ${t_1}$ is larger than the optimized value. The effective optical path increases with the increasing of ${t_1}$, which results in the red shift of absorption peak. In Fig. 4(b), the intensity of absorption peak firstly shows an obvious increasing and an expected red-shift with the increasing of ${w_1}$, and then absorptance becomes to decrease with the increasing of ${w_1}$. When the width of VO_{2} patch is $90\;\mu m$, maximal absorptance is achieved.

The dependence of the performance of such absorber on incident polarization and angle is also investigated. Figure 5(a) shows the evolution contour of absorptance at tuning polarization angles from ${0^\circ }$ to ${90^\circ }$ in a step of ${5^\circ }$. The results clearly indicate that absorptance is completely independent of polarization under normal incidence. The symmetry of the designed system ensures the polarization-insensitive behavior under normal incidence, which is very helpful in numerous applications. Figures 5(b) and 5(c) present the absorptance of transverse electric (TE) polarization and transverse magnetic (TM) polarization as a function of frequency and incident angle. Figure 5(b) is TE polarization and its electric field is always perpendicular to incident plane. Figure 5(c) is TM polarization and its magnetic field is always perpendicular to incident plane. According to the calculated results, the designed absorber shows excellent performances with stable absorptance and working bandwidth for TE waves over a wide range of incident angle from ${0^\circ }$ to ${60^\circ }$. When incident angle is larger than ${60^\circ }$, absorptance becomes to degrade. For TM polarized waves, the main absorption peak narrows as incident angle increases, and the corresponding absorptance remains high even at larger angle of incidence. At the same time, there are some higher-order diffractions due to the smaller ratio (1.67) of wavelength ($250\;\mu m$, 1.2 THz) to period ($150\;\mu m$). The results show that the designed absorber is insensitive to polarization at small incident angle and still works well at large incident angles. The incident angle- and polarization-roust characteristics may have lots of possible applications in energy harvesting and optical sensing.

#### 3.2 Designed switchable metasurface behaves as a broadband cross polarization converter when $V{O_2}$ is insulator

When VO_{2} is insulator, only the bottom structure works, which composes of gold strips, SiO_{2} spacer, and the gold continuous film. It allows for low absorption and broadband linear polarization conversion. Suppose that incident angle of a linearly incident wave is $\theta $ and its electric field is located in the XY plane, where TE wave can conform to this condition in the case of normal incidence and oblique incidence. The reflected wave generally consists of two components, the co-polarized component ${E_{||}}$ parallel to ${E_i}$ and the cross-polarized component ${E_ + }$ orthogonal to ${E_i}$. Reflection coefficients of co-polarized wave and cross-polarized wave are defined as ${r_{||}}$ and ${r_ + }$. ${r_ + }$ is calculated for normal incidence with polarization angle $\phi = {45^\circ }$ (or $\textrm{13}{5^\circ }$) for ${E_i}$. Taking into account normal incidence ($\theta = {0^\circ }$), $\phi $ is meaningless to define the direction of wave vector *k*, while it still makes sense for the definition of direction of ${E_i}$. As shown in Fig. 6(a), it can be found that cross reflectance is over 90% in the frequency range of 0.42-1.04 THz, and the corresponding bandwidth ratio is 85%. The calculated results show that ${R_ + }\;({|{{r_ + }} |^2})$ can reach almost 100%, indicating that polarization direction of the linearly polarized wave can be completely converted after reflection. This phenomenon can be explained by a simple demonstration. By decoupling electric field (${E_i}$) of incident wave into two independent direction (${E_x}$ and ${E_y}$), reflection coefficient of the normally incident wave along x and y directions are ${r_x}$ and ${r_y}$. If $|{{r_x}} |$ and $|{{r_y}} |$ are identical, and their reflection phase difference for these two directions is ∼${180^\circ }$, then a polarization conversion can be achieved. Because a gold film with the thickness of $0.5\;\mu m$ is used in the bottom layer, the entire structure has a perfect reflection of electromagnetic wave at the terahertz frequency, which is independent of incident angle and polarization. So it is not difficult to get $|{{r_x}} |$=$|{{r_y}} |$. Figure 6(b) shows the calculated reflection magnitudes ($|{{r_x}} |$ and $|{{r_y}} |$) for normally incident wave, and Fig. 6(c) shows the calculated reflection phase (${\varphi _x}$ and ${\varphi _y}$). It can be found in Fig. 6(d) that the relative phase difference between x and y directions approaches ${180^\circ }$. It perfectly matches the frequency range of the ${R_ + }$ peaks in Fig. 6(a).

The relation between cross-polarized reflectance and structure parameters (${t_2}$ and ${w_2}$) are studied. To illustrate this property briefly, we only discuss cross-polarized reflectance at normal incidence. Figure 7(a) illustrates the relation between cross-polarized reflectance and dielectric thickness when other structural parameters are fixed. As the thickness of dielectric layer increases from $20\;\mu m$ to $60\;\mu m$, working bandwidth will become broader and three peaks are conspicuous. But the intensity between peaks will continuously decrease. Figure 7(b) illustrates the relation between cross-polarized reflectance and the width of gold strip when other structural parameters are fixed. As the width of gold strip increases from $40\;\mu m$ to $80\;\mu m$, the performance firstly is improved and then deteriorates. These results show that structure parameters are important factors to determine the performance of the system.

The influences of polarization and incident angle are also investigated. The result in Fig. 8(a) is cross reflectance ${R_ + }$ as a function of polarization angle ($\phi $) for ${E_i}$ and frequency ($f$) when $\theta = {0^\circ }$. After anisotropy tunes on, ${R_ + }$ can take non-zero value, and polarization conversion effect is strongly related to polarization angle. In the case of $\phi = {45^\circ }$, reflectance of polarization conversion is maximized. Reflectance of polarization conversion disappeared with ${R_ + } = 0$ when polarization angle is ${0^\circ }$ or ${90^\circ }$. This phenomenon is reasonable, because E and H fields of incident wave are parallel to a coordinate axis so that electromagnetic wave cannot detect the anisotropy of the structure. Cross reflectance ${R_ + }$ as a function of $\theta $ and *f* with $\phi = {45^\circ }$ for *k* and ${135^\circ }$ for ${E_i}$ in the xy plane is shown in Fig. 8(b). It is calculated in TE mode with different incident angles, where E field is always in the xy plane. Numerical results show the stableness of ${R_ + }$ with the increasing of oblique incidence angle, even for incident angle reaching ${60^\circ }$. The curve with minimum in cross reflectance is mainly caused by the diffraction due to the existence of SiO_{2} with the thickness of $81\;\mu m$. This phenomenon is also obviously shown in Fig. 5(c).

## 4. Summary

To summarize, a switchable metasurface with bifunctionality is presented based on the phase-transition property of VO_{2}. When VO_{2} is metal, an isotropic absorber with a simple VO_{2} structure is proposed in the terahertz region. By adjusting geometrical parameters, simulated results show that absorptance is more than 90% in the frequency band of 0.52-1.2 THz. The condition of impedance matching is well satisfied and then the designed hybrid metasurface behaves as a broadband absorber. The absorptance spectra are independent of incident polarization at small incident angles. Absorptance has a good performance even at large incident angle. The present design may be used in stealth technology, terahertz detection, and other fields. When VO_{2} is insulator, the designed hybrid metasurface behaves as a high-efficient linear polarization converter. The linearly polarized state of terahertz wave can be effectively rotated to its orthogonal direction by using a simple design of anisotropic metasurface. Numerical results show that cross-polarized reflectance can reach 90% between 0.42 THz and 1.04 THz. The broadband performance remains unchanged over a wide range of incident angles. Our results confirm that by triggering the insulator-metal transition of VO_{2}, the designed hybrid metasurface can be switched from a broadband absorber to a broadband linear polarization converter in the same frequency band of 0.52-1.04 THz. In fact, some recent VO_{2} experiments are carried out in multilayer structure [42–47]. The dielectric spacer SiO_{2} can withstand temperature operation. To some extent, these successful examples show that our design can be realized in practice. It is a good approach for this design to excite phase transition of VO_{2} by optical method [48,49]. Our design could open up a new way for the development of switchable devices, which can realize completely different functionalities in a single device. It may be suitable for many potential applications in the fields of terahertz switchable plasmonics and photonics.

## Funding

National Natural Science Foundation of China (11974294).

## Disclosures

The authors declare that there are no conflicts of interest related to this article.

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