Numerical Simulations of Circular Dichroism and Polarization Conversion in VO₂-Based Terahertz Metamaterials

Abstract

Metamaterials with actively tunable functionalities are highly desirable for applications of advanced optoelectronic devices. In this paper, we theoretically present a metamaterial with diversified functionalities by availing of the phase transition characteristics of vanadium dioxide (VO₂) in terahertz frequency regions. The research results demonstrate that the function of the designed metamaterial can be switched from giant circular dichroism (CD) to a reflecting broadband half-wave plate (HWP) and a quarter-wave plate (QWP). When VO₂ is in the isolating state, the metamaterial exhibits a quite distinct transmission efficiency for circularly polarized lights, thus resulting in a maximum CD value ~0.97 at the resonant frequency. When VO₂ is operating in the metallic state, the metamaterial performs like a broadband HWP, in which the nearly perfect linear polarization conversion can be achieved at the frequency range from 3 to 7 THz. Moreover, the structure can play a role of a high-efficiency QWP that can simultaneously convert the incident linear polarized light to left-handed and right-handed circularly polarized light. The calculated ellipticity indicates a good polarization conversion at the frequency of 2.4 THz and 7.4 THz, respectively. The physical mechanism of the discussed features and effects can be explained by exploring the electric field distributions. Furthermore, the structural parameters also exert great influences for achieving giant CD and HWP as well as QWP. The proposed metamaterial may offer a new approach for designing metamaterial devices with multi-functions in THz regions.

1. Introduction

Circular dichroism (CD) [1,2], refers to the difference of light transmission, reflection or absorption efficiencies between left-handed circularly polarized (LCP) light and right-handed circularly polarized (RCP) light, which has attracted a growing amount of attention due to its wide applications [3,4]. However, the CD response obtained by utilizing natural materials is weak to detect. Therefore, extensive research works have been proposed to design and achieve the highest possible CD values in metamaterial-based nanostructures [5,6,7,8,9]. As for metamaterial [10], it is a kind of artificial material possessing exotic electromagnetic characteristics achieved by carefully constructing the structural units [11,12]. Over the past few years, amounts of functional optoelectronic devices have been proposed at the frequency ranges from the visible lights to terahertz (THz) waves [13,14]. It is also worth noting that terahertz waves have been widely utilized in imaging, photoelectric detection and spectroscopy in recent years. Furthermore, another significant application of terahertz metamaterial, polarization conversion [15], plays an important role in manipulating the polarization state of electromagnetic waves [16]. Generally, the half-wave plate (HWP) and quarter-wave plate (QWP) are two typical kinds of waveplates among the polarization optical components [17]. The HWP can rotate the azimuth of the polarized light at any arbitrary degree, and the QWP can convert linearly polarized light to circularly polarized and vice versa. In terahertz frequency regions, traditional wave plates are made of birefringent materials, which usually work at a fixed single function or limited operating frequency bandwidth.

In practical applications, photonics devices with actively tunable functionalities are highly desirable to be compatible with integrated metamaterials [18,19,20,21,22]. However, it is hard to realize tunable functionality for typical metamaterials consisting of precious metals and dielectric elements once the architecture is designed and fabricated. Thus, strategies have been proposed by integrating active materials with nanostructures, such as two-dimensional materials [23], semiconductors [24], etc. As alternative materials, phase change materials [25], e.g., vanadium dioxide (VO₂), has attracted much interest as its optoelectronic properties can go through dramatic change during phase transition at the critical temperature about 68 °C [26,27,28,29]. Recently, varieties of VO₂-based metamaterial nanostructures have been proposed to acquire multiple functions [30,31,32,33,34,35,36]. For example, Ding et al. theoretically suggested a VO₂-based metasurface which can achieve switchable functionalities between a broadband absorber and a reflecting HWP [37]. Luo et al. designed a metal-VO₂-assisted metamaterial which can be utilized as broadband terahertz HWP and QWP [38]. Very recently, Tang et al. proposed an actively tunable metamaterial device based on the hybrid VO₂–graphene integrated configuration [39], in which the switching between asymmetric transmission and polarization conversion can be achieved. However, as far as we know, there have been no reports of metamaterial devices that can switch between optical CD and HWP, as well as QWP in the terahertz range.

In this paper, we propose a metamaterial with diversified functionalities that can switch from giant CD to a reflecting broadband HWP and QWP by availing of insulator-to-metal transition in VO₂ in terahertz regions. When VO₂ is in the isolating state, the metamaterial exhibits distinct transmission efficiency for circularly polarized light, and a maximum value of CD exceeds 0.97 at the resonant frequency. When VO₂ is in the metallic state, the metamaterial acts as a broadband HWP, and the nearly perfect linear polarization conversion can be obtained at the frequency range from 3 to 7 THz. Moreover, the metamaterial can play a role of a high-efficiency QWP that can simultaneously convert the incident linear polarized light to left-handed and right-handed circularly polarized light, and the calculated ellipticity indicates a good polarization conversion at the frequency of 2.4 THz and 7.4 THz, respectively. The physical mechanism of the above phenomena can be explained by exploring the electric field distributions. Furthermore, the structural parameters also exert great influences for achieving giant CD and HWP as well as QWP. The proposed metamaterial may offer a new approach for developing nanophotonic devices with diversified functions in THz region.

2. Structural Design and Methods

Figure 1a depicts the polarization conversion function of designed metamaterial under the illumination of linearly polarized waves when VO₂ is in the metallic state. As illustrated in Figure 1b, the designed metamaterial is utilized to realize circular dichroism under the illumination of circularly polarized waves when VO₂ is in the isolating state. Figure 1c shows the schematic of a unit cell, which is composed of a Au strip, SiO₂, a Au split ring, VO₂, SiO₂ and a Au strip from top to bottom. The upper and bottom Au strips have the same rotation angle θ with respect to the y-axis. Figure 1d shows the side view of the designed metamaterial in the x-z plane. The optimized geometric parameters are listed in the caption of Figure 1. SiO₂ is selected as the dielectric layer, and the refractive index is 1.45. According to Drude model, the effective permittivities of VO₂ and Au at terahertz frequency can be expressed as follows [30]:

$${\epsilon }_{\mathrm{Au}}\left(\omega \right)=1-\frac{{\omega }_{p\mathrm{Au}}^2}{{\omega }^2+i{\gamma }_{\mathrm{Au}}\omega }$$

(1)

$${\epsilon }_{{\mathrm{VO}}_2}\left(\omega \right)={\epsilon }_{\infty }-\frac{{\omega }_p^2\left(\sigma \right)}{{\omega }^2+i{\gamma }_{{\mathrm{VO}}_2}\omega }$$

(2)

$${\omega }_p^2\left(\sigma \right)=\frac{\sigma }{{\sigma }_0}{\omega }_p^2\left({\sigma }_0\right)$$

(3)

where the plasma frequency ${\omega }_{p\mathrm{Au}}$ of Au is $1.37\times {10}^{16}$ $rad/s$, the collision frequency ${\gamma }_{\mathrm{Au}}$ is $4.08\times {10}^{13}$ $rad/s$. ${\epsilon }_{\infty }=12$ is the dielectric permittivity at the infinite frequency for VO₂, ${\gamma }_{{\mathrm{VO}}_2}$ is $5.75\times {10}^{13}$ $rad/s$, ${\omega }_p(\sigma )$ is the plasma frequency based on conductivity $\sigma$, ${\sigma }_0=3\times {10}^5 S/m$, ${\omega }_p({\sigma }_0)=1.4\times {10}^{15} rad/s$. In simulation, the conductivities of VO₂ in the metallic state is set as $3\times {10}^5 S/m$, and the conductivities of VO₂ in the isolating state is set as $10 S/m$. In this work, the three-dimensional finite-difference time-domain (FDTD) method was utilized to perform the electromagnetic simulations. The spatial mesh dimensions were set to Δ𝑥 = Δ𝑦 = Δ𝑧 = Δ𝑠 = 5 nm, and the time step was taken as Δ𝑡 = Δs/2c (c is the velocity of light in vacuum) and the total time step number was 2 × 10⁵, which ensures that the electromagnetic fields were stable and convergent. The optimized geometric parameters are listed in the caption of Figure 1. To obtain the optimum values of the parameters, the parameter sweeps were made in simulations. The optimizations of these parameters were performed by altering the sizes and the positions of the elements, and the periodic boundaries were set in both the x and y directions, while in the z direction, perfectly matched layers were utilized.

Based on the polarization conversion theory, one can build a connection between the reflected electric fields and the incident electric field with a Jones matrix. The incident and reflected electric fields can be described as [34]:

$$E_i\left(r,t\right)=\left(\begin{array}{c}{I}_x\\ I_y\end{array}\right)e^{i\left(kz-\omega t\right)}$$

(4)

$$E_r\left(r,t\right)=\left(\begin{array}{c}{R}_x\\ R_y\end{array}\right)e^{i\left(kz-\omega t\right)}$$

(5)

where ω represents the angular frequency, k denotes the wave vector, and the complex amplitudes of the incident wave components in the x-and y-directions are represented by $I_x$ and $I_y$, respectively. Similarly, the complex amplitudes of the reflected wave components in the x- and y-directions are represented by $R_x \mathrm{and} R_y$, respectively. The complex amplitudes of the reflected light can be expressed as [38]:

$$\left(\begin{array}{c}{R}_x\\ R_y\end{array}\right)=\left(\begin{array}{cc}{r}_{xx}& r_{xy}\\ r_{yx}& r_{yy}\end{array}\right)\left(\begin{array}{c}{I}_x\\ I_y\end{array}\right)$$

(6)

The polarization conversion ratio (PCR) can be defined as the ratio of the power of the converted cross-polarized light and the total transmitted powers. Herein, PCR for linearly polarized lights can be calculated as [40]:

$$PCR\left(x\right)=\frac{|t_{yx}{|}^2}{\left|t_{xx}{|}^2+\right|t_{yx}{|}^2}=\frac{T_{yx}}{T_{xx}+T_{yx}}$$

(7)

$$PCR\left(y\right)=\frac{|t_{xy}{|}^2}{\left|t_{xy}{|}^2+\right|t_{yy}{|}^2}=\frac{T_{xy}}{T_{xy}+T_{yy}}$$

(8)

where PCR(x) and PCR(y) denote the polarization conversion ratio for x- and y-polarized lights, respectively. t_ij (i(j) = x,y) denotes i-polarized transmission coefficient from j-polarized incident lights, and $T_{ij}=|t_{ij}{|}^2$.

In addition, to quantify the efficiency of the linear-to-circular polarization conversion, the ellipticity (χ) can be defined as $\chi =S_3/S_0$, in which the Stokes parameters (S) are given by the following formulas [17]:

$$S_0=\left|r_{xx}{|}^2+\right|r_{yx}{|}^2$$

(9)

$$S_1=\left|r_{xx}{|}^2-\right|r_{yx}{|}^2$$

(10)

$$S_2=2\left|r_{xx}\right|\left|r_{yx}\right|\cos \left(\mathsf{\Delta }\Phi \right)$$

(11)

$$S_3=2\left|r_{xx}\right|\left|r_{yx}\right|\sin \left(\mathsf{\Delta }\Phi \right)$$

(12)

where $\mathsf{\Delta }\Phi$ represents the phase difference between two orthogonal polarizations.

3. Results and Discussion

When VO₂ is in the isolating state, the substrate enables the optical transmission of incident lights along the forward (-z) direction. Figure 2a shows the calculated optical transmission spectra for the designed metamaterial when illuminated by circularly polarized lights. One can clearly see from Figure 2a that the optical responses exhibit distinct transmission efficiencies for both circularly polarized lights. Specifically, there exists an obvious transmission resonant peak at the frequency of 2.95 THz for the illumination of RCP light. By contrast, there appears a transmission dip at the same frequency for the illumination of LCP light. As a result, the circular dichroism (CD) response can be achieved according to the difference in transmittance between LCP and RCP light illuminations [1], which can be calculated by the formula CD = T_RCP − T_LCP. The corresponding optical CD spectrum is given in Figure 2b, in which the maximum value of CD exceeds 0.97 at the frequency of 2.95 THz. To understand the operation mechanism of CD, Figure 2c,d illustrate the electric field distributions at x-z plane when illuminated by RCP and LCP lights, respectively. One can obviously find from Figure 2c that a strong electric field is excited at the resonant frequency of 2.95 THz in each part of Au nanostructure. Thus, most of the radiative photons can be emitted out of the structure under the illumination of RCP light. However, the excited electric field in the corresponding part of Au nanostructure becomes much weaker under LCP illumination, as depicted in Figure 2d. As a result, most of the incident photon energies are reflected due to the scattering effect occurring in the split ring. Therefore, a strong CD response can be achieved when VO₂ is in the isolating state.

When VO₂ is transformed from dielectric state to the metallic state, the VO₂ film serves as a metal background that blocks the light transmission. Figure 3a depicts the reflection amplitude components of forward propagating light with x-polarization. One can find that R_yx and R_xx show a great discrepancy across the operating frequency range, indicating that the incident x-polarized light is almost converted into y-polarized light. Moreover, the total reflected power reaches over 90% at the frequency range from 3 to 7 THz, manifesting that the designed metamaterial can act as an HWP. Figure 3b illustrates the spectra of two reflection phases and the corresponding phase difference ΔΦ between two reflection phases. It is obviously that the phase difference ΔΦ goes through great change from ~−π/2 to ~3π/2 across the whole frequency range. Figure 3c depicts the PCR spectra for forward incident x-polarized light, where nearly perfect linear polarization conversion can be obtained at the frequency range from 3 to 7 THz. Figure 3d shows the calculated ellipticity spectra for forward incident x-polarized light. According to the definition of ellipticity ($\chi$), it indicates a perfect LCP light when the ellipticity $\chi =1$, and a perfect RCP light when $\chi =-1$. In particular, it should be noted that the linear-to-circular polarization conversion can be achieved if the reflection amplitudes satisfy the relationships as follows: $R_{xx}=R_{yx}$ and $\mathsf{\Delta }\Phi ={\Phi }_{yx}-{\Phi }_{xx}=2m\mathsf{\pi }\pm \mathsf{\pi }/2$, where m is an integer, and “+” and “−” manifest the RCP and LCP lights. Based on the above, one can find that perfect linear-to-circular polarization conversion can be achieved for the proposed structure at the frequency of 2.4 THz and 7.4 THz, respectively. That is to say, the metamaterial device serves as a QWP which can transform the incident x-polarized light into reflected RCP and LCP lights. Therefore, the designed device can simultaneously play the role of HWP and QWP at different working frequencies when VO₂ is in the metallic state.

In addition, it is worth noting that the geometrical parameter, i.e., the rotation angle θ, has great influences on the optical responses and polarization conversion. When VO₂ is in the isolating state, Figure 4 depicts the calculated optical transmission spectra and CD responses as a function of the rotation angle and wavelength under the illumination of LCP and RCP lights, respectively. It can be seen that with the increase of θ, the transmission efficiency exhibits huge differences for both polarizations and the optical CD responses go through dramatic changes. When the rotation angle θ is fixed at 0°, the transmission efficiency for RCP and LCP lights is nearly same, thus the calculated CD response is near zero. In particular, one can clearly find from Figure 4a that with the increase of the rotation angle from 15° to 75°, the resonant dip of the optical transmission spectra for the illumination of LCP light takes on a low value and shows a blueshift at the frequency range from 2.5 to 3.4 THz. Meanwhile, as shown in Figure 4b, the resonant peak of the optical transmission spectra for the illumination of RCP light keeps a high value and also displays a blueshift at the corresponding frequency range. Therefore, the optical CD responses calculated in Figure 4c remain over 0.9 at the resonant frequency when the rotation angle θ increases from 15° to 75°. This can be attributed to that the chirality of the structural changes when the rotation angle θ is altered.

When VO₂ acts as a metal, the polarization conversions are calculated in Figure 5 for the designed metamaterial device with different rotation angles θ. Figure 5a,b depict the reflection amplitude components R_xx and R_yx of the x-polarized light propagating along the forward direction, respectively. One can find that R_xx remains at low values whereas R_yx remains at high values when the rotation angle θ increases from 30° to 60° at the operating frequency range from 2.3 to 6.5 THz, indicating that the significant polarization conversion occurs for the incident x-polarized light. The corresponding PCR spectra are illustrated in Figure 5c, in which the maximum PCR reaches over 99.9% at the frequency range from 2.3 to 6.5 THz. Figure 5d shows the calculated ellipticity with various rotation angles θ. It can be found that the calculated ellipticity maintains the maximum and minimum values at the corresponding frequency peak when the rotation angle θ increases from 30° to 60°.

Next, we will discuss the influences of the dielectric layer thickness h on the optical CD response and polarization conversion ratio for the designed metamaterial device when VO₂ is in the isolating state. Figure 6a,b show the optical transmission spectra versus different h under the illumination of LCP and RCP lights, respectively. Comparing Figure 6a,b, the optical spectra exhibit huge difference near the resonant frequency of 3 THz due to the different transmission efficiencies for both polarizations. One can clearly find that with the increase of h, the resonant dip of optical transmission for the illumination of LCP light always maintains a low value. Meanwhile, the resonant peak of optical transmission for the illumination of RCP light shows a high transmission efficiency and has a slight redshift. Therefore, the calculated CD responses reach over 0.9 when the height h increases from 4 to 10 μm, as depicted in Figure 6c.

When VO₂ is in the metallic state, the polarization conversions are studied for the designed metamaterial device with different h. Figure 7a,b depict the reflection amplitude components R_xx and R_yx of the forward propagation for x-polarized lights, respectively. One can find from Figure 7a,b that the dielectric layer thickness h has an obvious effect on the reflection amplitude components R_xx and R_yx. When the dielectric layer thickness h takes a small value, i.e., h = 4 μm, the incident x-polarized light is partially converted into y-polarized light. With the further increasing of h, the polarization conversion efficiency is improved gradually. Correspondingly, the PCR spectra undergo a change from dual-band to broadband, as indicated in Figure 7c, in which the maximum PCR value reaches over 99.9% at the frequency range from 2.3 THz to 6.2 THz, indicating that the significant polarization conversion occurs for the incident x-polarized light. Meanwhile, the calculated ellipticity for forward propagated x-polarization light is depicted in Figure 7d. It can be found that the calculated ellipticity maintains the maximum and minimum values at the corresponding frequency peak except for a redshift. Moreover, the frequency regions of the converted LCP gradually become narrow while the frequency regions of the converted RCP gradually become broad.

Finally, the changes of gap distance g of the Au split ring are investigated since it is a vital factor which can highly affect the CD response and polarization conversion ratio. When VO₂ is in the isolating state, the transmission efficiency is calculated for the designed metamaterial device with different gap distances g. Figure 8a,b show the optical transmission spectra versus different gap distances g under the illumination of LCP and RCP lights, respectively. From Figure 8a,b, one can find that the transmission efficiency exhibits huge difference with the increase of g. The resonant dip of optical transmission for the illumination of LCP light always maintains a low value and shows a blueshift as the gap distance g increases gradually from 4 μm to 12 μm. By contrast, the resonant peak of optical transmission for the illumination of RCP light maintains a high value, especially when g > 5 μm, thus resulting in the optical CD responses depicted in Figure 8c.

When VO₂ is in the metallic state, the polarization conversion for the designed metamaterial device with different gap distances are graphically illuminated in Figure 9. Figure 9a,b depict the reflection amplitude components R_xx and R_yx of the forward propagated x-polarization lights, respectively, when the gap distance g increases from 4 to 12 μm. One can find that R_xx remains at nearly zero, whereas R_yx reaches up to 1 at the frequency range from 2.3 to 6.2 THz, indicating that the significant polarization conversion occurs for the incident x-polarized lights. The corresponding PCR spectra are illustrated in Figure 9c, in which the PCR values remain over 99% in the above frequency range. In addition, it can be seen in Figure 9d that the calculated ellipticity reaches the maximum value (+1) and minimum value (−1) at the corresponding frequency peak apart from a redshift. Moreover, the frequency regions of the converted LCP lights gradually become narrow, while the frequency regions of the converted RCP lights gradually become broad with the increase in g.

4. Conclusions

In this paper, we theoretically propose a metamaterial device with diversified functionalities by availing of the insulator-to-metal transition in VO₂ at THz frequencies. The simulated results indicate that the designed metamaterial can transition from having a giant circular dichroism function to exhibiting reflective broadband behavior as a half-wave plate (HWP) and quarter-wave plate (QWP). When VO₂ is in the isolating state, the metamaterial exhibits distinct transmission efficiency for circularly polarized lights, and the maximum value of CD exceeds 0.97 at the resonant frequency of 2.95 THz. Once VO₂ is operating in the metallic state, the metamaterial acts as a broadband HWP which has a nearly perfect linear polarization conversion at the frequency range from 3 to 7 THz. Moreover, the metamaterial can play a role of a high-efficiency QWP that can simultaneously convert the incident linear polarized light to left-handed and right-handed circularly polarized light. The calculated ellipticity indicates a good polarization conversion at the frequency of 2.4 THz and 7.4 THz, respectively. The physical mechanism of the above phenomena can be explained by exploring the electric field distributions. Furthermore, the structural parameters also exert great influences for achieving giant CD and HWP as well as QWP. Finally, it should be mentioned that the proposed design is feasible at the current level of fabrication technology. For our presented metamaterials, a sacrificial layer (e.g., Cr layer) can be utilized to obtain a self-contained VO₂–gold-based nanostructure. Firstly, the Cr layer with a thickness of 0.6 µm is deposited on the silicon substrate by using electron beam evaporation (EBA), and then a 0.7 µm VO₂ film is deposited using the magnetron sputtered technique, followed with the deposition of a 0.6 µm Au layer and the spin-coating resist layer (i.e., poly methyl methacrylate (PMMA)). The nanostructure is patterned by using electron beam lithography (EBL) to form the Au split-ring pattern, and then the pattern is transferred into the Au layer through ion beam milling (IBM). Secondly, a SiO₂ layer with the thickness of 9.65 µm is coated on the sample by using EBA to make sure the Au split-ring is well embedded in SiO₂ layer. Next, after stripping the PMMA, the SiO₂ layer is coated on the structure through EBA, followed with the deposition of a 0.7 µm Au layer and a PMMA layer. Thirdly, the nanostructure is patterned by utilizing EBL again to form the upper Au-rod pattern, and then the pattern is transferred into the Au layer with EBL. At last, after stripping the PMMA, the Cr sacrificial layer is removed by Cr etchant, and the final self-contained VO2–gold-based structure is realized. The proposed structure may provide a new approach for developing diversified functional metamaterial devices in THz regions.