Introduction

Polarization has become such an enormous important property of the electric–magnetic wave that it can provide real application in information processing, imaging, and sensing [1,2,3,4]. As a fundamental device, polarization converter, that is traditionally accomplished by natural birefringent material or dichroic crystals, has become acquiring more and more attentions from researchers in different areas. The results could be attributed to the advent of metamaterials (MMs), of which the ability is not only overcome shortcomings of the effect weakly and the volume bulky incurred by traditional materials but also open a promising platform to control the polarization states of light [5, 6]. With regard to MM converter, many interesting phenomena have been reported in THz spectrum, such as dual-band [7], tri-band [8], multi-band [9], and broadband [10, 11] polarization converter. However, only a few attempts have been implemented to realize dynamic modulation.

Actually, to our knowledge, phase change materials (PCMs) including GeSbTe (GST) [12], graphene [13], semiconductors [14], and vanadium dioxide (VO2) [15,16,17,18] are capable of accomplishing the phase modulation excited by external factors, for instance electric bias, temperature, and photo excitation. Thus, the MMs integrated with dynamic such inclusions above mentioned can accomplish tunable polarization conversion modulation. Currently, among PCMs, since the studied structure was developed and improved using VO2 [19, 20], there must be more stress on the properties, critical temperature, and other important factors of that. It is well-known that VO2 exhibits an insulator-to-metal phase transition [21, 22] due to changeable conductivity depending on the various temperatures. Based on this point, a tunable polarization converter with superior performance becomes more and more anticipated. In [15, 18, 19], authors provide analogical multi-layer metamaterial device, among which the middle VO2 layer behaves as absorptance or reflectance at the metal phase. In [16], the polarization converter works merely at the specific frequency of 0.468 and 0.502 THz with the phase transition of VO2, respectively. However, previous works rarely focus on simple and single-layer polarization converter device characterized with high polarization conversion efficiency within relatively broad absolute bandwidth in THz regime to our knowledge. In contrast, our manuscript has proposed and demonstrated this point.

Stimulated by essential need above, a simply single-layer and tunable reflective polarization converter based on metamaterial is proposed in THz spectrum, which consists of vanadium dioxide film (VO2) inserted by a two-corner-cut square patch resonator with a slit and reflective ground layer. Numerical calculation shows that high polarization conversion properties can be quantitatively described by polarization conversion ratio (PCR) and qualitatively confirmed by polarization azimuth angle (θ) and ellipticity (η). According to analyzed results, cross-polarized conversion occurs at three resonant peaks (2.39, 3.78, and 5.27 THz) along with high PCR (above 90%) in the frequency of 2.22 to 5.42 THz. Thereafter, to obtain tunable polarization conversion performance, the frequency spectrum characteristics of PCR can be gradually varied from high tri-band to eventually unity close to nearly zero with increases of conductivities of VO2 and verified by distributions of current densities. Last but not least, the reason for specific superior performance due to a slit has been illustrated in comprehensively. Therefore, such dynamic changes of phase transition metamaterial offer a new route for acquiring multifunctional devices, such as switches and polarization modulators.

Descriptions of the Designed MMs and Simulation Model

The proposed MMs (Fig. 1(a)) consist of periodical identical unit cells (Fig. 1(b)) which composed of hybrid layer and metallic ground layer separated by polyimide dielectric layer with a relative dielectric constant of 3.5 [23] and a thickness (t1) of 10 µm (Fig. 1(d)), as schematically shown in Fig. 1(c). Obviously, the hybrid layer (first layer) comprises a metallic two-corner-cut square patch resonator with a slit and VO2 film. The top and bottom metallic layers are made by the same gold dealt with the Drude model (\(\omega_{p} = 2\pi \times 2175\,{\text{THz}},\,\omega_{c} = 2\pi \times 4.35\,{\text{THz}}\)) [24] and the thickness (t2) of 0.2 µm. Among the hybrid layer, the properties of VO2 film can be expressed by the Bruggeman effective model [25, 26]:

$$\begin{aligned}\varepsilon\left(VO2\right)= & \frac14\left\{\varepsilon_d(2-3V)+\varepsilon_m(3V-1) \right. \\ & \left. +\sqrt{\left[\varepsilon_d(2-3V)+\varepsilon_m(3V-1)^2+8\varepsilon_d\varepsilon_m\right]}\right\},\end{aligned}$$
(1)
Fig. 1
figure 1

Schematic diagram of the designed polarization converter. (a) Titled extended periodic array view, (b) magnified front view of a unit cell, (c) perspective view of a unit cell, (d) right view of a unit cell

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where \(\varepsilon_{d}\) and \(\varepsilon_{m}\) denote dielectric constants of the insulating and metallic phase, respectively. Moreover, V indicates the volume fraction of the metallic regions. According to the above parameters, generally, the complex dielectric constant of VO2 in THz frequency domain can be described by the Bruggeman effective-medium theory (EMT). Also, for simplicity, the conductivity of VO2 can alternatively characterize dynamic insulator-to-metal phase change of VO2 films [17, 27, 28]. Thus, in our simulation, the relative permittivity and conductivity of VO2 can be set as 9 [25] and 200 S/m [25] at the temperature about 25 °C, respectively. All the designs, of which the relevant other parameter given below (Table 1), can be carried out by CST Microwave Studio based on frequency domain solver. Periodic boundary condition and port boundary condition are applied to X/Y direction and Z direction, respectively.

Table 1 All dimension parameters of the designed polarization converter
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To better understand the performance of the designed polarization converter, the polarization conversion ratio (PCR) can be adopted. Concerning the polarization of incident wave that exists along the y-direction, the PCR can be calculated by Eq. (2) as follows. Moreover, for the x-polarized wave incidence, the subscripts about x and y in Eq. (2) can be merely interchanged:

$$PCR = \frac{{\left| {r_{xy} } \right|^{2} }}{{\left| {r_{xy} } \right|^{2} + \left| {r_{yy} } \right|^{2} }},$$
(2)

where rxy = Erx/Eiy and ryy = Ery/Eiy are reflective coefficients for cross-polarized and co-polarized wave. The alphabet i and r denote incidence and reflection, respectively. For the incident circular polarization, the subscripts about y and x can be replaced L and R, respectively.

Results and Discussions

Discussion of Fixed Metasurface Device

To characterize polarization conversion performance of the designed MMs, the reflective amplitude (|rij|) and PCRi for linear and circular polarization incident wave have been investigated, respectively. The subscript i and j represent either x, y or R, L. As exhibited in Fig. 2(a), cross-reflective coefficients |rxy| and |ryx| indicate the same characteristics which hold above 0.85 from around 2.22 and 5.42 THz. At the same time, it is worth noticing that the curves of cross-reflection coefficients exist three resonant peaks at 2.39, 3.78, and 5.27 THz, while both the co-polarized reflective coefficients |rxx| and |ryy | are much lower than cross-polarized |ryx| and |rxy|, where especially beneath 0.07 at frequency of 2.39, 3.78, and 5.27 THz. In other words, nearly total the y- (x-) polarized wave could be converted the cross polarized, i.e., x- (y-) polarized wave at the three resonant peaks. The conclusion can also be furtherly inferred from Fig. 2(b) that the PCR more than 0.99 stands at the nearby frequency points of 2.39, 3.78, and 5.27 THz due to the resonant effects, while high polarization conversion efficiency (PCR above 0.9) can be quantitatively achieved with broad frequency domain from 2.22 to 5.42 THz. In addition, more interesting phenomenon can be witnessed from Fig. 2(c) and (d) that the reflective parameters under circular polarized wave keep same trends with the reflective parameters under linear polarized wave, namely, |rxy| =|ryx| =|rRL| =|rLR|, |rxx| =|ryy| =|rRR| =|rLL|, and PCR(y) = PCR(x) = PCR(R) = PCR(L). Based on analysis above, the designed MMs can be acted as linear polarization as well as circular polarization converter.

Fig. 2
figure 2

(a) Simulated reflective coefficient and (b) PCR for incident linear polarization. (c) Simulated reflective coefficient and (d) PCR for incident circular polarization

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To better qualitatively verdict the polarization state of electromagnetic wave under normal illumination, the formula can be expressed as follows [24]:

$$\theta = \frac{{1}}{{2}}{\text{arctan}}\left( {\frac{{{2}p_{r} {\text{cos}}\left( {\varphi_{r} } \right)}}{{{1} - \left| {p_{r} } \right|^{{2}} }}} \right){,}$$
(3)
$$\eta = \frac{{1}}{{2}}{\text{arcsin}}\left( {\frac{{{2}p_{r} {\text{sin}}\left( {\varphi_{r} } \right)}}{{{1} + \left| {p_{r} } \right|^{{2}} }}} \right){,}$$
(4)

where pr =|rxy|/|ryy| and φr = arg(rxy) − arg(ryy). The θ denotes the angle between reflective and incident polarization plane, while the η characterizes the polarization state of the reflective wave. When the η = 0° and θ ≠ 90°, the reflective wave keep linear polarization state with an angle of θ referred to the incident wave, but not cross-polarization state. What is more, the pure cross-polarization wave can be obtained when η = 0° and θ = 90°. As is shown in Fig. 3, the ellipticity η of the incident y-polarized wave stands less than 18° from 2.22 to 5.42 THz at whole frequency band and keeps nearly 0° at the around resonant frequency of 2.39, 3.78, and 5.27 THz. The deep meaning implies that a near linear polarization wave is obtained around the three resonant frequencies. Moreover, furtherly the cross-polarization conversion can be maintained when the polarization azimuth angle θ keeps ± 90° at the same three resonate frequency points in Fig. 3.

Fig. 3
figure 3

The polarization azimuth angle (θ) and ellipticity (η) under the normal incident y-polarized wave

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Discussion of Changeable Metasurface Device

To further obtain interesting dynamic tunable reflective polarization conversion for the enhanced hybrid metamaterial, more attentions have been paid on the specific kind thermal material, i.e., VO2. As we all know, the conductivities for VO2 film change with the changeable temperature, thus resulting into incident electromagnetic wave phase-transition when VO2 film acts as from insulator state to metallic state. To be concreted, the VO2 film exhibits an insulating state when the value for conductivity is lower than 200 S/m controlled by the temperature labeled with 25 °C, while shows an metallic state with the conductivity exceed higher than 105 S/m attained at the temperature of 85 °C [25]. To be convinced, as is demonstrated in Fig. 4, the PCR for incident y-polarized wave decreases obviously with the conductivity increasing from 200 to 105 S/m. Eventually, the PCR is almost 0 when the VO2 film is metal state with the conductivity set as 105 S/m. That means almost all of the incident y-polarized components penetrate through the top hybrid layer and could be transformed into x-polarized component when σVO2 = 200 S/m at the temperature of 25 °C. However, the incident y-polarized component reflects by the top hybrid layer when σVO2 = 105 S/m at the temperature of 85 °C. According to such analysis above, it can be concluded that actively dynamic changeable polarization conversion device can be designed based on MMs with VO2.

Fig. 4
figure 4

The PCR of incident y-polarized wave under the different VO2 film conductivities

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To understand the physic mechanism, the current densities of incident y-polarized wave are depicted as shown in Fig. 5. The conductivities of 200, 104, and 105 S/m at 5.27 THz are taken as example to describe thermal control effects. It is obviously that strong parallel currents called electric resonance [29,30,31,32,33] can be observed between the top and bottom layer in Fig. 5(a) and (b) at the conductivity of 200 S/m. The decomposed Ex component of induced E contributes to cross-polarization conversion. The Ey component of induced E has no impact on polarization for its same direction with incident Ei [34]. However, the current densities reflect gradually weakly between top and bottom layer when σVO2 increases from 104 to 105 S/m as shown in Fig. 5(c), (d) and (e), (f). Moreover, induced E rotates parallel to incident Ei gradually from Fig. 5(c), (d) to (e), (f). Thus, it can be inferred that the incident wave can change from penetrating state to not penetrating the top layer state with utilizing the thermal controllable VO2. In other words, as the temperature increases, the y to x cross-polarized component conversion decreases sharply.

Fig. 5
figure 5

Simulated current densities at 5.27 THz at the conductivities of 200, 104, and 105 S/m

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Last but not least, in connection to discussion above, to further reflect the cleverly design characterized with a slit, relevant theory analysis on polarization converter metadevice with and without gap has been investigated in Fig. 6. Obviously, we can see that enhanced polarization conversion effect based on single-layer metadevice with gap occurs, while it disappear when the metadevice without gap. Of course, also, the micro-mechanism about corresponding E-field map [35] with and without gap has been discussed. Obviously, for the gap contained shown in Fig. 6(b), the E-field concentrates at the gap position of the inclined resonator, while E-field concertation at connection section without gap is nearly zero in Fig. 6(c), transporting certain amount of charges to two corners of the inclined resonator. This result is consistent with charge transfer for nanoscale system [36], further reflecting low conversion efficiency. All in all, the specific designed metadevice just yet achieve high polarization conversion efficiency with tunable bandwidth.

Fig. 6
figure 6

(a) PCR with and without gap under incident y-polarized wave when σVO2 = 200 S/m. (b) and (c) Corresponding E-field map with and without gap σVO2 = 200 S/m at 5.27 THz

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Conclusions

Based on metamaterial, a simply single-layer and tunable reflective polarization converter is proposed in THz spectrum, which composed of vanadium dioxide film (VO2) inserted by a two-corner-cut square patch resonator with a slit and reflective ground layer. The calculated results show that high PCR (above 90%) can be obtained within the frequency range from 2.22 to 5.42 THz for the incident linear and circular polarization wave. In addition, the dynamic thermal changed polarization converter can also be accomplished by adjusting the conductivities of VO2. To be demonstrated, the mechanism of tunable polarization conversion is also analyzed by investigating the current densities at the top and bottom layer under the condition of changeable conductivities. Last but not least, the reason for adding a slit on middle resonator has been illustrated in comprehensively. According to analysis above, the designed metamaterial with cleverly specific assemble could be applied in the area of temperature-controlled sensing, THz wireless communication, tunable polarized devices.