Switchable Multifunctional Terahertz Metamaterials Based on the Phase-Transition Properties of Vanadium Dioxide

Currently, terahertz metamaterials are studied in many fields, but it is a major challenge for a metamaterial structure to perform multiple functions. This paper proposes and studies a switchable multifunctional multilayer terahertz metamaterial. Using the phase-transition properties of vanadium dioxide (VO2), metamaterials can be controlled to switch transmission and reflection. Transmissive metamaterials can produce an electromagnetically induced transparency-like (EIT-like) effect that can be turned on or off according to different polarization angles. The reflective metamaterial is divided into I-side and II-side by the middle continuous VO2 layer. The I-side metamaterials can realize linear-to-circular polarization conversion from 0.444 to 0.751 THz when the incident angle of the y-polarized wave is less than 30°. The II-side metamaterials can realize linear-to-linear polarization conversion from 0.668 to 0.942 THz when the incident angle of the y-polarized wave is less than 25°. Various functions can be switched freely by changing the conductivity of VO2 and the incident surface. This enables metamaterials to be used as highly sensitive sensors, optical switches, and polarization converters, which provides a new strategy for the design of composite functional metamaterials.


Introduction
The electromagnetically induced transparency (EIT) effect has attracted extensive attention since it was proposed and discovered by Harris et al. [1,2]. It is a destructive quantum interference between two different excitation transition pathways in atomic systems. Due to the suppression of the electronic transition, an obvious transmission window is generated at the frequency of the original absorption resonance [3]. The EIT window has a large group refractive index, so it is suitable for optical switches and slowlight devices [4,5]. The realization of EIT in atomic systems requires a high-intensity pulsed laser and extremely low experimental temperature, which affect the application and development of EIT technology. In 2008, Zhang et al. [6] used metamaterials to achieve electromagnetically induced transparency-like (EIT-like) effects at room temperature, which not only avoided the various constraints of EIT in atomic systems but also increased the controllability of the EIT. EIT-like effects can be achieved by introducing bright mode and dark mode with different resonance frequencies and intensities into the metamaterials and controlling the near-field coupling between them. Currently, EIT-like metamaterials (EIT-like MM) are widely used in many fields, such as high-sensitivity sensors [7][8][9], optical switches [10][11][12], slow-light devices [13,14], and modulators [15,16].
The effective regulation of electromagnetic wave polarization is of great significance in the fields of electromagnetic wave communication, terahertz (THz) imaging, and fundamental physics [17][18][19]. As polarization-control elements of electromagnetic waves, traditional polarization converters mainly rely on the phase accumulation on the propagation path Figure 1 shows the structure of the multifunctional THz metamaterials, which is divided into two parts, the I-side and the II-side, by a VO 2 layer with a thickness of 0.5 µm. For the I-side part, the 3 micrometer-thick surface resonator layer contains three differently shaped structures: X-shape (XS), small double-L-shape (SDLS), and large double-L-shape (LDLS). XS and SDLS are made of copper with electric conductivity of σ = 5.8 × 10 7 S/m, and the material of LDLS is VO 2 . For the II-side part, surface resonator layer is composed of the VO 2 resonant structure with a thickness of 4 µm. The intermediate insulating layer is composed of the cyclic olefin copolymer (COC) with a relative permittivity of 2.1 + 0.006i and a thickness of 30 µm. The structural parameters of metamaterial are as follows: l 1 = 100 µm, l 2 = 71.5 µm, l 3 = 65.5 µm, l 4 = 80 µm, l 5 = 30 µm, g 1 = 4.5 µm, g 2 = 4 µm, g 3 = 30 µm, w 1 = 20 µm, w 2 = 2 µm, w 3 = 7 µm, w 4 = 20 µm, w 5 = 10 µm. The metamaterial's structure was simulated using the 3D full-wave electromagnetic field simulation software CST Studio Suite 2020. To simulate infinite periodic arrays, the periodic boundary conditions were set in the X and Y directions and the open boundary conditions were set in the Z direction. Figure 1 shows the structure of the multifunctional THz metamaterials, which is divided into two parts, the I-side and the II-side, by a VO2 layer with a thickness of 0.5 μm. For the I-side part, the 3 micrometer-thick surface resonator layer contains three differently shaped structures: X-shape (XS), small double-L-shape (SDLS), and large double-Lshape (LDLS). XS and SDLS are made of copper with electric conductivity of σ = 5.8 × 10 7 S/m, and the material of LDLS is VO2. For the II-side part, surface resonator layer is composed of the VO2 resonant structure with a thickness of 4 μm. The intermediate insulating layer is composed of the cyclic olefin copolymer (COC) with a relative permittivity of 2.1 + 0.006i and a thickness of 30 μm. The structural parameters of metamaterial are as follows: l 1 = 100 µ m, l 2 = 71.5 µ m, l 3 = 65.5 µ m, l 4 = 80 µ m, l 5 = 30 µ m, g 1 = 4.5 µ m, g 2 = 4 µ m, g 3 = 30 µ m, w 1 = 20 µ m, w 2 = 2 µ m, w 3 = 7 µ m, w 4 = 20 µ m, w 5 = 10 µ m. The metamaterial's structure was simulated using the 3D full-wave electromagnetic field simulation software CST Studio Suite 2020. To simulate infinite periodic arrays, the periodic boundary conditions were set in the X and Y directions and the open boundary conditions were set in the Z direction. VO2 is a temperature-dependent phase-change material whose electrical conductivity and relative permittivity change during the phase-transition process. In the THz frequency band, the relative permittivity of VO2 is described by the Drude model [32,33]:

Structure Model
where ∞ is the permittivity at infinite frequency, with a value of 12, and is the collision frequency, with a value of 5.75 × 10 13 rad/s. The relationship between the plasma frequency ( ) and the conductivity is as follows: where 0 = 3 × 10 5 S/m, 2 ( 0 ) = 1.4 × 10 15 rad/s. In the simulation, = 30 S/m represents the insulating state of VO2 at room temperature and = 90,000 S/m represents the conducting state of VO2 at 89 °C [34]. The transition between VO2 insulating state and conducting state can produce the transmission and reflection conversion of metamaterials.

Electromagnetically Induced Transparency-like Effect of Metamaterials
The metamaterial is excited by the incident THz wave to produce an EIT-like effect when the VO2 is in the insulating state. The metal resonant unit of the EIT-like MM is composed of XS and SDLS. The THz wave with the electric field along the y-axis and the VO 2 is a temperature-dependent phase-change material whose electrical conductivity and relative permittivity change during the phase-transition process. In the THz frequency band, the relative permittivity of VO 2 is described by the Drude model [32,33]: where ε ∞ is the permittivity at infinite frequency, with a value of 12, and γ is the collision frequency, with a value of 5.75 × 10 13 rad/s. The relationship between the plasma frequency ω p (σ) and the conductivity σ is as follows: where σ 0 = 3 × 10 5 S/m, ω 2 p (σ 0 ) = 1.4 × 10 15 rad/s. In the simulation, σ = 30 S/m represents the insulating state of VO 2 at room temperature and σ = 90,000 S/m represents the conducting state of VO 2 at 89 • C [34]. The transition between VO 2 insulating state and conducting state can produce the transmission and reflection conversion of metamaterials.

Electromagnetically Induced Transparency-like Effect of Metamaterials
The metamaterial is excited by the incident THz wave to produce an EIT-like effect when the VO 2 is in the insulating state. The metal resonant unit of the EIT-like MM is composed of XS and SDLS. The THz wave with the electric field along the y-axis and the wave vector along the z-axis is vertically incident on the surface of the metamaterial. Figure 2 shows the transmission curves of each individual XS, SDLS, and EIT-like MM resonator under the same polarization conditions. The XS and SDLS are excited by incident radiation and resonate at 0.805 THz and 0.935 THz, respectively. The resonant frequencies of the two bright modes are similar and the quality factors of the resonant windows are obviously different, which meets the necessary conditions for an EIT-like effect. The transmission curve of the EIT-like MM is coherently superimposed by the transmission curves of the bright modes. The EIT-like transmission window is formed between 0.796 THz and 0.939 THz, with a peak frequency of 0.881 THz and a transmission peak amplitude of 0.692.
wave vector along the z-axis is vertically incident on the surface of the metamate ure 2 shows the transmission curves of each individual XS, SDLS, and EIT-like M nator under the same polarization conditions. The XS and SDLS are excited by radiation and resonate at 0.805 THz and 0.935 THz, respectively. The resonant freq of the two bright modes are similar and the quality factors of the resonant wind obviously different, which meets the necessary conditions for an EIT-like effect. Th mission curve of the EIT-like MM is coherently superimposed by the transmissio of the bright modes. The EIT-like transmission window is formed between 0.796 T 0.939 THz, with a peak frequency of 0.881 THz and a transmission peak ampl 0.692. The generation mechanism of the EIT-like was further analyzed based on the field distribution of the metamaterial's resonant surface. The electric-field distr corresponding to the trough and peak frequencies are shown in Figure 3a,b. At th frequency of 0.796 THz, the bright modes are excited by the incident THz wave. T tric-field strengths of XS and SDLS are different. The electric field is mainly conc on the XS. The XS generates electric dipole resonance, and the weak coupling betw XS and the SDLS makes the electric dipole of the SDLS rotate under the action of inal electric field, so that its electric dipole moment turns to the direction of the electric field. Therefore, the electric field on the SDLS is not concentrated at the the L-shaped structure. At 0.939 THz, the SDLS produces electric dipole resona the electric field plays a leading role in the structure. The resonant intensities of th modes are different. Due to the weak hybridization between the bright modes, the field strength of the structure is significantly weakened, and an obvious transmiss dow is induced at 0.881 THz.  The generation mechanism of the EIT-like was further analyzed based on the electricfield distribution of the metamaterial's resonant surface. The electric-field distributions corresponding to the trough and peak frequencies are shown in Figure 3a,b. At the trough frequency of 0.796 THz, the bright modes are excited by the incident THz wave. The electricfield strengths of XS and SDLS are different. The electric field is mainly concentrated on the XS. The XS generates electric dipole resonance, and the weak coupling between the XS and the SDLS makes the electric dipole of the SDLS rotate under the action of the original electric field, so that its electric dipole moment turns to the direction of the external electric field. Therefore, the electric field on the SDLS is not concentrated at the ends of the L-shaped structure. At 0.939 THz, the SDLS produces electric dipole resonance and the electric field plays a leading role in the structure. The resonant intensities of the bright modes are different. Due to the weak hybridization between the bright modes, the electric-field strength of the structure is significantly weakened, and an obvious transmission window is induced at 0.881 THz.
wave vector along the z-axis is vertically incident on the surface of the metamaterial. Figure 2 shows the transmission curves of each individual XS, SDLS, and EIT-like MM resonator under the same polarization conditions. The XS and SDLS are excited by incident radiation and resonate at 0.805 THz and 0.935 THz, respectively. The resonant frequencies of the two bright modes are similar and the quality factors of the resonant windows are obviously different, which meets the necessary conditions for an EIT-like effect. The transmission curve of the EIT-like MM is coherently superimposed by the transmission curves of the bright modes. The EIT-like transmission window is formed between 0.796 THz and 0.939 THz, with a peak frequency of 0.881 THz and a transmission peak amplitude of 0.692. The generation mechanism of the EIT-like was further analyzed based on the electricfield distribution of the metamaterial's resonant surface. The electric-field distributions corresponding to the trough and peak frequencies are shown in Figure 3a,b. At the trough frequency of 0.796 THz, the bright modes are excited by the incident THz wave. The electric-field strengths of XS and SDLS are different. The electric field is mainly concentrated on the XS. The XS generates electric dipole resonance, and the weak coupling between the XS and the SDLS makes the electric dipole of the SDLS rotate under the action of the original electric field, so that its electric dipole moment turns to the direction of the externa electric field. Therefore, the electric field on the SDLS is not concentrated at the ends of the L-shaped structure. At 0.939 THz, the SDLS produces electric dipole resonance and the electric field plays a leading role in the structure. The resonant intensities of the bright modes are different. Due to the weak hybridization between the bright modes, the electricfield strength of the structure is significantly weakened, and an obvious transmission window is induced at 0.881 THz.  The EIT-like MM is a two-fold rotational symmetry structure, which is usually sensitive to changes in polarization angle [35]. To deeply study the effect of different polarization angles on the EIT-like characteristics, the transmission properties of the metamaterial under different polarization angles were simulated, and the results are shown in Figure 4a. The peak frequency and frequency range of the EIT-like window do not change significantly when the polarization angle is changed from 0 • to 30 • . As the polarization angle increases from 30 • to 60 • , the amplitude of the transmission peak and the frequency range of the transmission window decrease. When the polarization angle is greater than 60 • , the EITlike effect disappears and the metamaterial produces a single resonance. In summary, the appearance and disappearance of the EIT-like are related to the response of the bright modes to different polarization angles. The XS is a centrosymmetric structure and is insensitive to changes in polarization angle. Figure 4b shows the simulation results of the SDLS with different polarization angles. The degradation of the resonance corresponds to the degradation of the EIT-like, and the changes to the EIT-like are determined by the response of the SDLS to different polarization angles. The sensitivity of the metamaterial to the polarization angle can be applied in the field of optical switches.
The EIT-like MM is a two-fold rotational symmetry structure, which is usually sen sitive to changes in polarization angle [35]. To deeply study the effect of different polari zation angles on the EIT-like characteristics, the transmission properties of the metamate rial under different polarization angles were simulated, and the results are shown in Fig  ure 4a. The peak frequency and frequency range of the EIT-like window do not chang significantly when the polarization angle is changed from 0° to 30°. As the polarization angle increases from 30° to 60°, the amplitude of the transmission peak and the frequenc range of the transmission window decrease. When the polarization angle is greater than 60°, the EIT-like effect disappears and the metamaterial produces a single resonance. In summary, the appearance and disappearance of the EIT-like are related to the response o the bright modes to different polarization angles. The XS is a centrosymmetric structur and is insensitive to changes in polarization angle. Figure 4b shows the simulation result of the SDLS with different polarization angles. The degradation of the resonance corre sponds to the degradation of the EIT-like, and the changes to the EIT-like are determined by the response of the SDLS to different polarization angles. The sensitivity of the met amaterial to the polarization angle can be applied in the field of optical switches. In order to obtain further insights into the EIT-like characteristics, the effects of th structural parameters were simulated. Only one parameter was changed at a time, and the other parameters remained unchanged. Figure 5a shows that when the l 2 length in creases, the transmission window is red-shifted, and the amplitude of the transmission peak becomes larger. The transmission peak of the EIT-like can be regulated by changin the length of l 2 . Figure 5b shows the simulation results of changing g 1 . When g 1 in creases from 0.5 µ m to 4.5 µ m, the amplitude of the transmission peak remains un changed, and the peak frequency is slightly red-shifted. It is worth noting that the ful width at half maximum of the transmission window decreases significantly. The qualit factor of the metamaterial sensor is defined as = − / .The − is th peak frequency of the EIT-like window and FWHM is the full width at half maximum When the metamaterial is used as the sensor, the increase in g 1 corresponds to a highe quality factor. In order to obtain further insights into the EIT-like characteristics, the effects of the structural parameters were simulated. Only one parameter was changed at a time, and the other parameters remained unchanged. Figure 5a shows that when the l 2 length increases, the transmission window is red-shifted, and the amplitude of the transmission peak becomes larger. The transmission peak of the EIT-like can be regulated by changing the length of l 2 . Figure 5b shows the simulation results of changing g 1 . When g 1 increases from 0.5 µm to 4.5 µm, the amplitude of the transmission peak remains unchanged, and the peak frequency is slightly red-shifted. It is worth noting that the full width at half maximum of the transmission window decreases significantly. The quality factor of the metamaterial sensor is defined as Q = f EIT−like /FW HM. The f EIT−like is the peak frequency of the EIT-like window and FWHM is the full width at half maximum. When the metamaterial is used as the sensor, the increase in g 1 corresponds to a higher quality factor. Micromachines 2022, 13, x 6 of 13

Simulation Results
At 89 °C , the continuous VO2 layer in the conducting state divides the metamaterials into I-side and II-side parts, which can be used as reflective polarization converters. To analyze the degree of the polarization conversion of the metamaterial when the y-polarized THz wave is incident, the Stokes parameters [36,37] are introduced as follows: where | | is the reflection coefficient of the y-to-y polarization conversion, | | is the reflection coefficient of the y-to-x polarization conversion, and Φ and Φ are the phases corresponding to the reflected waves, ΔΦ = Φ − Φ . When | | ≈ | | and ∆Φ ≈ 2nπ ± π/2 (n is an integer), the metamaterials can achieve linear-to-circular polarization conversion. The calculated ellipticity can be used to describe the performance of the polarization converter. The ellipticity, defined as = 3 / 0 . χ = −1, indicates that the reflected THz wave is a typical right-hand circular polarization (RHCP) wave. By contrast, χ = 1 means that the reflected THz wave is a typical left-hand circular polarization (LHCP) wave. When | | ≈ | | and ∆Φ ≈ 2nπ ± π (n is an integer), the metamaterial can realize linear-to-linear polarization conversion, and its polarization conversion characteristics can be described by the polarization conversion rate and the degree of linear polarization [38]. The polarization conversion rate is defined as = | | 2 / 0 , and the degree of linear polarization is defined as = √ 1 2 + 2 2 / 0 . PCR = 1 indicates that the incident ypolarized wave is completely transformed into the reflected x-polarized wave. DoLP = 1 means that the degree of linear polarization is the highest, and the reflected THz waves are stable linear polarization waves.
The u-v coordinate system is obtained by rotating the x-y coordinate system by 45° around the z-axis, where the incident and reflected waves are decomposed into mutually orthogonal u and v components [39,40]. The electric field of the incident wave is expressed as = + = | | ( ) + | | ( ) . The electric field of the reflected wave is expressed as = + . The symbols and are the unit direction vectors in the u-axis direction and v-axis direction, respectively. Jones calculus is used to explain the relationship between the incident and reflected waves [41]. The component of the reflected wave in the u-direction is expressed as = | | ( ) +

Simulation Results
At 89 • C, the continuous VO 2 layer in the conducting state divides the metamaterials into I-side and II-side parts, which can be used as reflective polarization converters. To analyze the degree of the polarization conversion of the metamaterial when the y-polarized THz wave is incident, the Stokes parameters [36,37] are introduced as follows: S 2 = 2 r yy r xy cos ∆Φ S 3 = 2 r yy r xy sin ∆Φ where r yy is the reflection coefficient of the y-to-y polarization conversion, r xy is the reflection coefficient of the y-to-x polarization conversion, and Φ yy and Φ xy are the phases corresponding to the reflected waves, ∆Φ = Φ yy − Φ xy . When r yy | ≈ |r xy and ∆Φ ≈ 2nπ ± π/2 (n is an integer), the metamaterials can achieve linear-to-circular polarization conversion. The calculated ellipticity can be used to describe the performance of the polarization converter. The ellipticity, defined as χ = S 3 /S 0 . χ = −1, indicates that the reflected THz wave is a typical right-hand circular polarization (RHCP) wave. By contrast, χ = 1 means that the reflected THz wave is a typical left-hand circular polarization (LHCP) wave. When r yy | ≈ |r xy and ∆Φ ≈ 2nπ ± π (n is an integer), the metamaterial can realize linear-to-linear polarization conversion, and its polarization conversion characteristics can be described by the polarization conversion rate and the degree of linear polarization [38]. The polarization conversion rate is defined as PCR = r xy 2 /S 0 , and the degree of linear polarization is defined as DoLP = S 2 1 + S 2 2 /S 0 . PCR = 1 indicates that the incident ypolarized wave is completely transformed into the reflected x-polarized wave. DoLP = 1 means that the degree of linear polarization is the highest, and the reflected THz waves are stable linear polarization waves.
The u-v coordinate system is obtained by rotating the x-y coordinate system by 45 • around the z-axis, where the incident and reflected waves are decomposed into mutually orthogonal u and v components [39,40]. The electric field of the incident wave is expressed as E i = E ui u + E vi v = |E ui |exp(jϕ)u + |E vi |exp(jϕ)v. The electric field of the reflected wave is expressed as E r = E ur u + E vr v. The symbols u and v are the unit direction vectors in the u-axis direction and v-axis direction, respectively. Jones calculus is used to explain the relationship between the incident and reflected waves [41]. The component of the reflected wave in the u-direction is expressed as E ur = |r uu |exp (jϕ uu )E ui + |r uv |exp (jϕ uv )E vi . The component of the reflected wave in the V direction is expressed as E vr = |r vu |exp (jϕ vu )E ui + |r vv |exp (jϕ vv )E vi . The symbols r uu , r vv , r vu , and r uv represent the polarization of u to u, v to v, u to v, and v to u, respectively. In order to illustrate the polarization conversion properties of the metamaterial, the v-and u-polarized waves are incident from the I-side of the metamaterial, and the simulation results are shown in Figure 6a,b. In the frequency range of 0.444 to 0.751 THz, the cross-polarized reflection amplitudes are approximately equal to 0, the co-polarized reflection amplitudes are nearly equal, and the phase difference is close to 90 • and −270 • . The amplitude curves of r yy and r xy are shown in Figure 6c. The I-side metamaterial resonates at 0.419 THz and 0.778 THz, which causes r yy and r xy to intersect between the two frequencies.
The resonance at 0.659 THz brings the amplitudes of the reflected polarization waves close to each other. The calculated χ is shown in Figure 6d. In the frequency range of 0.444-0.751 THz, χ > 0.92 indicates that the I-side metamaterials can convert the y-polarized incident wave to the LHCP wave. , and represent the polarization of u to u, v to v, u to v, and v to u, respectively. In order to illustrate the polarization conversion properties of the metamaterial, the v-and u-polarized waves are incident from the I-side of the metamaterial, and the simulation results are shown in Figure 6a,b. In the frequency range of 0.444 to 0.751 THz, the cross-polarized reflection amplitudes are approximately equal to 0, the co-polarized reflection amplitudes are nearly equal, and the phase difference is close to 90° and −270°. The amplitude curves of r yy and r xy are shown in Figure 6c. The I-side metamaterial resonates at 0.419 THz and 0.778 THz, which causes r yy and r xy to intersect between the two frequencies. The resonance at 0.659 THz brings the amplitudes of the reflected polarization waves close to each other. The calculated χ is shown in Figure 6d. In the frequency range of 0.444-0.751 THz, χ > 0.92 indicates that the I-side metamaterials can convert the y-polarized incident wave to the LHCP wave.  THz, the amplitudes of r uu and r vv are gradually close to unity, and the phase difference is close to ± 180°. The simulation and calculation results of the II-side metamaterials in the x-y coordinate system are shown in Figure 7c,d. The amplitude of r xy is higher than 0.72 and the amplitude of r yy is lower than 0.2 in the frequency range. The incident y-polarized wave is largely converted into an x-polarized wave. The PCR is greater than 0.94 and the DOLP is close to 1 in the frequency range, which indicates that the II-side metamaterial has the ability to achieve linear-to-linear polarization conversion.  Figure 7a,b show the simulation results of the II-side metamaterials in the u-v coordinate system. The amplitudes of r vu and r uv are 0. In the frequency range of 0.668-0.942 THz, the amplitudes of r uu and r vv are gradually close to unity, and the phase difference is close to ± 180 • . The simulation and calculation results of the II-side metamaterials in the x-y coordinate system are shown in Figure 7c,d. The amplitude of r xy is higher than 0.72 and the amplitude of r yy is lower than 0.2 in the frequency range. The incident y-polarized wave is largely converted into an x-polarized wave. The PCR is greater than 0.94 and the DOLP is close to 1 in the frequency range, which indicates that the II-side metamaterial has the ability to achieve linear-to-linear polarization conversion.

Mechanism Analysis
The mechanism of the linear-to-circular polarization conversion can be further ana lyzed by analyzing the resonance of r yy at 0.419 THz, 0.659 THz, and 0.778 THz. Figure  8a,b show the current distribution of the I-side metamaterials for v-and u-polarized inci dent waves, respectively. When the v-polarized wave is incident, the resonant layer cur rents at 0.419 THz and 0.659 THz are opposite to those of the VO2 layer, forming a loop to excite the magnetic dipole resonance. The resonant layer and VO2 layer have neither in duced current nor resonance at 0.778 THz. Similarly, when the u-polarized wave is inci dent, the magnetic resonance is excited at 0.659 THz and 0.778 THz due to the opposite current directions of the metamaterial resonant layer and the VO2 layer. There is no reso nance at 0.419 THz. The I-side metamaterial exhibits plasmonic resonance eigenmodes a 0.419 THz and 0.778 THz [42], where the eigenmodes are not a vector synthesis of the u and v components, but are generated by only one component. In the frequency range o 0.419-0.778 THz, the u and v components appear with the degradation of the eigenmodes Magnetic resonance controls the magnitude and phase of the reflected electric field along the u-and v-axes to achieve the condition of circular polarization, and the superposition of the three resonances achieves broadband linear-to-circular polarization conversion.

Mechanism Analysis
The mechanism of the linear-to-circular polarization conversion can be further analyzed by analyzing the resonance of r yy at 0.419 THz, 0.659 THz, and 0.778 THz. Figure 8a,b show the current distribution of the I-side metamaterials for v-and u-polarized incident waves, respectively. When the v-polarized wave is incident, the resonant layer currents at 0.419 THz and 0.659 THz are opposite to those of the VO 2 layer, forming a loop to excite the magnetic dipole resonance. The resonant layer and VO 2 layer have neither induced current nor resonance at 0.778 THz. Similarly, when the u-polarized wave is incident, the magnetic resonance is excited at 0.659 THz and 0.778 THz due to the opposite current directions of the metamaterial resonant layer and the VO 2 layer. There is no resonance at 0.419 THz. The I-side metamaterial exhibits plasmonic resonance eigenmodes at 0.419 THz and 0.778 THz [42], where the eigenmodes are not a vector synthesis of the u and v components, but are generated by only one component. In the frequency range of 0.419-0.778 THz, the u and v components appear with the degradation of the eigenmodes. Magnetic resonance controls the magnitude and phase of the reflected electric field along the u-and v-axes to achieve the condition of circular polarization, and the superposition of the three resonances achieves broadband linear-to-circular polarization conversion. Similarly, the mechanism of linear-to-linear polarization conversion is explained by analyzing the resonance of r yy at 0.698 THz and 0.882 THz. Figure 9a,b show the current distribution of the II-side metamaterials for the v-and u-polarized incident waves, respectively. The II-side metamaterial induces opposite currents in the resonant layer and VO2 layer for the incident v-polarized waves and u-polarized waves. Therefore, the metamaterial produces magnetic resonances at 0.698 THz and 0.882 THz, which also show the degeneration and hybridization of plasmonic resonance eigenmodes [43]. Magnetic resonance controls the magnitude and phase of the reflected electric field along the u-and vaxes to achieve linearly polarized conditions, and, thus, linear-to-linear polarization conversion is achieved in the range of 0.668-0.942 THz.

Influence of Incidence Angle and Structural Parameters
It is of great significance to investigate how the incidence angle (θ) of THz waves affect the polarization conversion properties of metamaterials. In order to understand the stability of the polarization converter to the change in θ, the θ of the THz waves was changed for simulation. Figure 10a,b show the simulation spectrum of the I-side and IIside metamaterials when changing the θ, respectively. For the I-side metamaterial, when the θ changes from 0° to 30°, the bandwidth of the polarization conversion increases slightly, and the ellipticity remains around 1. When the θ continues to increase, a dual- Similarly, the mechanism of linear-to-linear polarization conversion is explained by analyzing the resonance of r yy at 0.698 THz and 0.882 THz. Figure 9a,b show the current distribution of the II-side metamaterials for the v-and u-polarized incident waves, respectively. The II-side metamaterial induces opposite currents in the resonant layer and VO 2 layer for the incident v-polarized waves and u-polarized waves. Therefore, the metamaterial produces magnetic resonances at 0.698 THz and 0.882 THz, which also show the degeneration and hybridization of plasmonic resonance eigenmodes [43]. Magnetic resonance controls the magnitude and phase of the reflected electric field along the u-and v-axes to achieve linearly polarized conditions, and, thus, linear-to-linear polarization conversion is achieved in the range of 0.668-0.942 THz. Similarly, the mechanism of linear-to-linear polarization conversion is explained by analyzing the resonance of r yy at 0.698 THz and 0.882 THz. Figure 9a,b show the current distribution of the II-side metamaterials for the v-and u-polarized incident waves, respectively. The II-side metamaterial induces opposite currents in the resonant layer and VO2 layer for the incident v-polarized waves and u-polarized waves. Therefore, the metamaterial produces magnetic resonances at 0.698 THz and 0.882 THz, which also show the degeneration and hybridization of plasmonic resonance eigenmodes [43]. Magnetic resonance controls the magnitude and phase of the reflected electric field along the u-and vaxes to achieve linearly polarized conditions, and, thus, linear-to-linear polarization conversion is achieved in the range of 0.668-0.942 THz.

Influence of Incidence Angle and Structural Parameters
It is of great significance to investigate how the incidence angle (θ) of THz waves affect the polarization conversion properties of metamaterials. In order to understand the stability of the polarization converter to the change in θ, the θ of the THz waves was changed for simulation. Figure 10a,b show the simulation spectrum of the I-side and IIside metamaterials when changing the θ, respectively. For the I-side metamaterial, when the θ changes from 0° to 30°, the bandwidth of the polarization conversion increases slightly, and the ellipticity remains around 1. When the θ continues to increase, a dual-

Influence of Incidence Angle and Structural Parameters
It is of great significance to investigate how the incidence angle (θ) of THz waves affect the polarization conversion properties of metamaterials. In order to understand the stability of the polarization converter to the change in θ, the θ of the THz waves was changed for simulation. Figure 10a,b show the simulation spectrum of the I-side and II-side metamaterials when changing the θ, respectively. For the I-side metamaterial, when the θ changes from 0 • to 30 • , the bandwidth of the polarization conversion increases slightly, and the ellipticity remains around 1. When the θ continues to increase, a dual-band polarization-converting metamaterial is achieved, but the ellipticity decreases significantly. For the II-side metamaterial, when the θ changes from 0 • to 25 • , the frequency range of the polarization conversion is stable, and the degree of polarization conversion remains high. However, when the θ continues to increase, the polarization conversion range gradually decreases. Based on the above research, when θ < 30 • , the I-side metamaterial can be used as a stable QWP in the frequency range of 0.444-0.751 THz. When the θ < 25 • , the II-side metamaterial can be used as a stable HWP in the frequency range of 0.668-0.942 THz.
Micromachines 2022, 13, x 10 of 13 band polarization-converting metamaterial is achieved, but the ellipticity decreases significantly. For the II-side metamaterial, when the θ changes from 0° to 25°, the frequency range of the polarization conversion is stable, and the degree of polarization conversion remains high. However, when the θ continues to increase, the polarization conversion range gradually decreases. Based on the above research, when θ < 30°, the I-side metamaterial can be used as a stable QWP in the frequency range of 0.444-0.751 THz. When the θ < 25°, the II-side metamaterial can be used as a stable HWP in the frequency range of 0.668-0.942 THz. Except for the θ of the THz waves, the internal conditions, such as structural parameters, can also affect the polarization conversion properties. The influence of the key structural parameters on the polarization conversion properties of the metamaterial was studied. When the other parameters of the I-side metamaterial remain unchanged, the length of l 1 changes uniformly from 90 μm to 110 μm in steps of 5 μm; the simulation results of the ellipticity are shown in Figure 11a. Two narrow polarization conversion ranges are gradually merged into a broadband when l 1 increases from 90 μm to 100 μm. As l 1 continues to increase, the ellipticity decreases significantly at high frequencies. Figure 11b shows the calculated χ after changing the length of w 1 . As w 1 increases from 5 µ m to 25 µ m, the bandwidth for χ > 0.9 first increases and then decreases. The l 4 and g 2 of the IIside metamaterial were changed separately for simulation, and the calculated PCR values are shown in Figure 11c,d. The increase in l 4 not only broadens the frequency range of the polarization conversion, but also maintains a high PCR in the range. As g 2 increases from 2 µ m to 10 µ m, the PCR grows closer to 1, although the corresponding bandwidth decreases. Except for the θ of the THz waves, the internal conditions, such as structural parameters, can also affect the polarization conversion properties. The influence of the key structural parameters on the polarization conversion properties of the metamaterial was studied. When the other parameters of the I-side metamaterial remain unchanged, the length of l 1 changes uniformly from 90 µm to 110 µm in steps of 5 µm; the simulation results of the ellipticity are shown in Figure 11a. Two narrow polarization conversion ranges are gradually merged into a broadband when l 1 increases from 90 µm to 100 µm. As l 1 continues to increase, the ellipticity decreases significantly at high frequencies. Figure 11b shows the calculated χ after changing the length of w 1 . As w 1 increases from 5 µm to 25 µm, the bandwidth for χ > 0.9 first increases and then decreases. The l 4 and g 2 of the II-side metamaterial were changed separately for simulation, and the calculated PCR values are shown in Figure 11c,d. The increase in l 4 not only broadens the frequency range of the polarization conversion, but also maintains a high PCR in the range. As g 2 increases from 2 µm to 10 µm, the PCR grows closer to 1, although the corresponding bandwidth decreases.

Conclusions
In summary, this paper closely studied a multilayer terahertz metamaterial. The metamaterial exhibited different functions when the VO2 was in the insulating and conducting states. The metamaterial can exert an EIT-like effect that can be turned on or off, according to different polarization angles, when the VO2 is in the insulating state. The metamaterial was divided into I-side and II-side by the middle continuous VO2 layer when the VO2 was in the conducting state. The I-side metamaterial can achieve linear-to-circular polarization conversion from 0.444 to 0.751 THz when the incident angle of the y-polarized wave is less than 30°. The II-side metamaterial can achieve linear-to-linear polarization conversion from 0.668 to 0.942 THz when the incident angle of the y-polarized waves is less than 25°. The two types of polarization converter were freely switched by changing the incident surface of the y-polarized wave. Because the EIT-like window of the metamaterial is very sensitive to the change in the dielectric constant of the surrounding environment, the metamaterial can be used as a highly sensitive metamaterial sensor. The metamaterial can also be used as an optical switch according to the polarization-sensitive characteristics of the EIT-like. In a specific frequency range, the I-side and II-side metamaterials can be used as QWP and HWP, respectively. The multilayer terahertz metamaterial has potential applications in substance detection, ultrafast switches, THz communication, and THz imaging.

Conclusions
In summary, this paper closely studied a multilayer terahertz metamaterial. The metamaterial exhibited different functions when the VO 2 was in the insulating and conducting states. The metamaterial can exert an EIT-like effect that can be turned on or off, according to different polarization angles, when the VO 2 is in the insulating state. The metamaterial was divided into I-side and II-side by the middle continuous VO 2 layer when the VO 2 was in the conducting state. The I-side metamaterial can achieve linear-to-circular polarization conversion from 0.444 to 0.751 THz when the incident angle of the y-polarized wave is less than 30 • . The II-side metamaterial can achieve linear-to-linear polarization conversion from 0.668 to 0.942 THz when the incident angle of the y-polarized waves is less than 25 • . The two types of polarization converter were freely switched by changing the incident surface of the y-polarized wave. Because the EIT-like window of the metamaterial is very sensitive to the change in the dielectric constant of the surrounding environment, the metamaterial can be used as a highly sensitive metamaterial sensor. The metamaterial can also be used as an optical switch according to the polarization-sensitive characteristics of the EIT-like. In a specific frequency range, the I-side and II-side metamaterials can be used as QWP and HWP, respectively. The multilayer terahertz metamaterial has potential applications in substance detection, ultrafast switches, THz communication, and THz imaging.

Conflicts of Interest:
The authors declare no conflict of interest.