1. Introduction

Terahertz waves have received significant attention from researchers due to their penetrating nature and excellent operability [1,2]. Terahertz technology is an important cross-cutting frontier field with promising applications in wireless communications [3], filtering [4] and imaging [5]. Metamaterial is a kind of artificial material. It uses a large number of subwavelength-sized components arranged in a certain pattern to achieve specific electromagnetic or acoustics or thermal properties, including the arrangement of these subwavelength elements in one, two or three dimensions. A metasurface can be seen as a special two-dimensional metamaterial. It is a two-dimensional planar structure composed of artificial atoms arranged in a certain way, which enables flexible modulation of the amplitude, phase and polarization of the incident waves and has powerful field manipulation capabilities. [6–8]. Due to their ultra-thin thickness and excellent performance, metamaterials and metasurface are conducive to the preparation of terahertz devices. Recent years, metamaterials/metasurface have been successfully introduced in a variety of terahertz functional devices such as polarization converters [9,10], absorbers [11–20]. With continuous research, it has been increasingly evident that conventional single terahertz devices are unable to meet the requirements of various applications. This limitation arises from their lack of adjustability once the design is finalized. To overcome that deficiency, several kinds of switchable multifunctional devices have been designed. Luo et al. designed a graphene-based metasurface, which can switch from a half-wave plate (HWP) to a quarter-wave plate (QWP) with an ellipticity of over 0.92 in the range of 0.78 THz-1.33 THz by changing the Fermi energy level of the graphene [21]. Liu et al. designed a dynamically tunable terahertz broadband absorber based on a hybrid metamaterial of VO₂ [20]. In that design, when VO₂ is in metallic state, the absorption ratio is greater than 90% and the absorption bandwidth reaches to 1 THz, with a relative bandwidth of about 83%. VO₂ is widely used to construct terahertz metasurface devices because its conductivity can be significantly changed under a wide range of excitations [22–25]. Jin et al. proposed an ultra-broadband absorber based on a four-ring structure of VO₂, which can achieve a broadband absorbance of 90% between 1.85 THz and 4.3 THz, and the absorbance can be dynamically adjusted from 4% to 100% by changing the conductivity of VO₂ [26]. Zhao et al. used the insulator-metal phase transition and current resonance principles of VO₂ to achieve dynamically tunable polarization transitions from double-broadband 0.45 THz-0.77 THz and 0.97 THz-1.2 THz to ultra-wideband 0.38 THz-1.20 THz at high polarization conversion ratios [27]. Dai et al. proposed a tunable broadband cross-polarization converter consisting of a single layer bulk Dirac semimetal metamaterials (BDSMM) on a Dirac semimetal-based silicon substrate for dynamic adjustment of linear and circularly polarized waves. The converter operates in transmission mode and can convert linear x-polarized incident waves to linear y-polarized waves in the frequency range 3.82 THz - 7.88 THz with relatively high polarization conversion efficiency [28]. Serebryannikov et al designed a VO₂-based transmissive terahertz metasurface that enables switching between different functions of polarization manipulation and asymmetric transmission in a terahertz system with good asymmetric transmission capability [29].

Although a lot of studies, as mentioned above, have been carried out in multifunctional device design, there are still two limitations. Firstly, many designs have realized dynamically switching between two functions. In some occasions, multifunction may be required. But a few devices can cover three or more functions. Secondly, most of the previous multifunctional devices broken the reciprocity because of the asymmetrical structure, which makes them unidirectional. In comparison to non-reciprocal structures, the response of a reciprocal device remains unaffected by the direction of the incident wave. Attention is solely focused on the physical structure and parameters of the metasurface, without the need to consider the incident wave's direction. This may simplify the design process, and reduce the manufacturing and assembling complexity. [30,31]. Based on these considerations, a new structure is proposed in this paper. In the surface 2 × 2 composite unit array is constructed as the basic cell instead of a single unit, while along the propagation direction symmetrical layers is used to maintain the reciprocity. VO₂ is inserted into the structure, so that multifunctionalities are achieved by changing the state of VO₂. It can switch among functions of linear polarization conversion, band-stop filtering, and perfect absorption. Due to the reciprocity, it is effective for the incident waves from either positive or negative direction in all functions, and insensitive to the polarization angle. These features make it adaptable and flexible in many potential applications, such as switches, sensors, and modulators.

2. Model design

The device model and a brief analysis of the transmission property are given in this section. To simplify the analysis without losing generality, the surface of the structure is centered in the x-y plane, and the wave propagates in + z/−z direction. The incident transverse electric (TE) mode electromagnetic wave is written as $\dot{{\boldsymbol E}}_{}^{in} = {\left[ {\begin{array}{cc} {\dot{E}_x^{in}}&{\dot{E}_y^{in}} \end{array}} \right]^\textrm{T}}$. If the incident wave E is treated as a wave vector, and the transmission matrix T is treated as an operator, then the outgoing wave can be expressed as

Polarization convertor is a special electromagnetic device that can change the polarization mode of the incident waves, and is of great value in many applications. In recent years, researchers have investigated many kinds of special materials and structures which can be used to construct high-performance polarization converters of transmission or reflection type. However, most of them are effective for a specific polarized wave, horizontal or vertical polarized wave for example, and invalid for the other polarized waves [27–29,31–33]. So that in the T matrix, t_xy or t_yx is dominant, and the other three elements are negligible.

In addition to the polarization conversion, some other functions such as filtering or absorption have been compatible in some designs [34,35]. These multifunctional devices are usually nonreciprocal. Reciprocity refers to the property where the same incident wave, regardless of its direction of arrival, generates an identical response. Conversely, nonreciprocity implies that the same incident wave generates different responses. Reciprocal and nonreciprocal systems possess distinct properties and find important applications. Nonreciprocity enables unidirectional transmission, which is crucial in micro-resonators, isolators, circulators, and other devices [36,37]. On the other hand, reciprocity is essential in bidirectional systems. For instance, certain electromagnetic/optical systems necessitate the transmission and reception of signals in the same mode, making reciprocal devices indispensable. However, the asymmetrical structure of many devices breaks reciprocity. Take the polarization converter as an example; most converters are unidirectional, transmitting x/y polarized waves but unable to receive waves of the same polarization, which is undesirable in certain applications. Consequently, the designed multifunctional reciprocal device may find utility in such systems.

In order to get a device that maintains the reciprocity and is effective to incident wave at any polarization angle, a composite and symmetrical structure is proposed. The full structure is shown in Fig. 1. It has five symmetric layers. The top and bottom layers are square split rings made of copper. The second and fourth layers are polyimide with permittivity ɛ_r= 3.5 and loss tangent tanδ=0.0027, which is commonly used in terahertz devices [22,25]. The middle layer is a VO₂ thin film. In the structure p is the period of the cell, a is the side length of the metal square ring, w is the line width of the metal square ring, k and l are the position and length of the VO₂ embedded in the metal square ring. And h and h_in represent the thickness of the polyimide substrate, t_in is the thickness of the VO₂ layer. After a series of parameter optimizations, the optimal values are p = 200, h = h_in= 12, a = 90, w = 17.2, t = t_in= 1, k = 23 and l = 20.45. (the unit is microns).

 

Fig. 1. Structure of the device. (a) Top layer, (b) Bottom layer, (c) Side view. The device consists of square split rings made of copper in the top and bottom layers, while the second and fourth layers are composed of polyimide with ɛ_r= 3.5 tanδ=0.0027. The middle layer comprises a thin film of VO₂. The optimal values for the structure parameters are as follows: p = 200, h = h_in= 12, a = 90, w = 17.2, t = t_in= 1, k = 23 and l = 20.45 (unit: µm).

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The fabrication process for the device can be carried out using the following steps. Firstly, photolithography, film sputtering, and inductively coupled plasma etching (ICPE) technology can be sequentially employed to pattern the split square copper rings and VO₂ strips on the polyimide substrate. Subsequently, the polyimide layer with patterned unit cells, the VO₂ film, and another polyimide layer with patterned unit cells are carefully bonded together.

The square ring is a widely used and effective structure in metasurfaces, as it can be directly applied in various applications such as frequency selective surfaces (FSS), wave absorbers, and polarization converters [9,22,25]. Multiple functions including polarization conversion, filtering, and perfect absorption can be achieved with this structure in this design. Coupled split ring resonators are used to realize the linear polarization conversion. Instead of typical single cell, a 2 × 2 array is used as the basic unit in the surface as shown in Fig. 1(a). Geometrically, the array is rotational symmetric. In the 2 × 2 composite unit array, the two elements in the main diagonal are utilized to achieve orthogonal deflection for y-polarized waves, while the two elements in the counter-diagonal are employed to achieve orthogonal deflection for x-polarized waves. It is important to note that any linearly polarized wave can be decomposed into x and y components. Hence, by employing this configuration, orthogonal deflection of the incident wave can theoretically be achieved at any polarization angle, which will be validated in the following simulations. Layers 1 and 5 are mirror-rotationally symmetrical. From the Fig. 1 can easily find that the whole structure remains the same whether viewed from the left or the right, which ensures the reciprocity of the system. The gaps in the rings are filled with VO₂. The phase transmission behavior of VO₂ provides the device with switchable multi-functions.

Specifically, from the symmetrical characteristics of the 2 × 2 array and layers, it can be deduced that

So, the transmission matrices can be simplified as:

It indicates that the matrices T⁺ and T⁻ are anti-symmetrical, and ${{\boldsymbol T}^ + } = {{\boldsymbol T}^ - }$.

3. Function analyses

In this section, a detailed analysis of the device's functions will be conducted, focusing on the -z direction for simplicity in the discussion. The functions of the device are switchable by changing the state of the VO₂. Its optical properties are described by Drude model. It is written as $\varepsilon (\omega ) = {\varepsilon _\infty } - \omega _\rho ^2(\sigma )/({\omega ^2} + i\gamma \omega )$ where ɛ_∞=12 is the permittivity at the infinite frequency and γ=5.75 × 10¹³rad/s is the collision frequency. The plasma frequency at σ can be expressed by $\omega _\rho ^2(\sigma ) = \omega _\rho ^2({\sigma _0})\sigma /{\sigma _0}$ with σ₀= 3 × 10⁵S/m and ω_ρ(σ₀) = 1.4 × 10¹⁵rad/s. The relationship between the permittivity, conductivity, and frequency is established in this model. The conductivity of the VO₂ is controlled by temperature. The diagrams of the change of the conductivity/permittivity of VO₂ with temperature or frequency are available in several Refs. [38,39]. In this study, the conductivities of VO₂ in the insulator state and the conductor state are set to be 1 S/m and 1.5 × 10⁵ S/m, which are within its variation range.

3.1 Polarization conversion

When all the VO₂ is in the insulating state, the whole structure constitutes a linear polarization converter. In a certain frequency range, the cross-polarized field is dominate. As analyzed above, there should be $t_{xy}^ -{=} - t_{yx}^ - $, $t_{xx}^ -{=} t_{yy}^ -{\approx} 0$. And Eq. (1) becomes

Using the vector operation knowledge, we can see that the wave vector Eⁱⁿ⁻ is rotated by +90°, which indicates that polarization conversion of arbitrary incident wave is achieved.

Ideal polarization conversion given in Eq. (3) is impossible, and co-polarized fields are unavoidable. To quantitatively describe the polarization conversion efficiency, PCR (Polarization Conversion Ratio) is defined:

Similarly, in some frequency bands the device exhibits co-polarized transmission mode. In this case the co-polarized field is dominate and cross-polarized field is ignored. Equation (1) is written as

Here $t_{xx}^ - $ represents the transmission efficiency. And PRR (polarization retention ratio) is defined to quantify the polarization retention efficiency:

3.2 Frequency selection

When the VO₂ in the top and bottom layers are set to metallic state and the VO₂ thin film of the third layer is set to insulating state, the overall structure can be seen as a metal square ring resonator. It is approximately equivalent to a frequency selective surface (FSS), which presents a band-stop filtering function. The transmission matrix degenerates to a one-dimensional coefficient in the stop band, and its value should be as low as possible. The equivalent circuit (EC) model offers a simple and fast method in FSS analysis. The resonator is equivalent to a series-connected LC resonant circuit, which is shown in Fig. 2. For TE mode wave incidence, the vertical strips act as a L impedance, and the horizontal gratings as a C impedance. L1C1 and L2C2 represent the resonator of the top layer and bottom layer, respectively. Because the top and the bottom square rings are symmetrical, there are L1 = L2, and C1 = C2. TL1-TL3 are the equivalent resistances corresponding to the three dielectric layers. Similarly, there is TL1 = TL3. In microwave domain, the quasi-static EC approximation of conducting strips developed by Marcuvitz allows the computation of the values for L and C [40,41]. But in this design, the behavior of VO₂ is slightly different from that of copper, even in its metallic state. Therefore, when using the EC model to describe this device, the precise calculation of LC values becomes challenging. Anyway, both a synthesis result using classic filter design technology and simulation results of the device are provided in section 4.

 

Fig. 2. Equivalent circuit model of the filter.

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3.3 Wave absorption

When all the VO₂ are set to the metallic state, the square rings form an FSS, and the VO₂ film forms a reflector. The whole structure is combined into two back-to-back resonant absorbers. In this mode, impedance matching theory can be used to explain the physical mechanism of perfect absorption. The effective impedance of the absorber is defined as $Z(\omega ) = \sqrt {\mu (\omega )/\varepsilon (\omega )}$, where ɛ(ω) and µ(ω) are the equivalent relative permittivity and permeability of the absorber respectively. When the effective impedance Z(ω) of the absorber matches the impedance Z₀(ω) of the free space at the resonant frequency, the reflection of the incident wave is minimized. Generally, the absorption ratio is given by A(ω) = 1-R(ω)-T(ω). If the thickness of the metal layer is greater than the penetration depth of the terahertz wave, the transmittance T(ω) is negligible and perfect absorption can be achieved. The absorption ratio is then calculated by:

In the equation, Z_r = Z/Z₀ is called the relative impedance. It can also be expressed by S parameters as:

It can be seen from the equations that if Z is close to Z₀, i.e., the relative impedance Z_r is close to 1, then the reflection of the device will get towards 0. As a result, A(ω) is close to 1, which means that the absorption reaches its maximum peak.

The single-resonant behavior can be explained by the Fabry–Pérot cavity theory [42,43]. The micro-nano structures and periodically arranged cells in the metasurface play a role like that of a reflector. Fabry-Perot cavity-like interference effects occur when the incident light waves interact with the microstructure of the metasurface. If the micro-nano structure of the metasurface matches the wavelength of the incident light wave, an interference enhancement phenomenon occurs, leading to energy localization and absorption enhancement. This resonance phenomenon allows the metasurface to selectively absorb electromagnetic waves in a specific frequency range.

Thus, the multiple functions of the device have been elaborated. In summary, the transmission matrix T is antisymmetric in polarization conversion function (cross-polarization transmission mode). It degenerates to a one-dimensional coefficient in the co-polarization transmission mode and filtering mode, and is ignored in the absorption mode. The polarization-independence and reciprocity have been proved theoretically.

4. Simulation validation and discussion

In this section, a series of simulations are carried out to validate the design and theoretical analyses.

4.1 Validation of the linear polarization conversion

Firstly, let’s validate the polarization conversion function. Figure 3 shows the transmission coefficient curves for electromagnetic waves incident along the -z and + z directions, respectively. Figure 3(a)(c) show the magnitudes, and Fig. 3(b)(d) show the phases. In the Fig. 3 it can find that $|{t_{xy}^ - } |= |{t_{yx}^ - } |$, $|{t_{xy}^ + } |= |{t_{yx}^ + } |$, $|{t_{xx}^ - } |= |{t_{yy}^ - } |$, $|{t_{xx}^ + } |= |{t_{yy}^ + } |$ and phase($t_{xx}^ - $)=phase($t_{yy}^ - $), phase($t_{xx}^ + $)=phase($t_{yy}^ + $), phase($t_{xy}^ - $)−phase($t_{yx}^ - $)=π, phase($t_{xy}^ + $)−phase($t_{yx}^ + $) = −π, which clearly validates the relations revealed in Eq. (5). Through comparison between the pictures it can further get that $|{t_{xy}^ - } |= |{t_{yx}^ - } |= |{t_{xy}^ + } |= |{t_{yx}^ + } |$, $|{t_{xx}^ - } |= |{t_{yy}^ - } |= |{t_{xx}^ + } |= |{t_{yy}^ + } |$ and phase($t_{xx}^ - $) = phase($t_{yy}^ - $) = phase($t_{xx}^ + $)= phase($t_{xx}^ + $), phase($t_{xy}^ - $) = phase($t_{yx}^ + $), phase($t_{yx}^ - $) = phase($t_{xy}^ + $), which also agree with the relations given in Eq. (3). In Fig. 3(a), the maximus value of $t_{xy}^ - $ and $t_{yx}^ - $ is about 0.86 at 1.472 THz, and the value of $t_{xx}^{}$ and $t_{yy}^{}$ is about 0.03, exhibiting a high transmittivity of cross-polarized wave. Correspondingly, the PCR is shown in Fig. 4. The value is higher than 0.95 in the frequency band of 1.457 THz to 1.517THz, indicating an extremely high conversion efficiency.

 

Fig. 3. Magnitude and phase of the transmission coefficients. (a) (b) the wave propagates in -z direction. (c) (d) the wave propagates in + z direction.

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Fig. 4. PCR and PRR of the device.

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In order to verify the polarization insensitivity of the composite structure more clearly, waves with different polarization angle φ are employed, and the results are given in Fig. 5. Figure 5(a)(b) show the $t_{xy}^ - $ and PCR at 4 different φ which is set at 0°, 45°, 90° and 135° respectively. Although the curves in the Fig. 5(a)(b) correspond to different φ, all of them coincide with each other. The result indicates that the proposed structure does not depend on the polarization mode of the incident wave. It is effective for electromagnetic waves with arbitrary polarization angles.

 

Fig. 5. (a) Magnitude of $t_{xy}^ - $ at different polarization angles. (b) PCR at different polarization angles.

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To further reveal the polarization conversion mechanism of the device, surface current distributions are simulated to describe the transmission of incident wave at arbitrary polarization angles. Figure 6 shows the cases of φ=0°, 90°, and 45° at frequency 1.472THz. When φ=0°, the incident field has only x component. Intense surface currents are induced on the first and third rings, and the surface currents are weak on the second and fourth rings, as shown in Fig. 6(a). Besides, the current on the top layer and bottom layer is in opposite direction. Thus, magnetic dipoles are formed. Consequently, the outgoing field in y-direction is excited. Similarly, when φ=90°, the incident field has only y component. Intense surface currents are induced on the second and fourth rings, and the surface currents are weak on the first and second rings, as shown in Fig. 6(b). The outgoing field in -x direction will be excited. When φ=45°, the incident field can be decomposed into an x-component and a y-component with equal magnitudes. Intense surface currents are induced on the 4 rings, as shown in Fig. 6(c). Finally, x-component of the incident field excites an outgoing field in y-direction, at the same time, y-component of the incident field excites an outgoing field in -x-direction. The polarization angle of the combined outgoing field will be −45°.

 

Fig. 6. Surface current distribution. The polarization angle of the incident wave is (a) φ=0°, (b) φ=90°, and (c) φ=45°.

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For linearly polarized plane waves, the direction of the electric field remains constant in any plane perpendicular to the direction of propagation. To demonstrate the polarization angles of the incident wave and outgoing wave, Fig. 7 shows the field distributions in both the incident and exit planes. The polarization angle of the incident wave is 0°, 45°, 90° and 135°, respectively. Apparently, the polarization angle of the transmitted wave in the 4 cases is approximately 90°, 135°, 180° and 225°, respectively. It demonstrates that the deflection of the polarization angle is 90° in each case. These results visually verify that the structure can achieve orthogonal deflection of incident waves at any polarization angle.

 

Fig. 7. Electric field distribution in an incident plane and an exit plane, respectively. The polarization angle of the incident wave is (a) φ=0°, (b) φ=45°, (c) φ=90°, and (d) φ=135°.

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4.2 Validation of frequency selection

The simulation results above have demonstrated the polarization transition properties of the structure when VO₂ is in the insulating state. Moving forward, the conductivity of the top and bottom layers in VO₂ is set to 1.5 × 10⁵S/m, while it remains at 1s/m in the middle layer. Thereupon, the device is switched from polarization conversion to band-stop filtering function.

Figure 8 gives the simulated S-parameter when an electromagnetic wave is incident in -z direction. The center frequency of the filter's stopband is about 0.896 THz and the stopband is in the range of 0.616 THz-1.176 THz. The stopband bandwidth with −20 dB attenuation is 0.56THz. A synthesis result applying filter design technology is also given in this figure. In the synthesis, a second-order model is used. The passband frequency range is 0.66THz-1.1THz. The M-coupling matrix derived from the simulation is m_1,1 = 0.0, m_2,2 = 0.0, m_S,1 = m_1,S = 1.47537, m_1,2 = m_2,1 = 2.2887, m_2,L = m_L,2 = 1.47537, where S and L represent the sending and receiving of signals in the simulation. The two results are roughly consistent, which validate that EC method is effective in describing the model. On the other hand, the deviation between the two curves indicates that the inserted VO₂ affects the property of the filter.

 

Fig. 8. S11 and S21 of the filter.

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To reveal the physical mechanism of the filter, for TE mode wave incidence, the distributions of the surface electric field, current, and magnetic field are given in Fig. 9. The excited surface electric field is relatively strong near the upper and lower outer edges of the loops as shown in Fig. 9(a). Then vertical currents are formed as shown in Fig. 9(b). And magnetic field is generated, which is relatively strong at the left and right inner edge of the loops as shown in Fig. 9(c). The results verify that the vertical strips act as a L impedance, and the horizontal gratings as a C impedance. Thus, an LC resonance is formed. One can further found that the vertical current is blocked by the VO₂. It makes the current inhomogeneous. As a result, the filtering property is slightly different from the synthesis result.

 

Fig. 9. The device is the filtering function. (a) Surface electric field distribution; (b) surface current distribution; (c) surface magnetic field distribution.

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4.3 Validation of wave absorption

When all the VO₂ is in metallic state, the function of the structure will be switched to wave absorption. As discussed in section 3.3, the reflection of the absorber will be minimized when the effective impedance of the absorber matches the effective impedance in free space. Moreover, when the thickness of the metal ground exceeds the penetration depth of the terahertz wave, the transmission is severely limited. Then perfect absorption can be achieved. The absorption and relative impedance are determined by Eqs. (10) and (11). Figure 10 gives the real and imaginary parts of the relative impedance Zr of the device in this state. According to Eq. (10), if the ratio Z_r(ω)=Z(ω)/Z₀ is close to 1, the reflection R(ω) will be close to 0, and the absorption A(ω) will be close to 1. In the Fig. 10 Zr = 1.01 + j0.11 at 0.565 THz is the point closest to 1. Figure 10 shows that the maximum absorption of approximately 99% is achieved at 0.565 THz. In addition, the performance of the absorber at different polarization angles is investigated. Figure 10(b) depicts the absorption spectrum for a normal incident wave at polarization angle between 0° and 90°. It can be seen that the absorption spectrum does not change with the polarization angles, which indicates that the absorber is also polarization insensitive.

 

Fig. 10. (a) Absorption characteristics of the device. Inset: the real and imaginary parts of Zr(ω). (b) Color map of the absorption spectrums with different polarization angles.

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5. Dual-band device

Multi-functionality, polarization-insensitivity, and reciprocity of the device have already been confirmed. One can find that it has only one working band as shown. Multi-band may be required in some applications. Fortunately, dual-band device can be easily constructed based on the structure given in Fig. 11. It just needs to employ a dual-ring instead of the original single-ring in the structure as shown in Fig. 1. After a series of optimizations, the final values are p = 200, h = h_in= 12, t = 1, a = 90, w = 15.5, k = 10, l = 11, a_in= 52, w_in= 12, k_in= 13 and l_in= 23.75, all in microns. The settings and steps for simulation of the dual-band device is like that of the single-band device, which are not described anymore. The results are given as follows.

 

Fig. 11. Structural of the dual-band device.

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The polarization conversion property is provided in Fig. 12. The coefficient $t_{xy}^ - $ has two peaks at 1.086THz and 1.856THz respectively. Correspondingly, the PCRs are higher than 95% in the bands of 1.022THz-1.126THz and 1.848THz-1.932THz.

 

Fig. 12. Polarization conversion characteristics of the dual-band device. (a) Magnitude of $t_{xy}^ - $, and (b) PCR at different polarization angles.

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The filtering property of the device is given in Fig. 13. Two stop-band can also be figured out at 0.638THz-0.875THz, and 1.265THz-1.375THz, although the performance of the high-frequency band is not so perfect. Figure 14 shows the distributions of the electric field, magnetic field, and the surface currents at f = 0.757 THz and f = 1.322 THz, which are two frequencies in the lower and higher stopbands, respectively. Like the single ring case, vertical electric field and current, horizontal magnetic field are excited. Then the resonances are formed at two frequencies.

 

Fig. 13. S11 and S21 of the dual-band filter.

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Fig. 14. (a) Surface electric field distribution, (b) surface current distribution; and (c) surface magnetic field distribution at f = 0.757 THz and f = 1.322 THz when the dual-band device works in filtering function.

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Finally, the absorption property is shown in Fig. 15. Figure 15(a) and (b) give the real and imaginary parts of the relative impedance Z_r in frequency bands of 0.4THz-0.7THz and 1.1THz-1.4THz. Z_r1= 0.94-j0.09 at 0.555 THz and Z_r2= 1.3-j0.03 at 1.195 THz are two points close to 1. Correspondingly, the absorption ratios are shown in Fig. 15(c), from which one can find A(ω) is about 98% at these two frequency points. And the absorption spectrum is given in Fig. 15(d). The spectrum does not change with the polarization angles, and two absorption frequencies can be found.

 

Fig. 15. Absorption characteristics of the dual-band device. (a) (b) The real and imaginary parts of Zr at 0.4THz-0.7 THz and 1.1THz-1.4THz, respectively; (c)Absorption ratio of the device;(d) Color map of the absorption spectrums with different polarization angles.

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In the end, it needs to be pointed out that in the filtering function of the designed device, the top and bottom VO₂ layers are in a metallic state, while the third layer of VO₂ is in a medium state. Achieving independent control of VO₂ in different layers at the micro-nano scale remains a significant challenge, which we were unable to address in the current work. However, with advancements in temperature control technology, precise temperature control within the micro-nano scale may become possible in the future. It is important to note that the phase change material used in the design is not limited to VO₂. There are several alternatives, such as photosensitive silicon and graphene. For instance, by replacing the VO₂ in the third layer and the polyimide in the second and fourth layers with photosensitive silicon and glass, respectively, while maintaining the overall structure, the device's performance remains almost the same as the previous configuration. In this case, the VO₂ in the top and bottom layers can be controlled by temperature, while the photosensitive silicon in the middle layer can be controlled by illumination. These two independent manipulation methods may make the device practically controllable using current technical conditions.

6. Conclusion

This paper presents a multifunctional device that can switch between linear polarization conversion, filtering, and absorption functions. Unlike most previous multifunctional devices, this device utilizes a composite structure. The surface consists of a 2 × 2 array serving as the basic unit, while the 5-layer structure along the propagation direction maintains symmetry. As a result, the device is both polarization-insensitive and reciprocal. When operating as a linear polarization converter, it effectively handles incident waves at any polarization angle, achieving a high polarization conversion ratio (PCR) of over 95% within the frequency range of 1.457 THz to 1.517 THz. Switching to the filtering function, the device exhibits a stopband ranging from 0.616 THz to 1.176 THz, with a bandwidth of 0.56 THz. Additionally, as a resonant absorber, it demonstrates an absorption ratio exceeding 99% at 0.565 THz. The paper also explores the potential for developing a dual-band device. Although the study focuses on the terahertz range, the proposed method can be extended to the microwave and optical domains.