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Abstract
In the design of metasurfaces, integrating multiple tasks into a single small unit cell and achieving regulation through various paths pose a serious challenge. In this paper, a multipath-controlled bidirectional metasurface (MCBM) is designed to achieve polarization regulation, perfect absorption and total reflection as multitasking functions. The findings demonstrate that under different excitation conditions, when co-planar polarized terahertz (THz) waves are incident normally on the metasurface, the MCBM can convert co-planar polarization to cross-polarization, co-planar polarization to circular polarization wave in reflection mode, and co-planar polarization to cross-polarization in transmission, respectively. When co-planar polarized THz waves are incident from the back side of the metasurface, the tasks of MCBM change to broadband perfect absorption, total reflection, and transmission co-planar polarization to cross-polarization conversion. Remarkably, all operating frequency bands of these tasks are very approximate. Additionally, the multitasking functions can be switched by altering the excitation conditions, and their performance can be regulated through multipath controls, such as the temperature, voltage, and polarization status. Our design provides an effective strategy for multipath-controlled multitasking integrated devices in the THz band.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As electromagnetic (EM) waves with wavelengths from 30 µm to 3 mm, THz waves occupy the range between high-frequency microwave and far-infrared regions. They have several advantageous features, including high carrier frequency, excellent penetrability, and low photon energy. By skillfully manipulating the characteristics, one can apply THz waves in diverse fields, such as bioscience [1], medical imaging [2,3], and sensing [4]. In recent years, EM metasurfaces, which constitute a type of artificially synthesized 2-D material, have garnered significant attention. The material properties are primarily determined by the sub-wavelength periodic or non-periodic super-atomic arrays that are artificially arranged instead of the material itself. This property enables the design to satisfy specific application requirements and offers unprecedented opportunities for freely manipulating the attributes of EM waves [5,6]. In addition, THz devices based on metasurface design have excellent thickness advantages and can satisfy most THz application scenarios even with the integration technology of multilayer metasurface stacking. Therefore, research on THz wave modulation devices based on EM metasurfaces with multitasking holds profound significance.
At present, the implementation strategies to integrate multiple processing tasks in a single unit cell metasurface installation can be divided into two main categories. One category involves embedding controllable materials or devices such as photosensitive semiconductors [7–10], graphene [11–15], and vanadium dioxide (VO2) [16–19] in the single metasurface layer. When the controllable materials are in different states, the metasurface can accomplish different tasks. For example, Kindness et al. proposed a graphene-integrated metamaterial all-electrical polarization control device that demonstrated active polarization modulation of a THz quantum cascade laser [12]; Zhang et al. presented a multitasking tailored device to convert ultra-broadband absorption and polarization by embedding a phase-change material and a photoconductive semiconductor in intersecting and concentric circular metasurfaces to regulate the multitasking functionality [17]. The other category uses multilayered metasurfaces that are stacked and integrated together [20–24]. Here, each metasurface layer is assigned a different task; by eliminating the interlayer coupling, filtering or transmission effects, the layers can achieve more operation modes. For example, Burokur et al. introduced a non-interleaved and non-segmented bidirectional Janus metasurface that encoded multiple functionalities in full-space scattering channels with different propagation directions and polarization by rotating and adjusting the elementary double-arrow-shaped structure within the same meta-atom [21]; An et al. synthesized a multilaminate metastructure by overlaying a microwave absorption layer and an infrared stealth layer, which achieved the dual-stealth function of high-temperature radar-infrared bi-stealth [24]. The aforementioned switchable or reconfigurable metasurfaces can only operate in two or three modes. Most recently, the integration of different tunable materials in multilayer metasurfaces to independently control multiple functionalities has garnered significant attention [25–29]. Wang et al. proposed an electrically and thermally tunable multitasking metasurface, which incorporated VO2 and graphene materials in a two-layer metasurface structure to achieve reflective band-stop filtering, beam steering, and beam splitting functions [26]; Lian et al. also utilized VO2 and graphene as switching devices to design a metasurface with perfect absorption and reflective polarization conversion [29]. However, these multitasking metasurfaces only focus on the reflective operation mode for incident EM waves in the forward direction, and there is limited attention to the backward incident and transmission operation modes. Therefore, it is urgent to design a multitasking metasurface that can respond to bidirection incident THz waves and possess multiple-control paths.
In this paper, by combining the advantages of the two aforementioned strategies to integrate multitasking metasurface devices, we adopt a multilayer metasurface superimposed structure and embed two control materials (VO2 and graphene) to skillfully design and avoid interference among multilayer structures. This design enables the proposed metasurface to produce different responses to bidirectional EM waves and achieve multipath-controlled multitasking operating modes. Under different excitation conditions, when a linear co-planar polarized THz wave is incident on the metasurface from the forward side, the MCBM can convert the linear co-planar polarization to linear cross-polarization (LTL) at 0.45-1.10 THz, linear polarization to circular polarization (LTC) in reflection mode at 0.42 THz, 1.21 THz, and 1.61 THz, and transmission mode LTL at 0.48-0.58 THz. When the linear co-planar polarized THz wave is incident from the backward side of the metasurface, the tasks of the MCBM change to broadband perfect absorption with an absorptivity over 90% at 0.54-1.18 THz, total reflection, and transmission LTL at 0.56-0.75 THz. In addition, by controlling the excitation states of VO2 and graphene, we can regulate the performance of the proposed multitasking metasurface. Due to the multiple tasks, the proposed MCBM can be more flexibly used in many different situations.
2. Design, method, and multiple tasks
The immense challenge in designing multitasking metasurfaces is how to converge different functions within a similar frequency band while avoiding mutual interference between them. The proposed MCBM adopts a three-layer integration structure, as depicted in Fig. 1. It incorporates a top EM wave guidance layer (EGL), a middle polarization modulation layer (PML), and a bottom EM wave dissipation layer (EDL). Within each layer, functional control materials are embedded and appropriately biased to achieve the tailored performance. This enables all functions to operate within a similar frequency band and freely switch between them. The EGL is attached to the front of Substrate I, comprising a lateral metal grating with embedded graphene blocks. A biased voltage is applied to the graphene through metal lines on both sides regulates its Fermi level µc1. This regulates whether linearly polarized EM waves from the front can pass through the metasurface. The PML is attached to the front and back of Substrate II, featuring patterned arrays and longitudinal metal-VO2 gratings. By modulating the temperature of the phase-change material VO2, incoming EM waves can be controlled to either pass through or reflect from the metasurface, whilst also regulating their polarization properties. The EDL attached to the back of Substrate III, comprises continuous diamond-shaped graphene arrays. Biased by metal lines on either side to regulate Fermi level µc2, it dictates whether incoming EM waves will pass through or be dissipated by the metasurface.
Fig. 1. Schematic diagram of the proposed MCBM for multitasking and multipath-controlled, (a) high temperature scenario, (b) low temperature scenario.
Design and analysis reveal that the proposed MCBM can manipulate the properties of bidirectionally incident EM waves through temperature and bias voltage excitations. Specific multitasking operating modes and corresponding excitations are shown in Fig. 1 and Table 1. When the MCBM is in a high-temperature environment (T > 340 K), applying different bias voltages on graphene layers, achieves forward reflection LTL in the range of 0.45-1.10 THz; forward reflection LTC with right-handed circular polarization (RHCP) at 0.42 THz or left-handed circular polarization (LHCP) at 1.21 THz and 1.61 THz, and backward absorption in the 0.54-1.18 THz and total reflection in the 0.10-2.0 THz. While in a low-temperature environment (T < 340 K), the MCBM achieves forward transmission LTL in the range of 0.48-0.58 THz, and backward transmission LTL in the range of 0.48-0.58 THz. Moreover, we note that different operating modes frequency bands are close, giving the device great advantage for various functional requirements within a uniform frequency band.
Table 1. Multitasking operating modes of MCBM under different excited conditions
For the reflection polarization conversion operation modes, the performance can be characterized by Stokes parameters [30,31]:
where ${r_{yy}}$ and ${r_{xy}}$ are the co-planar polarization reflection coefficients and cross-polarization reflection coefficients with the electric field polarized along the Y direction and X direction, respectively; $\Delta \varphi = {\varphi _{yy}} - {\varphi _{xy}}$ is the phase difference between Y and X direction components of the reflected THz wave. Stokes parameters S0–S4 represent the total reflection, linearly polarized state of the reflection along the Y direction, linearly polarized state of the reflection along the 45°-direction, and circular polarization state, respectively. For the LTL operating modes, the performance of polarization conversion can be characterized by the polarization conversion ratio (PCR) [32]: $PC{R_r} = {{|{r_{xy}}{|^2}} / {({|{r_{xy}}{|^2} + |{r_{yy}}{|^2}} )}}$. When $|{r_{xy}}|$ is close to 1 and $|{r_{yy}}|$ is close to 0, the incident co-planar polarization THz wave is be almost completely converted to a cross-polarization THz wave. For the LTC operating modes, when $|{r_{xy}}|\approx |{r_{yy}}|$ and $\Delta \phi = n\pi \pm {\pi / 2}$ (n is an integer) are simultaneously satisfied, the incident co-planar polarization wave is converted to a circular polarization wave. Here, “${\pi / 2}$” and “$- {\pi / 2}$” indicate that the reflected wave is LHCP and RHCP, respectively. The ellipticity can be defined as $\chi = {{{S_3}} / {{S_0}}}$ to characterize the polarization state. When $\chi = 1$ and $\chi ={-} 1$, the corresponding polarization state of the reflection wave are LHCP and RHCP, respectively. The axial ratio, which is defined as $AR = 10\log (\tan \beta )$, is an important metric for evaluating the performance of circularly polarized waves [30,31], where $\beta = {1 / 2}{\sin ^{ - 1}}({{{{S_3}} / {{S_0}}}} )$ is the ellipticity angle. When the axial ratio is less than 3 dB, the reflected waves have superior circular polarization performance. Similarly, for the transmission polarization conversion operating modes, the characterization approach is approximate to the aforementioned description. For the absorption operating mode, the absorptivity $A(\omega )= 1 - |{r_{yy}}{|^2} - |{r_{xy}}{|^2} - |{t_{yy}}{|^2} - |{t_{xy}}{|^2}$ is used to quantify the absorption effect [33,34], where $|{t_{yy}}|$ and $|{t_{xy}}|$ are the co-planar polarization and cross polarization transmission coefficients, respectively.The proposed MCBM details are shown in Fig. 2. Figure 2(a) is the array decomposition with 6 × 6 unit cells, and Figs. 2(b)-(e) are the front and rear views of each layer in a MCBM unit cell. In the structure, the EGL, PML, and EDL are attached to the front of Substrate I, both sides of Substrate II, and the back of Substrate III, respectively. These three substrate layers are made of SiO2 with permittivity of ${\varepsilon _{Si{O_2}}}$ = 3.75 and thicknesses of t1 = 21 µm, t2 = 30 µm, and t3 = 30 µm. The EGL of the unit cell consists of two gold metal strips embedded in a square graphene block and connected to the periodic array's lateral metal wires for voltage excitation, as shown in Figs. 2(a) and (b). The metal strips have conductivity of σAu = 4.561 × 107 S/m. The resonator on the front of the PML comprises two intersecting diamond structures and symmetric W-shaped metal lines, with side length l1 and inner angle α1 for the diamonds, and arm lengths l2 and l3 forming adjacent angles α2 and α3 for the metal lines, as shown in Fig. 2(c). On the back of the PML, a gold-VO2 interdigitated ground plane is formed with line widths matching those of the EGL layer's metal line, as shown in Fig. 2(d). Additionally, the EDL comprises diamond graphene resonators and connecting wires, with wires connecting every column of diamond graphene resonators to the horizontal metal wires of the periodic array. The inner angle of the diamond is α1, and the connecting wire has line width of 0.2 µm. The optimized geometrical and dielectric parameters of the structure are obtained through joint simulation using MATLAB & CST. MATLAB’s Optimization Toolbox solver is utilized to enhance outcomes from CST post-processing. The structural dimensions are modified gradually using CstParameter, leading to the optimal solution. The optimized geometric parameters of the proposed MCBM are listed in Table 2.
Fig. 2. (a) Schematic of the proposed 6 × 6 MCBM unit cell array, the unit cell of (b) the front view of EGL, (c) the front view of PML, (d) the rear view of PML, and (e) the rear view of EDL.
Table 2. Optimized structure parameters of the proposed MCBM (in µm and degree)
To investigate the proposed MCBM performance, we utilize EM simulation software CST based on the finite integration technique (FIT) to model and simulate the structure. In the simulation configuration, the Unit cell boundaries are set along both the X and Y directions, simulating an infinite periodic array in the X and Y directions. The Z direction is set as Open (add space) boundary, allowing EM waves to propagate along the Z axis and impinge onto the designed metasurface with electric field and magnetic field polarizations along the Y and X axes, respectively, as shown in Fig. 2(a). Additionally, Bruggeman effective-medium theory is employed for VO2 modeling [35,36]:
Fig. 3. (a) Change in the structure of VO2 during the phase-change, (b) conductivity curves of VO2 during heating and cooling.
In the THz band, single-layer graphene can be modeled as an equivalent two-dimensional material without thickness. Its complex surface conductivity ${\sigma _{\textrm{gra}}}$ can be characterized by the Kubo equation [40], which comprises two parts: the intraband (${\sigma _{\textrm{intra}}}$) and the interband conductivity (${\sigma _{\textrm{inter}}}$):
Fig. 4. (a) Real part and (b) imaginary part of complex conductivity $\sigma _{{\rm gra}}$ under different Fermi level µc.
3. Results and discussions
3.1 Multitasking operating modes
For the forward incident operating modes, the simulated scattering parameters and PCRs are depicted in Fig. 5. When the external temperature is elevated and the Fermi levels are set to µc1 = 0 eV, µc2 = 0 eV, respectively, the graphene within the EGL manifests an insulating state, whereas the VO2 in the PML assumes a metallic state. Under these conditions, the PML functions a continuous metal-like ground plane capable of impeding EM wave transmission. Consequently, the MCBM operates in a reflective polarization conversion mode, as illustrated in Figs. 5(a) and (b). The figures reveal that the co-planar polarization reflection coefficients $|{r_{yy}}|$ or $|{r_{xx}}|$ for the TE and TM modes of the incident THz wave remain below 0.2 in the range of 0.45-1.10 THz. Concurrently, the cross-polarization reflection coefficient $|{r_{xy}}|$ and $|{r_{yx}}|$ approach 0.8, while the transmission coefficient approximates zero. In accordance with the PCR formula, the reflective polarization conversion rate (PCRr) of the MCBM exceeds 90%. Furthermore, at 0.42 THz, 1.21 THz, and 1.61 THz, the reflection coefficients $|{r_{yy}}|$ and $|{r_{xy}}|$, $|{r_{xx}}|$ and $|{r_{yx}}|$ are nearly equivalent, indicating that the reflected wave exhibits circular polarization characteristics.
Fig. 5. Simulated results for forward incident THz wave: (a) and (b) the scattering coefficients and PCRs for TE and TM modes under conditions of µc1 = 0 eV, µc2 = 0 eV, and high temperature, respectively, (c) and (d) the corresponding ellipticity and axial ratio; (e) and (f) the scattering coefficients and PCRs for TE and TM modes under conditions of µc1 = 1 eV, µc2 = 0 eV, and low temperature, respectively.
Figures 5(c) and (d) depict the corresponding ellipticity and axial ratio based on the Stokes parameters. It is evident from these figures that when the THz wave is incident in TE mode, the ellipticity is -0.987, 0.978, and 0.971 at 0.42 THz, 1.21 THz, and 1.61 THz, respectively, and the axial ratio is less than 2 dB. This confirms that the linearly polarized incident EM wave at these frequencies is converted into RHCP, LHCP, and LHCP waves, respectively. Similarly, when the THz wave is incident on the metasurface in TM mode, the ellipticity is 0.851, -0.986, and -0.911 at 0.42 THz, 1.21 THz, and 1.61 THz, respectively. This indicates that the linearly polarized THz wave is converted into LHCP, RHCP, and RHCP waves by the metasurface. For incident THz waves with TE and TM polarizations, the polarization directions are inclined at +45° and -45° with respect to the equivalent direction of the resonators. As TE and TM polarized waves pass through the resonators, the polarization directions are deflected in different directions, resulting in distinct circular polarization conversion performance. When the external temperature decreases to a low-temperature state and the Fermi levels change to µc1 = 1 eV, and µc2 = 0 eV, respectively, the graphene in the EGL enters a metallic state. The THz wave can pass through this layer and reach the interior of the structure, and the VO2 in the PML also transitions to an insulating state. At this point, the THz wave can be selectively transmitted based on its polarization characteristics. The operating mode of the MCBM is switched from reflective to transmissive as shown in Fig. 5(e). For TE mode THz waves, the transmission polarization conversion rate (PCRt) in the range of 0.48-0.58 THz exceeds 80%, with minimal energy being reflected by the metal-graphene gate in the EGL. For TM mode THz waves, according to the reflection rate calculation formula $R(\omega ) = {{|{r_{xx}}{|^2}} / {(|{r_{xx}}{|^2} + |{r_{yx}}{|^2} + |{t_{xx}}{|^2} + |{t_{yx}}{|^2})}}$, the reflection rate in the range of 0.10-2.0 THz exceeds 90%. Unlike the reflective polarization conversion mode, the transmissive mode requires THz waves to propagate through each layer of the structure. Due to the distinct polarization directions of THz waves, TE waves can propagate through the EGL and generate a transmissive polarization conversion function, whereas TM waves are nearly completely reflected. Analysis suggests that the proposed metasurface exhibits varying responses to TE and TM mode THz waves when subjected to different external temperatures and Fermi levels µc1 and µc2. It is capable of multitasking operating modes, including reflective LTL, LTC for both LHCP and RHCP, transmissive LTL, and total reflection.
Additionally, the scattering parameters, absorptivity, and PCR for the backward incident operating modes are illustrated in Fig. 6. At high external temperature, with Fermi levels at µc1 = 0 eV and µc2 = 1 eV, the gold-VO2 layer in the PML functions as a metal-like ground plane, effectively inhibiting the transmission of backward incident waves. The graphene in the EDL exhibits metallic behavior, resonating with the PML to absorb TE mode THz waves, achieving an absorptivity exceeding 90% in the range of 0.54-1.18 THz, as shown in Fig. 6(a). For TM mode THz waves, the polarization directions align with the short sides of the diamond-shaped graphene, and the equivalent lengths are inadequate to resonate with the THz waves within the target frequency range, leading in reflection of TM mode THz waves in the range of 0.10-2.0 THz, as shown in Fig. 6(b). Moreover, when the external temperature decreases to a low temperature and the Fermi levels are set to µc1 = 1 eV and µc2 = 0 eV, the gold-VO2 layer in the PML functions as a metal gate that selectively transmits TM waves while blocking TE waves. Concurrently, the metal gate in the EGL is disrupted, permitting THz waves to propagate through. Therefore, the linearly co-planar polarized TM waves in the range of 0.56-0.75 THz are modulated by the PML into cross-polarized waves, whereas the TE mode THz waves are reflected back, as shown in Figs. 6(c) and (d). In summary, the proposed MCBM is capable of achieving multitasking operating modes of THz wave polarization state control, absorption, and total reflection under varying temperatures and excitation voltages, as listed in Table 1. All tasks are interchangeable under different excitation conditions.
Fig. 6. Simulated results for backward incident THz wave: (a) and (b) the scattering coefficients and absorptivity for TE and TM modes under conditions of µc1 = 0 eV, µc2 = 1 eV, and high temperature, respectively, (c) and (d) the scattering coefficients, reflectivity and PCRs for TE and TM modes under conditions of µc1 = 1 eV, µc2 = 0 eV, and low temperature, respectively.
3.2 Multipath-controlled modes
Based on the characteristics of the phase-change material VO2 discussed in Section 2, it is understood that its crystal structure can be controlled through temperature, optical, and electrical means to transform from a monoclinic crystal system to a diamond-phase tetragonal crystal system. This phase transformation results in a reversible change in electrical properties from metallic to dielectric, with conductivity increasing from 102 S/m to 105 S/m. Therefore, the performance of the proposed MCBM can be modulated by temperature. Taking the forward incident reflection LTL operating mode as an example, we analyze the temperature control mechanism, as depicted in Fig. 7. Observations from the figure indicate that as the temperature of the PML decreases from high to low temperature conditions, the conductivity diminishes progressively. This reduction weakens the blocking effect on the THz wave, allowing a significant portion of EM energy to transmit through the designed structure. Consequently, there is a gradual decline in the performance of forward incident EM wave reflection polarization conversion, achieving temperature-dependent regulation of MCBM performance.
With regard to graphene materials, the Fermi level can be tuned using external voltage, chemical doping, and optical pumping. Here, we focus on controlling the Fermi level of graphene through electrical means to regulate the performance of the proposed metasurface. When the external environment is at low temperature and the Fermi levels are set to µc1 = 0 eV, µc2 = 1 eV, the co-planar polarized THz wave incident on the MCBM will convert into cross-polarized waves through transmission. As the Fermi level of graphene in the EGL progressively increases, the EGL will gradually transform into an equivalent metal gate, directionally shielding the incoming THz waves. Consequently, some THz waves polarized along the Y axis will be unable to pass through the EGL and reach the interior of the MCBM, resulting in a gradual decrease in polarization conversion performance as shown in Fig. 8(a). Moreover, when the external temperature changes to high and the Fermi levels are set to µc1 = 0 eV, µc2 = 1 eV, the THz wave incident on the metasurface from the backward direction will be completely dissipated by the EDL. As the Fermi level of graphene progressively decreases, its metallicity will weaken, causing resonance with the PML and incident THz wave to diminish. Therefore, the ability to dissipate THz waves will also decrease. As µc2 decreases to 0 eV, the THz wave incident from the backward direction will be almost completely reflected back, achieving a total reflection operating mode as shown in Fig. 8(b). Through electrical modulation, the regulated operating modes of MCBM are achieved.
Fig. 8. Electrical control for (a) transmission polarization conversion mode, (b) absorption operating mode.
Furthermore, it is worth noting that the proposed structure exhibits anisotropy, both in the metal pattern array within the PML and in the diamond-shaped graphene array within the EDL. This results in the MCBM's ability to elicit different responses to THz waves with varying polarization directions. For instance, considering the forward incident reflection polarization conversion mode and the backward incident absorption mode, THz waves polarized along the Y axis (TE mode) can interact with the metal pattern array in the PML to induce a phase shift that accomplishes polarization conversion. However, as the incident polarization angle varies, the degree of phase shift diminishes, leading to a decline in polarization conversion efficiency. At an incident polarization angle of 45°, the polarization conversion performance reaches its nadir, as depicted in Fig. 9(a). When a backward incident THz wave polarized along the Y axis interacts with the diamond-shaped graphene resonator, the diagonal edge of the resonator aligned with the Y axis can be effectively modeled as a linear resonator, engaging with the incident wave to achieve electromagnetic energy absorption. As the incident wave's polarization angle increases, the electric field's polarization component along the Y axis diminishes, reaching zero at a polarization angle of 90°, at which point the absorption performance is fully extinguished, as illustrated in Fig. 9(b). In summary, the multitasking operational modes of the MCBM can be freely manipulated through various means, including temperature, excitation voltages, and polarization angle.
Fig. 9. Polarization state control for (a) reflection polarization conversion operating mode, (b) absorption operating mode.
3.3 Operating mechanism
We analyze the polarization conversion mechanism of MCBM by considering the reflection polarization conversion operation mode of the forward incident THz wave. For the forward incident THz wave polarized along the Y axis, it can be decomposed into equivalent components ${E_{iu}}$ and ${E_{iv}}$ along the u and v axes, as depicted in Fig. 10(a). Thus, the incident electric field and reflected electric field can be represented as ${\vec{E}_i} = \overrightarrow u {E_{iu}}{e^{j\phi }} + \overrightarrow v {E_{iv}}{e^{j\phi }}$ and ${\vec{E}_r} = \overrightarrow u {r_u}{E_{iu}}{e^{j(\phi + {\phi _u})}} + \overrightarrow v {r_v}{E_{iv}}{e^{j(\phi + {\phi _v})}}$, respectively, where ${r_u}$ and ${r_v}$ are the reflection amplitudes along the u and v axes, and ${\phi _u}$ and ${\phi _v}$ are the corresponding phases. Due to the anisotropy of the pattern array in the PML, there is a phase difference $\Delta {\phi _{vu}}$ between the incident and reflected waves. If ${r_u} \approx {r_v}$ and $\Delta {\phi _{vu}} \approx{\pm} \pi$ are simultaneously satisfied, the reflected electric field is rotated 180°, and it is combined with ${E_{ru}}$ to form a reflected electric field ${E_r}$ that maintains its direction unchanged, as shown in Fig. 10(a). This achieves the conversion of incident co-planar polarization to cross-polarized waves. When ${r_u}$ and ${r_v}$ are approximately equal and $\Delta {\phi _{vu}} \approx n\pi \pm {\pi / 2}$, the incident co-planar polarized THz wave is converted into a circularly polarized wave. Figure 10(b) plots the reflection coefficient amplitude, phase, and phase difference of the electric field polarization direction along the u and v axes when a forward THz wave is incident on the metasurface. We can see from the figure that, in the range of 0.45-1.10 THz, the reflection amplitude is approximately equal (plotted with a red dashed line), and the phase difference is close to 180° (plotted with a blue solid line). This indicates that the incident co-planar polarized wave is converted into a cross-polarized wave in this frequency band. At 0.42 THz, 1.21 THz, and 1.61 THz, the phase differences are -97.2°, -264°, and -281°, respectively, indicating that the linearly polarized waves at these frequencies are converted into RHCP, LHCP, and LHCP, respectively.
Fig. 10. (a) Schematic illustration of the conversion characteristic (b) amplitudes, phases, and phase different of the reflection coefficients for forward incidence.
To further elucidate the working mechanisms of the polarization conversion and absorption modes, the surface electric field and magnetic field distributions at the resonance frequencies are plotted in Fig. 11. For the polarization conversion LTL mode, the surface currents are mainly concentrated on the W-shaped resonator arms in the PML at 0.48 THz with opposite direction to currents on the gold-VO2 plane in the PML, as shown in Figs. 11(a1) and (a2). This indicates that the magnetic resonance generated by the front and back layers of the PML plays a major role. Figures 11(a3) and (a4) show the magnetic field distribution on the front side of the PML and cross section along the XOZ plane, respectively. As can be seen from these figures, the magnetic field is mainly concentrated in the arms of the W-shaped resonator, the gold-VO2 plane, and the space between them. This verifies that magnetic resonance is the main cause at 0.48 THz. In contrast, as shown in Figs. 11(b1) - (b4), the current and magnetic field distribution are concentrated not only in the arm of the W-shaped resonator in the PML at 0.93 THz, but also at the edges of the intermediate double-diamond resonator. The equivalent length of this part of the current is obviously shorter than that at 0.48 THz, resulting in a higher operating frequency [42]. It is worth noting that at this operating frequency, the surface current and electric field on the gold-VO2 plane are very weak, and the current flows in the same direction on both sides of the PML, indicating that it is primarily formed by electric resonance. Similarly, when MCBM operates in absorption mode, at frequencies of 0.74 THz and 1.1 THz, the surface current on both sides of the PML flows in opposite directions as shown in Figs. 11(d1) and (d2), illustrating that the resonance modes at these two frequencies are magnetic resonance and electric resonance, respectively. The magnetic field distribution further confirms this view as shown in Figs. 11(d3) and (d4).
Fig. 11. Surface current and magnetic field distributions for LTC and absorption modes at resonant frequencies.
The EM features of the proposed MCBM can be calculated and verified using an equivalent circuit model. Taking the example of the reflection LTL and absorption modes with forward incidence, an equivalent circuit model is established and validated, as shown in Fig. 12. For the forward incidence LTL mode, the THz wave incident on the MCBM from free space can be regarded as a wave impedance connected to the free space Z0. The graphene-gold gate on the front side of EGL is periodically arranged along the X-axis, allowing TE-mode THz waves to pass through. When the THz wave passes through this layer, it undergoes negligible EM response and is slightly dissipated, therefore equivalent to a resistor R0. In the resonator array on the front side of PML, the surface currents flow on the W-shaped and double diamond resonators to form an inductor L1. There is a capacitor C1 between the W-shaped and double diamond resonators, and a resistor R1 is connected to the ground to form an LC resonant circuit, and a capacitor C2 exists between the pattern array and the gold-VO2 plane. Substrate II can be characterized as a transmission line stub, described by (Z, P, F), where Z is the equivalent impedance of the dielectric layer, P is the phase of the wave, and F is the frequency within the working band. The gold-VO2 plane at the back side of the PML can be equivalently short-circuited due to the weak EM wave energy transmission. Similarly, for the absorption mode with THz wave incident in backward direction, the gold-VO2 plane can also be regarded as short-circuited. Substrate III is characterized as a transmission line stub as a function of (Z’, P’, F’), and the capacitor C3 between the pattern array and the gold-VO2 plane. The inductor L2 of diamond graphene and capacitor C4 between graphene layers form an LC resonant circuit with damping R2. The periodic array of graphene in the back side of EDL can be characterized as distributed capacitance C5 and C6, inductance L3 and L4, and resistance R3 combinations [42,43]. This circuit is also connected to the free space impedance Z0. The optimized numerical values of the parameters obtained by the circuit simulation software Advanced Design System (ADS) are as follows: R0 = 0.027 Ω, R1 = 1.224 Ω, R2 = 6.74 Ω, R3 = 82.445 Ω, C1 = 0.588 pF, C2 = 0.662 fF, C3 = 0.539 fF, C4 = 0.297 pF, C5 = 8.312 fF, C6 = 0.092 fF, L1 = 4.228 fH, L2 = 2.174 fH, L3 = 16.339 pH, L4 = 64.282 pH. Figures 12(c) and (d) show the reflection coefficients and absorptivity obtained by EM and circuit simulation for both LTL and absorption modes. As observed from the figures, there is a good agreement between the two sets of calculation results, which validates the performance of the proposed MCBM.
Fig. 12. Equivalent circuit model of the MCBM for (a) LTL mode, and (b) absorption mode; simulated and calculated results by CST and ADS for (c) LTL mode, and (d) absorption mode.
3.4 Parameters and angular stability analysis
Finally, we examined the influence of major structural parameters and incident angles on the operation modes, using the reflection polarization conversion mode with forward incidence and the absorption mode with backward incidence as examples, as depicted in Fig. 13. As discussed in Section 3.3 which addresses the distribution of surface currents, the surface currents are mainly concentrated in the arms of W-shaped resonators within the PML. Consequently, we focused the analysis on the arm length l2 as the primary parameter. As illustrated in Fig. 13(a), an increase in the arm length l2 results in a redshift of the original low-frequency resonance. This shift occurs because the resonance frequency is closely correlated with the effective length leff of the current flows, i.e., $\omega \propto c\textrm{/}\pi {l_{eff}}\sqrt {{\varepsilon _r}}$ [44], and leff increases with an increment in l2, leading to a gradual decrease in the resonance frequency. Meanwhile, the high frequency resonance is primary determined by the double diamond-shaped resonators within the PML, and thus, the position of the high-frequency resonance is only marginally affected by the length l2. Furthermore, we observed that as l2 gradually increases, the bandwidth of the polarization conversion operation also increases, while the PCR becomes limited. Considering both bandwidth and efficiency, we ultimately determined that l2 = 30.8 µm provides the optimal solution. Regarding the absorption mode, absorption is mainly due to the dissipation of THz waves by graphene. When the side length l4 of the diamond-shaped graphene resonator decreases, both the bandwidth and efficiency of absorption operation are affected, as shown in Fig. 13(b). Additionally, in practical operations, THz waves do not always strike the surface of the device along the normal direction. Therefore, angle stability is an important metric. Figures 13(b) and (c) plot the results of polarization conversion and absorption performance at different incident angles. As demonstrated in these figures, for both polarization conversion and absorption modes, operational capabilities can be maintained within incident angles of 30° and 50°, respectively, indicating that the proposed MCBM exhibits a certain tolerance to incident angles.
Fig. 13. The polarization conversion and absorption performance under different parameters (a) l2, (b) l4, and (c), (d) different incident angles θ.
4. Conclusion
In this paper, we propose a MCBM based on a multilayer metasurface that can achieve the multitasking control of various operations for bidirectional incidence THz waves. By controlling the excitation conditions such as the environment temperature, bias voltage, and polarization mode, one can arbitrarily switch multiple tasks and modulate their amplitudes. When co-planar polarized THz waves are incident normally on the metasurface, the MCBM can convert co-planar polarization to cross-polarization in the range of 0.45-1.10 THz, co-planar polarization to RHCP (0.42 THz) and LHCP (1.21 and 1.61 THz) in reflection mode, and co-planar polarization to cross-polarization in the range of 0.48-0.58 THz in transmission mode. When co-planar polarized THz waves are incident from the back side of the metasurface, the task of the MCBM is changed to broadband perfect absorption in the range of 0.54-1.18 THz, total reflection, and transmission co-planar polarization to cross-polarization conversion in the range of 0.56-0.75 THz. We note that all of these operating modes are within a close operating frequency band, which facilitates the application of the MCBM. In addition, the proposed MCBM has a certain tolerance to incident angles. Our design provides an effective strategy for multipath-controlled multitasking integrated devices in the THz band.
Funding
National Natural Science Foundation of China (52175555); Shanxi Provincial Key Research and Development Project (201803D421043); Fundamental Research Program of Shanxi Province (20210302123074, 202203021212120); Shanxi ‘1331 Project’ Key Subject Construction, Innovation Community (51821003).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. G. Markelz and D. M. Mittleman, “Perspective on terahertz applications in bioscience and biotechnology,” ACS Photonics 9(4), 1117–1126 (2022). [CrossRef]
2. Z. Y. Yan, L. G. Zhu, K. Meng, et al., “THz medical imaging: from in vitro to in vivo,” Trends Biotechnol. 40(7), 816–830 (2022). [CrossRef]
3. S. X. Yang, L. Ding, S. Wang, et al., “Studying oral tissue via real-time high-resolution terahertz spectroscopic imaging,” Phys. Rev. Applied 19(3), 034033 (2023). [CrossRef]
4. H. Sun and Y. S. Lin, “Tunable terahertz metamaterial with multi-resonance characteristic for refractive index sensing application,” APL Mater. 11(8), 081111 (2023). [CrossRef]
5. Y. Y. Jing, L. K. Liu, S. Y. Li, et al., “Highly efficient decoupled triple-channel OAM generation with a single-layer shared aperture reflective metasurface,” Adv. Optical Mater. 11(3), 220207 (2023). [CrossRef]
6. P. Wang, J. C. Su, P. Ding, et al., “Graphene-metal based tunable radiative metasurface for information encryption and anticounterfeiting,” Diam. Relat. Mater. 131, 109548 (2023). [CrossRef]
7. J. C. Zhao, Y. Z. Chen, and Z. Z. Cheng, “Design of a photo-excited switchable broadband reflective linear polarization conversion metasurface for terahertz waves,” IEEE Photonics J. 10(1), 1–10 (2018). [CrossRef]
8. S. Yuan, R. C. Yang, J. P. Xu, et al., “A photoexcited switchable single-/dual-band terahertz metamaterial absorber,” Mater. Res. Express 6(7), 075807 (2019). [CrossRef]
9. L. L. Hale, H. Jung, S. D. Gennaro, et al., “Terahertz pulse generation from GaAs metasurfaces,” ACS Photonics 9(4), 1136–1142 (2022). [CrossRef]
10. Q. G. Zhou, W. L. Ma, T. T. Wu, et al., “Metasurface terahertz perfect absorber with strong multi-frequency selectivity,” ACS Omega 7(41), 36712–36727 (2022). [CrossRef]
11. H. Cheng, S. Q. Chen, P. Yu, et al., “Dynamically tunable broadband mid-infrared cross polarization converter based on graphene metamaterial,” Appl. Phys. Lett. 103(22), 223102 (2013). [CrossRef]
12. S. J. Kindness, N. W. Almond, W. Michailow, et al., “Graphene-integrated metamaterial device for all-electrical polarization control of rerahertz quantum cascade lasers,” ACS Photonics 6(6), 1547–1555 (2019). [CrossRef]
13. M. Y. Wang, Q. S. Zeng, L. Deng, et al., “Multifunctional graphene metasurface to generate and steer vortex waves,” Nanoscale Res. Lett. 14(1), 343 (2019). [CrossRef]
14. I. Mazraeh-Fard and A. Alighanbari, “Equivalent circuit model for the analysis and design of graphene-based tunable terahertz polarizing metasurfaces,” Appl. Opt. 61(19), 5760–5768 (2022). [CrossRef]
15. S. X. Xia, D. Zhang, X. Zhai, et al., “Phase-controlled topological plasmons in 1D graphene nanoribbon array,” App. Phys. Lett. 123(10), 101102 (2023). [CrossRef]
16. L. Lei, F. Lou, K. Y. Tao, et al., “Tunable and scalable broadband metamaterial absorber involving VO2-based phase transition,” Photon. Res. 7(7), 734–741 (2019). [CrossRef]
17. H. Zhang, X. C. He, D. Zhang, et al., “Multitasking device with switchable and tailored functions of ultra-broadband absorption and polarization conversion,” Opt. Express 30(13), 23341 (2022). [CrossRef]
18. Z. P. Zheng, Y. Zheng, Y. Luo, et al., “A switchable terahertz device combining ultra-wideband absorption and ultra-wideband complete reflection,” Phys. Chem. Chem. Phys. 24(4), 2527–2533 (2022). [CrossRef]
19. X. Y. Wang, M. Chen, W. L. Zhao, et al., “Terahertz broadband tunable chiral metamirror based on VO2-metal hybrid structure,” Opt. Express 31(13), 22144–22156 (2023). [CrossRef]
20. H. Pan, H. F. Zhang, X. L. Tian, et al., “Design, simulation, and analysis of an ultra-broadband polarization-insensitive terahertz metamaterial absorber,” J. Opt. Soc. Am. B 38(1), 95–103 (2021). [CrossRef]
21. G. Y. Shang, G. W. Hu, C. S. Guan, et al., “A non-interleaved bidirectional Janus metasurface with full-space scattering channels,” Nanophotonics 11(16), 3729–3739 (2022). [CrossRef]
22. J. F. Kang, H. H. Jing, C. W. Song, et al., “Research on multifunctional integrated multispectral stealthy metasurface absorbers for infrared and radar,” Infrared Phys. Techn. 131, 104665 (2023). [CrossRef]
23. S. X. Xia, X. Zhai, L. L. Wang, et al., “Plasmonically induced transparency in phase-coupled graphene nanoribbons,” Phys. Rev. B 106(7), 075401 (2022). [CrossRef]
24. Z. M. An, Y. P. Li, X. G. Luo, et al., “Multilaminate metastructure for high-temperature radar-infrared bi-stealth: topological optimization and near-room-temperature synthesis,” Matter 5(6), 1937–1952 (2022). [CrossRef]
25. Y. J. Zhao, R. C. Yang, Y. X. Wang, et al., “VO2-assisted multifunctional metamaterial for polarization conversion and asymmetric transmission,” Opt. Express 30(15), 27407–27417 (2022). [CrossRef]
26. Y. Wang, D. J. Cui, Y. Wang, et al., “Electrically and thermally tunable multifunctional terahertz metasurface array,” Phys. Rev. A 105(3), 033520 (2022). [CrossRef]
27. D. J. Wang, X. J. He, J. X. Jiang, et al., “Photoelectrically-excited terahertz metasurface for switchable and tunable broadband propagation and polarization manipulations,” Diam. Relat. Mater. 131, 109570 (2023). [CrossRef]
28. F. H. Yin, Y. L. Lv, D. Y. Xu, et al., “Multi-functional device: manipulating linear and circular-polarization conversion in a terahertz chiral metamaterial,” Opt. Express 31(17), 27171–27182 (2023). [CrossRef]
29. X. J. Lian, M. T. Ma, J. P. Tian, et al., “Study on a bifunctional switchable metasurface with perfect absorption and polarization conversion based on VO2 and graphene in THz region,” Diam. Relat. Mater. 136, 110060 (2023). [CrossRef]
30. L. Q. Cong, W. Cao, X. Q. Zhang, et al., “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013). [CrossRef]
31. X. R. Zhang, K. Zhang, B. Y. Chen, et al., “Switchable multi-functional broadband polarization converter in terahertz band,” Opt. Express 30(23), 41969–41979 (2022). [CrossRef]
32. J. M. Hao, Y. Yuan, L. X. Ran, et al., “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef]
33. M. S. Islan, J. Sultana, M. Biabanifard, et al., “Tunable localized surface plasmon graphene metasurface for multiband super absorption and terahertz sensing,” Carbon 158, 559–567 (2020). [CrossRef]
34. J. Y. Wang, R. C. Yang, R. B. Ma, et al., “Reconfigurable multifunctional metasurface for broadband polarization conversion and perfect absorption,” IEEE Access 8, 105815–105823 (2020). [CrossRef]
35. F. Fan, Y. Hou, Z. W. Jiang, et al., “Terahertz modulator based on insulator–metal transition in photonic crystal waveguide,” Appl. Opt. 51(20), 4589–4596 (2012). [CrossRef]
36. T. T. Lv, Y. X. Li, H. F. Ma, et al., “Hybrid metamaterial switching for manipulating chirality based on VO2 phase transition,” Sci. Rep. 6(1), 23186 (2016). [CrossRef]
37. D. X. Yan, M. Meng, J. S. Li, et al., “Vanadium dioxide-assisted broadband absorption and linear-to-circular polarization conversion based on a single metasurface design for the terahertz wave,” Opt. Express 28(20), 29843–29854 (2020). [CrossRef]
38. M. K. Liu, H. Y. Hwang, H. Tao, et al., “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef]
39. P. Baum, D. S. Yang, and A. H. Zewail, “4D Visualization of transitional structures in phase transformations by electron diffraction,” Science 318(5851), 788–792 (2007). [CrossRef]
40. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
41. X. Huang, W. He, F. Yang, et al., “Polarization-independent and angle-insensitive broadband absorber with a target-patterned graphene layer in the terahertz regime,” Opt. Express 26(20), 25558–25566 (2018). [CrossRef]
42. S. K. Ghosh, A. Chaudhuri, P. Pal, et al., “A broadband biosensor using graphene-metasurface based cross-polarization converter,” IEEE Sens. J. 22(13), 12820–12828 (2022). [CrossRef]
43. Y. R. Padooru, A. B. Yakovlev, C. S. R. Kaipa, et al., “Dual capacitive-inductive nature of periodic graphene patches: transmission characteristics at low-terahertz frequencies,” Phys. Rev. B 87(11), 115401 (2013). [CrossRef]
44. J. F. Zhou, L. Zhang, G. Tuttle, et al., “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006). [CrossRef]
