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Abstract
Aiming at the problems that most of the existing electromagnetic metasurfaces have single function and narrow application scope, a highly integrated lightning-type metasurface is proposed in this study. It can realize the functions of circular dichroism (CD), absorption of electromagnetic waves, broadband x-to-y cross polarization conversion (CPC) function, linear-to-circular polarization conversion (LTC-PC) function and asymmetric transmission (AT), and its functions are also analyzed and verified. The designed metasurface consists of the bottom grating structure, the lower SiO2, the middle lightning-type graphene, the upper SiO2, the top graphene and photosensitive silicon. Through numerical calculations, the CD of design can reach more than 85% at 4.22 THz. The function of bimodal absorption is achieved at 4.09 and 8.69 THz. At 7.41∼8.21 THz, the polarization conversion ratio (PCR) of the metasurface reaches more than 99%. Simultaneously, the function of LTC-PC can be formed when PCR is 50%. Finally, when the designed metasurface is in the transmissive state, the AT of design is close to 60% at 7.84 THz. This design provides a new design idea and method for biomedical detection, image processing, modulators, smart switches, optical diodes and other fields.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Manipulating electromagnetic waves in an ideal way is an important part of photonics research, and the optical properties of metasurfaces can be determined by artificially designed subwavelength structures, which provides many conveniences for wave manipulation [1]. Therefore, over the past decades, different metasurfaces have been designed for various functions, such as circular dichroism (CD), absorbers, polarizers, and asymmetric transmission (AT). However, with the development of science and technology, we have much higher requirements for the operating speed and memory of devices, which means higher electromagnetic integration. Metasurfaces are ideal candidates for device miniaturization and multifunctional integration [2].
However, in practical situations, tunable electromagnetic metasurfaces can better realize functional switching and dynamic manipulation of electromagnetic waves, so they have wider application value and application prospects. From the current research, tunable multifunctional metasurfaces are mainly realized by some active materials, such as graphene, VO2, photosensitive silicon and so on. Among them, graphene [3], as a two-dimensional material composed of a single layer of carbon atoms arranged in a honeycomb lattice, has good optical transparency and high electron mobility. It has obvious advantages to realize electrically tunable devices in the terahertz range. VO2 is a new type of phase change material with various modulation methods [4], such as temperature control [5], electric control [6–7] and so on. Among them, the bias voltage required for the voltage control is small, which has faster response speed and greater modulation depth. Photosensitive silicon [8] has recently been integrated into the design of metasurfaces due to its excellent optical tunability, which can be switched back and forth between dielectric and metallic states by pump light.
CD can be used in signal processing [9], optical computing [10] and so on. In 2014, Li et al. reported an example of providing absorption for only one circularly polarized wave; and obtained a huge CD through external chirality [11]. In 2017, Liu et al. designed a double-layer dolmen array nanostructure and exploited the coupling between the two layers to form a large CD effect [12]. In 2021, Zhang et al. proposed an actively tunable bi-functional metamirror, which realized better active switching between CD and cross polarization conversion (CPC) [13].
As an important branch of metamaterials, absorbers have also been developed vigorously. In 2008, Padilla's team experimentally demonstrated the first metasurface absorber using an electric ring resonator and a metal wire [14], achieving a single-peak perfect absorption. Subsequently, absorbers with various structures and functions, such as narrow-band absorbers [15], multi-peak absorbers [16], and broadband absorbers [17], have been proposed. This greatly enriches the types and functions of the absorbers.
Polarization switching provides the function of switching electromagnetic waves between two polarization modes, and polarization has also been extensively studied in metasurfaces [18,19]. In 2007, Hao et al. realized the idea of manipulating the polarization of electromagnetic waves in reflection geometry by anisotropic metasurfaces [20]. Li et al. designed a broadband linear-to-circular polarization conversion (LTC-PC) using a double-layer structure, covering the frequency range from 11.0 to 18.3 GHz, in 2015 [21]. Recently, Gao et al. designed a bifunctional metasurface that enables tunable focusing and deflection of visible light [22].
AT has many applications in optical diodes [23], optical non-reciprocal devices [24], and can generally be used to prevent damage to the laser caused by the returning laser beam. In 2010, Menzel first proposed AT of linearly polarized waves, finding a structure showing the behavior of an optical diode [25]. In 2017, Zhang et al. achieved broadband AT by asymmetric photon spin-orbit interactions [26]. In 2021, Ren et al. proposed a multifunctional terahertz metamaterial based on gold and VO2, which realized the switching between ideal absorption and broadband AT [27].
In this work, we demonstrate a lightning-type electromagnetic metasurface that can achieve five functions. It consists of a grating structure composed of gold and VO2 on the bottom, SiO2 on the lower layer, intermediate lightning- type graphene, SiO2 on the upper layer, graphene and photosensitive silicon strips on the top. By adjusting the Fermi level of graphene, the CD reaches more than 85% at 4.22 THz. A bimodal absorption function is achieved at 4.09 and 8.69 THz, and each absorption peak can be adjusted independently. At 7.41∼8.21 THz, the x-to-y CPC rate of the designed metasurface reaches more than 99%. Additionally, the metasurface can also switch from x-polarized to circularly polarized waves. Finally, when the designed metasurface is in the transmissive state, the AT of the design is close to 60% at 7.84 THz. Compared to most existing components that can only achieve two to three functions, our design uses two independent switches, providing metamaterials with greater flexibility. In this study, the integration of five functions has been realized, and the problem of crosstalk between various functions has been successfully solved, and each function is close to perfect. This design demonstrates the strong potential of metasurfaces in controlling electromagnetic waves, and provides a new design idea and method for imaging display [28], wave plate [29], optical absorber [30], optical diode [23], etc.
2. Design and simulation
The unit structure of the lightning-type metasurface is shown in Fig. 1(a). The period of the unit structure is set to P = 3 µm. From bottom to top, there are the bottom grating layer composed of gold and VO2, the lower SiO2, the middle lightning-type graphene, the upper SiO2, the top graphene and photosensitive silicon strips. The dielectric constant of SiO2 is set to 2.25 [31], and the conductivity of gold is 4.561×107 S/m, which can be selected in the material library. It is worth mentioning that the shape of lightning is formed by two equal right triangles. In each right triangle, the short right side is L1 = 0.6 µm, the long right side is L2 = 2 µm, and L3 is equal to 1 µm. The clockwise rotation angle of the two triangles is θ. The remaining geometric parameters are listed in Table 1. An external bias circuit is used to tune each layer of graphene and control the on-off state of VO2, as shown in Fig. 1(b). To control the Fermi level of graphene, a bias voltage V is placed between the graphene and bottom gold. The electrodes are placed on the corresponding graphene layers. The relation between Ef and V can be expressed as ${E_f} \approx \hbar {V_f}{({\pi {\varepsilon_0}{\varepsilon_r}V/({ed} )} )^{1/2}}$ [13]. $ {E_f}$ represents the Fermi level of graphene, ${V_f} = 1.1 \times {10^6}\; m/s$ is the Fermi velocity, ${\varepsilon _0} = 8.854 \times {10^{ - 12}}$ represents the permittivity of the vacuum, ${\varepsilon _r}$ represents the relative dielectric constant, V is the external gate voltage, and d represents the distance between the two electrodes. The Fermi level of the middle graphene is set to EF1, and the Fermi level of the top graphene is set to EF2. Two electrodes are placed at the bottom to control VO2, and changing the voltage V3 can switch the on-off state of VO2.
Fig. 1. (a) Schematic diagram of the unit structure of the proposed metasurface. (b) The schematic of the external bias circuit for the entire period structure.
Table 1. The geometric parameters of the designed metasurface elements.
The metasurface proposed in this study is simulated and verified by the finite integration method. In this simulation, the floquet port is applied in the z direction, and periodic boundary conditions are used in the x and y directions. The graphene is set as a two-dimensional plane. For the complex surface conductivity of graphene, we use Drude model to describe it [32]:
In the design process, we consider using an applied voltage to achieve the switching between two stable states of VO2 dielectric and metal [6,7], to achieve the performance of a switch. Therefore, we do not consider intermediate change states of VO2. The optical properties of VO2 can also be described by the Drude model [4]:
The dielectric constant of the top photosensitive silicon is 11.7 [8]. By changing the external pump light power, we can change the conductivity of the photosensitive silicon, to realize the switching between the dielectric and the metal state of the photosensitive silicon, and form an optical switch at the top. The conductivity change of photosensitive silicon with pump power can be expressed as [35]:
where l is the energy flux power of the pump beam. In the case of no pump beam illumination, the conductivity of the photosensitive silicon is set to 1 S/m, which appears as a dielectric state. When the pump light intensity reaches 294 µJ/cm2 [8], the conductivity of the photosensitive silicon is ${\sigma _{si}} = 1 \times {10^5}$ S/m, which is a metallic state. Furthermore, the optically pumped excitation intensity of VO2 is 8 mJ/cm2[36], so the properties of VO2 are hardly affected when photosensitive silicon is excited.3. Results and discussion
For the lightning-type metasurface, we consider full-space analysis from three aspects of absorption, reflection and transmission, to verify the versatility of the design and the advantages of various functions. Among them, VO2 is set as switch 1 (dielectric state VO2 is on, metal state VO2 is off), photosensitive silicon is set as switch 2 (dielectric state photosensitive silicon is on and metal state photosensitive silicon is off). In practical application, SiO2 not only plays the role of impedance matching, but also helps to fix the structure and prevent corrosion.
3.1 Absorption
Switch 1 remains closed, which forms a complete reflective layer with the bottom gold to prevent the transmission, and open switch 2 to not affect the absorption of the metasurface. Next, we consider incidence with circularly polarized waves to demonstrate the enormous CD of the metasurface and incidence with x-polarized waves for the design of an absorber.
3.1.1 Circular dichroism
Circular dichroism refers to the characteristic that chiral objects have differential absorption on right circular polarization (RCP) and left circular polarization (LCP) waves, which can be expressed as $C{D_A} = {A_R} - {A_L}$. Furthermore, the switch 1 is in the off state to prevent the transmission. Therefore, ${A_R} = 1 - {R_{RR}} - {R_{LR}}$ represents the absorptivity of RCP waves, and ${A_L} = 1 - {R_{RL}} - {R_{LL}}$ represents the absorptivity of LCP waves. When the circularly polarized waves are illuminated along the forward direction (+ z), the clockwise and counterclockwise rotations of the electric vector along the direction of propagation are defined as RCP and LCP waves, respectively. Therefore, the conversion relationship between incident and reflected waves can be expressed as Jones matrix [13,37]:
After knowing the above conversion relationship, the physical mechanism behind the CD can be analyzed. Figure 2 (a) shows the reflections of the designed metasurface under the incidence of LCP and RCP waves when the EF1 is 0.3 eV and the EF2 is 0.7 eV. The cross-polarized reflectivity of the RCP and LCP waves are equal, while their co-polarizations are different. At 4.22 THz, the value of rRR is close to 0, and the rLL is close to 0.85, which results in a CD of 0.85, as shown in Fig. 2(b). In the designed graphene structure, this CD originates from the interference of multiple reflections. The LCP and RCP waves are considered to be mirror images of each other with respect to the y-z plane. The mirror symmetry of the top graphene guarantees the same optical behavior for both circular polarization states. However, lightning-type graphene lacks mirror symmetry in the y-z plane, resulting in different phase shifts for the two polarization states. Lightning-type graphene is rotated by 45°, which allows LCP and RCP waves to produce 90° phase accumulations of opposite sign. Therefore, the total phase difference of the two circularly polarized waves is 180°, which leads to the simultaneous occurrence of destructive interference of RCP and constructive interference of LCP. Therefore, the RCP wave is almost completely absorbed, while the LCP wave is largely reflected, resulting in a maximum value of CD. Figure 2 (c) explores the effect of θ on CD. When θ = 0°, the CD at 4.22 THz disappears, and when θ = -45°, the spin-selective absorption is reversed, and the RCP waves are reflected, while LCP waves are absorbed. This proves that the CD is largely dependent on the rotation angle θ of the lightning-type graphene.
Fig. 2. Under RCP and LCP waves incidence, (a) reflectivity; (b) absorptivity and CD; (c) CD at different rotation angles θ; magnetic field profiles at 4.22 THz for RCP waves (d) and LCP waves (e) incidence.
To further reveal the cause of CD formation, the magnetic field distributions at 4.22 THz are shown in Fig. 2(d) and (e). When the RCP waves are incident, a magnetic field will be generated in the lower SiO2. This is because the lightning-type graphene interacts with the bottom to form a classical magnetic dipole resonance, which leads to huge absorption. Simultaneously, when the LCP waves are incident, the whole metasurface hardly forms a magnetic field, and most of the incident waves are reflected. The concentration of the magnetic field in the lower SiO2 proves that the main cause of CD generation is the symmetry breaking of the rotation of lightning-type graphene again [38,39].
To evaluate the effect of different layers of graphene on CD, Fig. 3 shows the change of CD on the metasurface when the Fermi level of graphene is changed separately. It can be seen from Fig. 3(a) that when the Fermi level of the top graphene is fixed at EF2 = 0.7 eV, the middle graphene is more sensitive, and the frequency corresponding to the maximum CD will be shifted. A larger CD can be formed only around EF1 = 0.3 eV. When EF1 = 0.3 eV, the EF2 is above 0.6 eV, which can produce a good CD effect, as shown in Fig. 3(b). This verifies the huge influence of the middle graphene on CD, while the top graphene has a larger range of choices when achieving larger CD.
Fig. 3. (a) The variation of CD with intermediate graphene Fermi level and frequency when EF2 = 0.7 eV. (b) The variation of CD with top graphene Fermi level and frequency when EF1 = 0.3 eV.
Figure 4 shows the CD effect at different incident angles α and polarization angles φ. It can be seen from Fig. 4(a) that even if the incident angle under the x-z plane reaches 50°, the designed metasurface can still maintain the CD of more than 0.8 at 4.22 THz. When the incident angle of the y-z plane is adjusted, the CD of the metasurface can also reach more than 0.8 in the case of α=50° (Fig. 4(b)). Furthermore, the incident waves cannot always remain at forward incidence in practice. Therefore, in Fig. 4(c), we analyze the influence of the orientation of the polarization angle on the CD when the incident angle α is 20°. It can be found that CD can remain stable at any polarization angle. Based on the above discussion, the lightning-type metasurface is angle-insensitive for the application of spin-selective absorbers.
Fig. 4. The variation of CD with different incident angles α and frequency under RCP and LCP waves; (a) α is in the x-z plane; (b) α is in the y-z plane; (c) CD varies with the polarization angle φ and frequency when α is fixed at 20°.
3.1.2 Absorption of linearly polarized waves
The absorption of linearly polarized waves has always been a hotspot in metasurface research due to its wide application in photodetection, photovoltaic cells, etc. [40,41]. Here, we take x-polarized waves incidence as an example. Similarly, its absorptivity can be calculated by A = 1-R-T, where R represents the reflectivity and T represents the transmittance. Since switch 1 is in the off state, waves cannot pass through the metasurface, that is, the transmittance is zero, so the absorptivity is determined only by the reflectivity. Since the designed metasurface is not symmetrical, there are two cases of co-polarized reflection Rxx and cross-polarized reflection Ryx. To obtain the best absorptivity, we must suppress these two reflections as much as possible. After parameter optimization, EF1 is set to 0.3 eV and EF2 is set to 1.2 eV. For the cross-polarized reflection Ryx, we consider adjusting the rotation angle θ to suppress. Figure 5(a) shows the variation of the cross-polarized reflectivity Ryx with the rotation angle θ. It can be seen intuitively that Ryx can be well suppressed in the full working range when θ is in the range of -25∼15°. Among them, the optimal value θ = -25° is selected for the following analysis and verification. Figure 5(b) depicts the reflectivity and transmittance of the designed metasurface. The transmission Txx, Tyx, and the cross-polarized reflection Ryx are well suppressed in the entire operating frequency band. At 4.09 and 8.69 THz, the co-polarized reflection Rxx is well suppressed, resulting in two perfect absorption peaks, as shown in Fig. 5(c). By comparing the solid and dashed lines, we can conclude that the entire absorption spectrum is approximately the spectral combination of top graphene and lightning-type graphene. Lightning-type graphene forms an absorption peak at 4.09 THz, and the absorption rate reaches 94.9%. The top graphene forms an absorption peak at 8.69 THz, and the absorption rate reaches 97.5%. When a voltage is applied to both layers of graphene simultaneously, a superposition of the two single absorption peaks described above is formed. The small interaction between graphene layers leads to a slight blue shift of the two absorption peaks. Figure 5(d) shows the impedance matching diagram of the designed metasurface when θ = -25°. The relative impedance of this design is expressed as ${Z_r} = Z/{Z_0} = 1$. The structural impedance can be obtained by the formula $Z = \sqrt {\frac{{{{({1 + r} )}^2} - {t^2}}}{{{{({1 - r} )}^2} - {t^2}}}} $ [42], where r is the reflection coefficient and t is the transmission coefficient. At 4.09 and 8.69 THz, the real and imaginary parts of the relative impedance are close to 1 and 0, respectively, thus verifying the effect of perfect double-peak absorption.
Fig. 5. Under x-polarized waves, (a) variation of cross-polarized reflectivity Ryx with rotation angle θ and frequency; (b) The reflectivity and transmittance of the designed metasurface when θ is equal to 25°; (c) Absorptivity when voltage is applied to different layers of graphene. (d) Schematic diagram of the real and imaginary parts of impedance matching.
To further analyze the formation mechanism of the absorption peak, the electric field distributions of two layers of graphene at different frequencies are shown in Fig. 6. It is found that a series of resonances occurred in this frequency range, corresponding to the excitation of the lightning-type graphene and the excitation of the top graphene. Surface plasmon resonance of graphene couples the patterned graphene to the electric field and provides electric dipole resonance. In Fig. 6(a1) and (a2), the electric field is mainly concentrated in the gap of the lightning-type graphene, which is caused by the plasmon resonance between the lightning-type graphene and the underlying metal reflective layer. The electric field is stronger at 4.09 THz and close to zero at 8.69 THz, which is a good proof that lightning-type graphene causes the absorption peak at 4.09 THz and has little effect on the absorption peak at 8.69 THz. In Fig. 6(b1) and (b2), the electric field is mainly concentrated on the long sides of the graphene strips, and the electric dipoles between adjacent graphene strips are coupled to each other to excite resonance. The electric field is stronger at 8.69 THz and close to zero at 4.09 THz. This also proves that the top graphene induces the absorption at 8.69 THz and has little effect on the absorption peak at 4.09 THz. In Fig. 6(c), when only EF1 is adjusted, the frequency corresponding to the low-frequency absorption peak starts to change, while the high-frequency absorption peak almost remains stable. In Fig. 6(d), when only EF2 is adjusted, the frequency corresponding to the high-frequency absorption peak changes while the low-frequency absorption peak remains stable. This demonstrates the individual modulation effects of the two layers of graphene on their corresponding absorption peaks. There is almost no coupling effect between the two layers of graphene.
Fig. 6. The electric field distributions at the middle graphene, (a1) 4.09 THz, (a2) 8.69 THz. The electric field distributions at the top graphene, (b1) 4.09 THz, (b2) 8.69 THz. (c) Absorption spectrogram of different EF1. (d) Absorption spectrograms of different EF2.
3.2 Reflective polarization conversion
Polarization is an important property of light due to many inherent polarization-sensitive phenomena. The ability to manipulate polarization states is of great interest for many applications [19,20]. Here, we design the lightning-type metasurface as a reflective polarization converter. Therefore, switch 1 is in the closed state to prevent the transmission of the waves, and switch 2 is in the open state so as not to affect the polarization conversion. We still choose to use the x-polarized waves, and the rotation angle θ is 45°. The Stokes parameter can be used to describe electromagnetic waves and their polarization states as follows [43]:
where Rxx and Ryx represent the reflection coefficients of co-polarization and cross-polarization, respectively. In, Qn, Un, Vn represent total reflectance, horizontal and vertical linear polarization states of reflection, +45° or -45° linear polarization states of reflection, and circular polarization state, respectively. $\Delta \phi = {\phi _{yx}} - {\phi _{xx}}$ represents the phase difference. When $\Delta \phi = 2n\pi \pm \pi $, the x-polarized waves can be converted into y-polarized waves. When $|{{R_{xx}}} |= |{{R_{yx}}} |$ and $\Delta \phi = 2n\pi \pm \pi /2$, linearly polarized waves can be converted to circularly polarized waves (n is the integer). To describe the resulting circularly polarized waves, we introduce the normalized ellipticity $\chi = V/I$. When χ is -1 and +1, they correspond to RCP and LCP waves, respectively. Correspondingly, the linear polarization can be displayed by the polarization conversion ratio (PCR) [20], $PCR = \frac{{{{|{{R_{yx}}} |}^2}}}{{{{|{{R_{xx}}} |}^2} + {{|{{R_{yx}}} |}^2}}}$.Figure 7 shows the reflectance (Rxx, Ryx), transmittance (Txx, Tyx), phase difference $\Delta \phi $, PCR, and corresponding ellipticity χ of the lightning-type metasurface as a reflective polarizer. After optimization, EF1 is set to 1 eV and EF2 is set to 0.7 eV. The PCR reaches the peaks at 7.60 and 8.06 THz, resulting in the PCR of the designed metasurface reaching more than 99% in the wide frequency range of 7.41∼8.21 THz, achieving a perfect x-to-y CPC function. Meanwhile, at 7.12 and 8.51 THz, the PCR is equal to 0.5, which means $|{{R_{xx}}} |= |{{R_{yx}}} |$. Additionally, the corresponding phase difference at these two points are also close to -90°, so the function of LTC-PC is realized. The ellipticity χ calculated in the figure is close to -1 at both points, that is, RCP waves are formed.
Fig. 7. Reflectance (Rxx, Ryx) and transmittance (Txx, Tyx), polarization conversion ratio PCR, phase difference Δϕ, and corresponding ellipticity χ under x-polarized waves incidence.
To better understand polarization conversion, the incident x-polarized wave is decomposed into two orthogonal components (u and v components), as shown in Fig. 8. The u-v coordinate system is a coordinate system rotated 45° around the z-axis from the x-y coordinate system. When the surface current directions of the two layers are the same, it means that the polarization switching is caused by electrical resonance. When the surface currents of the two layers are in opposite directions, they form a current loop in the dielectric material, so the type of resonance is considered to be magnetic resonance. Here, we selected the current distributions of 7.12, 7.60, 8.06 and 8.51 THz for the analysis. At 7.12 and 7.60 THz, when the u-polarized wave is incident, the surface current at the lightning-type graphene (Fig. 8 (a and f)) and the surface current at the bottom reflective layer (Fig. 8 (b and g)) form magnetic resonance and generate equivalent magnetic resonance moments m1, m3. Similarly, when the v-polarized wave is incident, the magnetic moment m2 is formed at 7.12 THz (Fig. 8 (c and d)). At 7.60 THz, the surface current at the lightning-type graphene (Fig. 8 (h)) and the surface current at the bottom reflective layer (Fig. 8 (i)) form an electrical resonance, thus generating an electrical moment p1. In Fig. 8 (e and j), m1, m2 and m3, p1 control the magnitude and phase of the reflected electric field along the u and v axes, respectively. Similarly, at 8.06 and 8.51 THz, the magnitude and phase of the reflected electric field are controlled by p2, p3, p4 and p5. The electrical moments p2, p4 are derived from the electrical resonance generated by the incidence of u-polarized waves (Fig. 8 (k, l, p and q)). The electrical moments p3 and p5 are derived from the electrical resonance generated by the incidence of v-polarized waves (Fig. 8 (m, n, r and s)). If the u and v components of the reflected electric field have equal amplitudes and the phase difference is close to 90°, the LTC-PC function can be realized. These two resonant modes are extremely important for realizing broadband and efficient polarization conversion.
Fig. 8. Surface current distribution maps. The images from the 1st to 4th row show the case for 7.12, 7.60, 8.06, and 8.51 THz, respectively. The 1st and 3rd columns show the current distributions on the lightning-type graphene, and the 2nd and 4th columns show those on the bottom reflector; the 1st and 2nd columns show those for the u-polarized incident wave, and the 3rd and 4th columns show those for the v-polarized incident wave. Column 5 shows the equivalent electric eoments and equivalent magnetic moments diagrams.
Figure 9 shows the variation of PCR with the Fermi level of graphene. It can be seen from Fig. 9(a) that the relatively low EF1 cannot produce the large PCR. When the EF1 reaches above 0.8 eV, the bandwidth of the PCR increases and widens with the increase of the Fermi level of the middle graphene, and the optimal value is reached when EF1 = 1 eV. Figure 9(b) shows the change of the PCR with the Fermi level of the top graphene. EF2 has less effect on the PCR than EF1 over the whole working frequency. It is basically stable in the range of 0.6∼0.8 eV, and finally EF2 is set to 0.7 eV for the best results. It can be seen from the above analysis that EF1 has a greater impact on the amplitude than EF2. The top graphene increases the asymmetry of the structure, and applying an appropriate voltage to it can promote the increase of PCR. In comparison, lightning-type graphene is more important, the symmetry breaking is used to form polarization conversion. It forms a good localized surface plasmon resonance under a certain voltage, and forms a magnetic resonance with the bottom reflective layer.
Since the polarization conversion comes from the anisotropic design of the lightning-type metasurface, it is also related to the polarization of the incident waves. Therefore, we show the PCR at different incidence angles in Fig. 10. Among them, Fig. 10(a) shows the effect of the incident angle α of the x-z plane on the PCR, while Fig. 10(b) shows the effect of the incident angle α of the y-z plane on the PCR. Whether in the x-z or y-z planes, the bandwidth of PCR inevitably decreases with the increase of incident angle. This is because the interaction between the metasurface and the incident electromagnetic waves is weakened with the increase of the incident angle, which weakens the intensity of the reflected waves. However, in the range of α=±30°, the PCR still maintains a high value.
Fig. 10. The variation of the PCR with the change of the incident angle α and frequency. (a) x-z plane; (b) y-z plane.
3.3 Asymmetric transmission
Asymmetric transmission has important applications in optical reciprocal devices [24] due to its properties similar to optical diodes. When the switch 1 is on, a grating structure is formed at the bottom to facilitate the transmission of waves. The switch 2 is closed so that the top photosensitive silicon and the bottom grating form an orthogonal structure to increase the transmission polarization conversion. Here, linearly polarized waves are still choosed, and the rotation angle θ is set to 45°. After parameter optimization, EF1 is set to 1 eV, and EF2 is set to 0.7 eV. The relationship between forward (+z) and backward (-z) incident polarized waves is expressed by Lorentz reciprocity theorem [27]:
To better explain the linear polarization conversion under the transmission of x and y linearly polarized waves, PCR is expressed as:
Figure 11(a) shows the transmittance under forward incidence of linearly polarized waves. At 7.84 THz, Tyx reaches its maximum value close to 0.6, while Tyy, Txx and Txy are all at lower levels. In Fig. 11(b), Txy is close to 0.6, while Tyy, Txx and Tyx are all at small values. Therefore, their total transmittance (Fig. 11(c)), AT, and PCR (Fig. 11(d)) are calculated, respectively. At 7.84 THz, the transmittance of the forwardly incident x-polarized waves and the backwardly incident y-polarized waves are higher, while the transmittance of the backwardly incident x-polarized waves and the forwardly incident y-polarized waves are lower. This proves that the lightning-type metasurface has a distinct difference in transmission for forward and backward linearly polarized waves. The AT under forward incidence of x and y polarized waves can be calculated by Eqs. (12) and (13), where AT reaches its maximum value at 7.84 THz. The AT corresponding to the x-polarized waves is close to +0.6, and the AT corresponding to the y-polarized waves is close to -0.6. This proves that the design of the lightning-type metasurface agrees well with the Lorentz reciprocity theorem. Additionally, we also calculate the PCR of x and y polarized waves under forward incidence through formulas (14) and (15). It can be found that PCRx is close to 1 and PCRy is close to 0. The great difference in polarization conversion between the two polarized waves also reveals the generation of the efficient AT.
Fig. 11. The transmittance under forward (a) and backward (b) incidence, and the total transmittance (c) are calculated when the linearly polarized waves are incident. (d) Asymmetric transmission and polarization conversion ratio under forward incidence of linearly polarized waves.
In Fig. 12, we present the electric and magnetic field distributions at 7.84 THz corresponding to different incident waves and incident directions. The Fabry-Pérot-like cavity model [44] is used to illustrate the specific operation mechanism, as shown in Fig. 12(a). The top grating formed by photosensitive silicon and the metal bottom grating can be regarded as two polarizers. Photosensitive silicon is used to transmit x-polarized waves and block y-polarized waves, and gold gratings are used to transmit y-polarized waves and block x-polarized waves. Lightning-type graphene is mainly used to convert the polarization state of waves. Taking the forward incidence of x-polarized waves as an example, the x-polarized waves can pass through the grating formed by the photosensitive silicon. When passing through the intermediate graphene, the x-polarized waves are divided into four parts (rxx, ryx, txx, and tyx). where rxx is the reflected x-polarized wave, which eventually exits the top layer since the top photosensitive silicon does not block the x-polarized wave. ryx represents the reflected y-polarized wave, which cannot pass through the silicon grating structure and can only be reflected again. It transmits back and forth between the silicon grating and the intermediate graphene to form the first F-P cavity. Due to the polarization coupling and constructive interference of lightning-type graphene, unconverted x-polarized wave (txx) and converted y-polarized wave (tyx) can be coupled with lightning-type graphene to achieve high transmission performance (Fig. 12(b1) and (b2)). After txx passes through the middle graphene, since the bottom gold grating cannot transmit the x-polarized wave, it can only transmit back and forth between the middle graphene and the bottom grating, thus forming the second F-P cavity. Multiple reflections and transitions result in high transmittance of txx. The bottom grating only blocks the transmission of the x-polarized waves, so tyx will not be blocked, and finally the larger AT and PCR are formed. From the above analysis, we know that the backward incidence of y-polarized waves is also this principle (Fig. 12(e1) and (e2)). The y-polarized forward and x-polarized backward waves cannot pass through the respective first gratings, so the transmittance is almost zero (Fig. 12(c1) - (d2)). Additionally, it should be noted that the top photosensitive silicon is only similar to the grating structure, so they cannot completely prevent the incidence of y-polarized waves, which will also cause weak transmission (Fig. 12(c1) - (c2)).
Fig. 12. (a) The Fabry-Pérot-like cavity model of the proposed structure. Electric (b1, c1, d1 and e1) and magnetic (b2, c2, d2 and e2) field distributions at 7.84 THz. (b1) and (b2) correspond to x-polarized forward incidence. (c1) and (c2) correspond to y-polarized forward incidence. (d1) and (d2) correspond to x-polarized backward incidence. (e1) and (e2) correspond to y-polarized backward incidence.
The variation of AT with EF1 and frequency is simulated in Fig. 13(a) when the x-polarized waves are incident in the forward direction. Generally, the AT increases with the increase of EF1. The value of AT is higher when EF1 is in the range of 0.8∼1 eV, and AT is lower when EF1 is below 0.8 eV. The larger change of AT with EF1 also demonstrates the dominant role of the intermediate graphene in polarization conversion. In Fig. 13(b), the change of AT with EF2 is relatively weak. We speculate that the main function of the top graphene is to prevent the reflection of excessive rxx, which increases the transmittance to a certain extent. Additionally, if the EF2 is too large, the polarized waves entering the metasurface will be reduced. Therefore, we set EF2 to be 0.7 eV after the actual simulation calculation.
Fig. 13. When the x-polarized waves are incident in the forward direction, (a) the variation of AT with EF1 and frequency; (b) the variation of AT with EF2 and frequency.
Finally, we summarize the functions of the metasurface and compare them with existing designs (Table 2). To demonstrate the versatility and utility of the proposed structure, photodetection is presented as a specific application scenario. When the metasurface is in the AT function, it can act as an optical non-reciprocal device [24] to select or decode light to obtain the desired signal. Then, when the metasurface is in the x-to-y CPC function and the LTC-PC function, it can be used to perform a full Stokes characterization of the desired optical signal [50], not just most current single point measurements. Through characterization, we can realize material structure detection, biological cell fluorescence measurement and so on. When chiral molecules such as amino acids and DNA need to be detected, the CD function can also be used for circular dichroism detection in the terahertz range. In addition, the narrow-band bimodal absorption function usually acts as a good sensor [51], and thus can also be used for substance detection. This is beneficial for improving detection accuracy and realizing diversified detection with a single device in the future.
Table 2. Comparison of the designed metasurface with existing multifunctional metasurfaces.
4. Potential fabrication process
In this section, the potential fabrication process of the designed structure is given, as shown in Fig. 14. The following steps can be followed: (a) The photoresist is spin-coated and deposited on the substrate by lithography technology to form the designed structure; (b) VO2 with a thickness of 0.1 µm is prepared by magnetron sputtering technique; (c) The VO2 grating structure is formed by the lift-off process, and the remaining VO2 is annealed at 450 °C; (d) Gold grating structures with a thickness of 0.1 µm are fabricated by lithography and metallization [52]. (e) The lower layer of SiO2 is deposited by low pressure chemical vapor deposition (LPCVD) [53] with 5 µm. (f) Graphene films are grown on SiO2 by plasma enhanced chemical vapor deposition (PECVD). (g) Then, the PMMA positive resist is spin-coated and dried. (h) The interlayer graphene is prepared by electron beam lithography and reactive ion etching system [54]. (i) LPCVD is used again to deposit 6 µm of upper SiO2. (j) Silicon of 0.2 µm is prepared on SiO2 by PECVD technology [8,55], and the rest is protected with PMMA. (k) Remove the PMMA protective layer. (l) Graphene films are grown on SiO2 by PECVD.
5. Conclusions
In conclusion, this study proposes a lightning-type metasurface that can realize multiple functions. The CD of the designed metasurface can reach more than 85% at 4.22 THz. The bimodal absorber function is realized at 4.09 and 8.69 THz. At 7.41∼8.21 THz, the PCR of the designed metasurface reaches more than 99%. Simultaneously, when the PCR is 50%, the function of LTC-PC can be formed. Finally, when the metasurface is in the transmissive state, the AT of this design approaches 60% at 7.84 THz. Compared with most of the previous metasurface designs, we demonstrate the omnidirectional control of metasurfaces and realize the integration of multiple functions, breaking the limitations of using a single function. We hope this research will convince readers that metasurfaces can indeed provide a good way to meet the challenges of multifunctional, efficient devices for future applications.
Funding
National Key Research and Development Program of China (2019YFB2203904); National Natural Science Foundation of China (62075047, 61965006, 61975038, 61964005); Natural Science Foundation of Guangxi Province (2020GXNSFDA297019, 2020GXNSFAA238040, 2021GXNSFAA075012); Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20107); Innovation Project of Guang Xi Graduate Education (YCSW2022272).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the corresponding author upon a reasonable request.
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