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Abstract
With the development of metasurfaces and the improvement of manufacturing technology, it is important and imperative to design novel metasurfaces that can flexibly manipulate terahertz (THz) waves. In this paper, a multifunctional metasurface (MFMS) based on graphene and photosensitive silicon (Si) is proposed, which integrates three functions: broadband absorption, broadband linear and circular polarization conversions in THz band. For absorption mode, the MFMS can absorb above 90% energy in the frequency band of 1.74-3.52 THz with the relative bandwidth of 67.6%. For both linear-linear and circular-circular polarization conversion modes, the relative bandwidth with over 90% polarization conversion rates (PCRs) reaches 49.3% in the frequency band of 1.54-2.55 THz. The working mechanism of the MFMS is analyzed by the surface current distributions, and its properties of the absorption and polarization conversion under oblique incident angles are investigated, respectively. The proposed metasurface has promising prospects in terahertz devices such as modulators, smart switches and other terahertz devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces are a kind of artificial layered electromagnetic (EM) metamaterials with 2D periodic structure and subwavelength thickness. By elaborately designing the unit structure of the metasurfaces, the amplitude, phase and propagation modes of the incident EM waves can be manipulated. Because of its unique EM response, metasurfaces attract extensive research interests and achieve rapid development in recent years, appearing many novel EM metasurface devices such as metalens imaging [1–3], beam steering [4–6], electromagnetically induced transparency [7], graphene biosensing [8], superconductors [9], stealth technology [10,11], absorbers [12–15] and polarization converters [16,17], etc.
Metasurface absorbers, which take advantage of its large loss characteristics, can effectively dissipate the incident EM waves. In 2008, Landy et al. innovatively proposed a perfect metasurface absorber composed of split-ring resonator and metal-wire structure, which achieved a single band perfect absorption [18]. After that, many researchers adopted different design schemes or materials, such as graphene [19–22], indium tin oxide (ITO) [23] vanadium dioxide (VO2) [24,25] and photosensitive Si [26,27], to design metasurface absorbers to expand the working frequency to dual-band [28,29], multi-band [30] and broadband [31,32]. For example, Liu et al. proposed a single-layer graphene absorber with annular grooves to achieve broadband absorption in the range of 7-9.25 THz [20]. Bai et al. demonstrated a high-temperature stability metasurface absorber based on ITO rectangular split ring pattern, which can realize broadband absorption in the microwave frequency band [23]. Yuan et al. designed a metasurface absorber with embedded photosensitive Si, which can achieve photoexcited switchable single-/dual-band terahertz metamaterial absorption [27].
On the other hand, polarization is an important characteristic of EM waves, which is usually described by the trajectory of the electric field vectors. Recently, some metasurface converters have been widely reported [33–38], which can regulate incident linear or circular polarized EM waves. For example, Grady et al. designed two polarization converters based on metal cut-wire array and gold gratings metasurface, which realized broadband linear polarization conversion in reflection and transmission modes, respectively [33]. Subsequently, Gao et al. proposed a polarization converter with double V-shaped resonators to achieve efficiently reflective broadband linear polarization conversion [34]. Sajjad et al. demonstrated two distinct cross-polarization converters based on graphene groove structure, achieving tri-band and broadband linear/circular cross-polarization conversion, respectively [37].
In practice, the metasurface absorbers or polarization converters with single function limit their application. Therefore, some MFMSs that combine absorption and polarization conversion have attracted the interest of researchers [39–45]. By embedding a variety of tunable medium such as diodes [39,40], VO2 [41–43] and graphene [44,45] into metasurfaces, some switchable MFMSs have been achieved. For example, Wang et al. designed a MFMS by embedding PIN diodes, which realizes switching between broadband absorption and linear polarization conversion functions [39]. Song et al. and He et al. respectively designed different bifunctional metasurface with perfect absorption and polarization conversion based on insulating-to-metallic state transition of VO2 [41,42]. Zhang et al. proposed a graphene-based MFMS that can be switched from a broadband half-wave plate to a broadband quarter wave plate for linear and circular polarization conversion [45].
However, these MFMS mentioned-above only realized the bifunctions that switches between absorption and linear polarization conversion, or the linear and circular polarization conversions. It is essential to design true MFMS for the development of highly integrated devices. In this paper, a graphene-based metasurface is firstly designed to realize broadband absorption, then, a MFMS integrated graphene and photosensitive Si is proposed to achieve broadband absorption, y/x-polarized to x/y-polarized and left-handed/right-handed circular polarization (LCP/RCP) to RCP/LCP conversion in one structure without reengineering it. Compared with the previous metasurfaces, the proposed MFMS has the advantages of diverse functions, broad operating frequency bands, high efficiency and flexible controllability.
2. Structure designs and simulation results
2.1 Dynamically tunable broadband GMA
We firstly design a graphene-based metasurface absorber (GMA) with tunable broadband absorption, whose perspective view of 4×4 array and patterned graphene layer are shown in Fig. 1. The structure consists of bottom metal (BM) layer, dielectric layer 1, continuous graphene (CG) layer, dielectric layer 2 and patterned graphene (PG) layer. The top PG layer is a periodically arranged graphene with four split semicircular and cross-shaped grooves. This structure can concentrate the electric field and charge carriers around the grooves, which can enhance the surface plasmons of the PG layer [44]. The CG layer will play a role of gated element, the EM response of the structure can be controlled by tuning Fermi level of the graphene layers [45]. The BM layer is used to block the transmission of EM waves. Both dielectric layer 1 and 2 are lossy cyclic olefin copolymer (COC) with the relative permittivity of ${\varepsilon _{\textrm{COC}}} = 2.1$ and the loss tangent of $\tan \delta = 0.0006$ [46]. The BM layer is gold with the conductivity of ${\sigma _{\textrm{gold}}} = 4.56 \times {10^7}\textrm{ S/m}$ and the thickness of 0.2 µm. The optimized geometric parameters are shown in Table 1.
Fig. 1. Schematic diagram of (a) the array with 4×4 unit cells and (b) the top view of the graphene pattern layer.
Table 1. The optimized geometric parameters of the GMA
All the spectra and results in this paper are obtained by CST simulation software based on the finite integral method. In the simulation, the EM wave is illuminated to the metasurface along the Z axis, the unit cell boundary condition is set along the X and Y axis directions, and the open (add space) is set along the Z axis direction. The absorptivity of the GMA can be calculated by the formula $A(\omega )\textrm{ = 1} - R(\omega ) - T(\omega )$, where $R(\omega )\textrm{ = |}{S_{\textrm{11}}}{\textrm{|}^\textrm{2}}$ is the reflectivity, $T(\omega )\textrm{ = |}{S_{\textrm{21}}}{\textrm{|}^\textrm{2}}$ is the transmissivity, and S11 and S21 are the scattering parameters of the reflected and the transmitted wave, respectively. Because the skin depth of the gold is less than the thickness of the BM layer at THz, the transmissivity is zero, and the absorptivity formula can be simplified as $A(\omega )\textrm{ = 1} - R(\omega )$ [47].
The properties of monolayer graphene are characterized by the complex surface conductivity, which are presented by Eqs. (4)–(8) in the Appendix. The surface conductivity of graphene can be effectively changed by adjusting the Fermi level. When ${\mu _\textrm{c}} = 0\textrm{ eV}$, the graphene is equivalent to a thin dielectric layer for EM waves; with the increase of the Fermi level, the surface conductivity of graphene will be gradually enhanced and the graphene will exhibit metallic state. In order to study the electrical tunable characteristics of the GMA, Figs. 2(a) and 2(b) present the reflection coefficients and absorptivity curves of the GMA at different Fermi levels of graphene, respectively. It can be seen from Fig. 2(a) that the reflection coefficients |rxy| of the cross-polarized wave are almost zero because the GMA has a fourfold rotational symmetry structure, and the reflection coefficients |ryy| of the co-polarized wave gradually decrease as the Fermi level of graphene increasing. According to the absorptivity formula $A(\omega ) = 1 - R(\omega )\textrm{ = 1} - \textrm{|}{r_{\textrm{yy}}}{\textrm{|}^\textrm{2}} - \textrm{|}{r_{\textrm{xy}}}{\textrm{|}^\textrm{2}}$, the absorption peak exhibits blue-shift and the absorptivity and bandwidth gradually increases as the graphene Fermi level increasing from 0.15 to 0.85 eV, as shown in Fig. 2(b). This indicates that the broadband absorption can be dynamically adjusted by changing the Fermi energy levels of the PG layer. The increased absorptivity arises from the increase of inherent loss of the GMA with the higher µc, it is beneficial to induce the stronger plasma oscillation and enhance absorption performance [19]. When the Fermi level of graphene reaches ${\mu _\textrm{c}}\textrm{ = 0}\textrm{.85 eV}$, the GMA can achieve a broadband absorption with the absorptivity of over 90% in the range of 2.06-3.71 THz, whose bandwidth and relative bandwidth are 1.65 THz and 57.2%, respectively. For the absorptivity of over 80%, the corresponding bandwidth and relative bandwidth can reach 2.28 THz and 82%, respectively.
Fig. 2. (a)The magnitudes of the co-polarized and cross-polarized reflection coefficients and (b) the absorption spectra of the GMA when graphene Fermi level increases from 0.15 to 0.85 eV, (c) the retrieved parameters of permittivity and permeability and (d) the normalized equivalent impedance for ${\mu _\textrm{c}}\textrm{ = 0}\textrm{.85 eV}$.
The broadband absorption of the GMA can be verified by the impedance matching. According to the relationship between the normalized equivalent surface impedance Z(f) and the scattering parameters, the impedance of the metasurface is defined as [48]:
The bottom layer of the GMA adopts a continuous gold to block the transmission of the EM waves, i.e. S21=0. Thus, when S11 is close to 0, $Z(f) \approx 1$, the equivalent impedance will match to the impedance in the free space, and the metasurface can achieve nearly perfect absorption. Figure 2(c) and 2(d) show the retrieved permittivity, permeability and the normalized equivalent impedance [48,49] of the GMA when the Fermi level ${\mu _\textrm{c}}\textrm{ = 0}\textrm{.85 eV}$.
In Fig. 2(d), the marked blue and red lines indicate the real and imaginary parts of the equivalent impedance, respectively, and the marked black line shows the absorptivity. It is clear that the real part of the equivalent impedance is close to 1 and the imaginary part is close to 0 in the range of 2.06-3.71 THz, so the GMA achieves a good broadband absorption with a bandwidth of 1.65 THz.
To better understand the broadband absorption physical mechanism of the GMA, Fig. 3 shows the electric field intensity distributions of GMA at 2.3 THz and 3.3 THz. Figures 3(c) and 3(d) are the side views of cross section at the position marked by the black dashed lines in Figs. 3(a) and 3(b), respectively. The electric field is mainly located at the grooves of the PG layer, and the EM wave energy is confined and dissipated to the interface between graphene and the dielectric, indicating that localized surface plasmon resonance is excited in GMA [50].
Fig. 3. Top view and side view of the electric field intensity distributions in a unit cell for x-polarized incident waves, (a) and (c) at 2.3 THz,(b) and (d) at 3.3 THz, respectively.
2.2 MFMS with switchable broadband absorption and polarization conversions
It has been demonstrated that a structure with anisotropy along the diagonal direction can realize polarization conversion of EM waves [33]. Here we introduce the anisotropy in the designed-above GMA to achieve a MFMS with absorption and polarization conversion functions. Therefore we keep the constituent materials and geometric parameters of the GMA in Section 2.1 unchanged, a thin COC dielectric layer 3 with a thickness of h3=1 µm is covered on PG layer of the GMA, a strip resonator consisting of rectangular gold patches and square photosensitive Si patches are located diagonally on the thin dielectric layer. Figures 4(a) and 4(b) show the 4×4 unit cells array structure and the perspective view of the unit cell, respectively. Figure 4(c) is the side view of the unit cell. The size of the strip resonator is l1=14.5 µm, l2=21 µm, the thickness of both gold and Si patches is 0.2 µm, the permittivity of the photosensitive Si is ${\varepsilon _{\textrm{Si}}} = 11.7$, and the conductivity σSi can be regulated by the intensity of external pump light. Without pump light illumination, the Si is in the insulating state with ${\sigma _{\textrm{Si}}} = 1\textrm{ S/m }$, and when the intensity of pump light is increased to 294 µJ/cm2, the conductivity σSi can reach 105 S/m and behaves as metallic state [27]. Thus, by adjusting the Fermi level of graphene and the intensity of pump light of photosensitive Si, the MFMS can be switched among multiple functions.
Fig. 4. Schematic diagrams of the proposed MFMS. (a) the 4×4 array of unit cells, (b) perspective view and (c) side view of a unit cell.
We adopt the same simulation settings as Section 2.1. The simulated results show that the MFMS can operate in the absorption mode when no pump light illumination and the Fermi level of graphene reaches ${\mu _\textrm{c}}\textrm{ = 0}\textrm{.85 eV}$. Figure 5(a) shows the reflection coefficients of the MFMS for y(x)-polarized wave, where |ryy|(|rxx|) and |rxy|(|ryx|) are the co- and cross-polarized reflection coefficient amplitudes of the incident y(x)-polarized wave, respectively. It can be seen from Fig. 5(a) that the reflection coefficients along the X- and Y-axis directions have the relationship of rxy=ryx and ryy=rxx after being reflected by the MFMS. This is because MFMS is symmetrical structure along the diagonal. According to the absorptivity formula $A(\omega ) = 1 - R(\omega )\textrm{ = 1} - \textrm{|}{r_{\textrm{yy}}}{\textrm{|}^\textrm{2}} - \textrm{|}{r_{\textrm{xy}}}{\textrm{|}^\textrm{2}}$, the absorptivity of incident EM wave polarized along the Y- and X-axis is equal, as the marked red and blue dotted lines shown in Fig. 5(b), respectively. It is clear to see that the absorptivity of the MFMS exceeds 90% in the range of 1.74-3.52 THz, the absorption bandwidth is 1.78 THz and relative bandwidth reaches 67.7%. In addition, the absorptivity curve of the GMA structure is also depicted for comparison in Fig. 5(b). Compared with the absorption characteristic of the GMA, the absorptivity of the MFMS in the high frequency is slightly reduced, but it is improved in the low frequency. This might arise from the gold resonators on the top of the structure, which enhances the surface plasmons of the graphene and increase the carrier concentration [44].
Fig. 5. (a) The magnitudes of the cross-polarized and co-polarized reflection coefficients when the proposed MFMS works in absorption mode. (b) Comparison of the absorptivity of the MFMS and the GMA.
When the external DC bias voltage is set to 0 V, the Fermi level of graphene is ${\mu _\textrm{c}}\textrm{ = 0 eV}$, the graphene layers are equivalent to a thin dielectric layer. As the increase of pump light intensity, the conductivity of Si can reach ${\sigma _{\textrm{Si}}}\textrm{ = 5} \times \textrm{1}{\textrm{0}^\textrm{5}}\textrm{ S/m}$, which behaves as metallic state. The strip resonators on the top layer are equivalent to the diagonal metal strip resonators with polarization conversion function [33]. Therefore, the MFMS works in the polarization conversion mode which can convert the co-polarized wave to cross-polarized wave for y/x-polarized wave. When the incident electromagnetic wave is LCP/RCP wave, it can be converted into RCP/LCP reflected wave [45]. The polarization conversion rates (PCRs) of linear-linear polarization and circular-circular polarization are respectively defined as:
Fig. 6. The magnitudes of the cross-polarized and co-polarized reflection coefficients, the corresponding absorptivity and the PCRs when the conductivity of Si is changing. (a), (c) and (e) for y-polarized or x-polarized incident wave. (b), (d) and (f) for LCP or RCP incident wave. The corresponding phase differences of the cross-polarized and co-polarized reflection coefficients when ${\sigma _{\textrm{Si}}}\textrm{ = 5} \times \textrm{1}{\textrm{0}^\textrm{5}}\textrm{ S/m}$ are plotted in (e) and (f), respectively.
Table 2. The comparison between previous MFMSs and this work.
With the development of micro-nano processing technology, many metamaterials with complex patterns have been fabricated by repeating the growth and transfer process, which provide useful references for manufacturing the proposed MFMS [45]. On a sacrificial silicon substrate layer, the bottom continuous gold films may be deposited by thermal evaporation system, and the COC sheet with required thickness is synthesized on a gold film by spin-coating and curing [51], a continuous graphene film is grown on COC dielectric by chemical vapor deposition (CVD) [52]. Then repeat the previous process of preparing the COC and graphene. An electron beam lithography and reactive ion etching system are be used to etch a pattern of grooves into the upper layer of graphene for forming the PG layer. Next, another COC layer is prepared, on which the gold film will be deposited and patterned by electron beam lithography. Through thermal evaporation system and electron beam lithography, the photosensitive square silicon resonator layer can be deposited and formed. Finally, the whole structure can be then exfoliated from the silicon substrate.
3. Analysis and discussions
3.1 Surface current distributions
In order to clarify the physical mechanism of the proposed MFMS for different operating modes, we analyze the current distributions of the top resonators (TR) layer, the PG layer, the CG layer and the BM layer at the resonance frequencies. When the MFMS works in the absorption mode, the surface current distributions of 2×2 unit cells at the resonant frequencies of 2.65 THz and 3.32 THz are shown in Fig. 7. It can be seen from Figs. 7(a1)–7(a4) that the currents are mainly concentrated on the corresponding positions of the PG layer under the rectangular gold sheets at 2.65 THz. It indicates that the absorption at low frequencies is due to the surface plasmon of CG layer enhanced by the TR layer, which increases the carrier concentration and excites the local surface plasmon resonance of the PG layer. For the current distributions at 3.32 THz, it can be seen from Fig. 7(b2) that the induced currents are concentrated on both sides of the transverse split semicircular rings and inside of the longitudinal split semicircular rings. The direction of the induced currents of the PG layer is parallel to the CG layer, so the absorption at high frequency is caused by electric resonance. The incident EM waves are mainly confined and dissipated in the PG layer.
Fig. 7. The surface current distributions of different layers for absorption mode at (a) 2.65 THz and (b) 3.32 THz, respectively.
When the MFMS works in the polarization conversion mode, the graphene is equivalent to a thin dielectric layer. The PG layer, CG layer and COC together constitute the dielectric spacer layer. When the Si is excited by pump light, the conductivity is ${\sigma _{\textrm{Si}}} = 5 \times {10^5}\textrm{ S/m}$, which behaves as metallic state. We display the current distributions of the TR layer and the BM layer at resonance frequencies of 1.84 THz and 2.43 THz. As shown in Fig. 8, the surface current distributions are similar at 1.84 THz and 2.43 THz. The induced currents on the TR layer and BM layer are parallel and in the same direction along the diagonal direction of the unit cells, which is equivalent to an induced electric dipole. The induced electric dipole generates an electric field E1 directed down the diagonal direction [34,53]. The component E1y of the induced electric field E1 is perpendicular to the incident electric field Ei, which can contribute to polarization conversion, while the component E1x of the induced electric field E1 cannot generate cross-polarization wave, but can promote the polarization conversion by interacting with the Ei with the opposite direction. Thus, the polarization conversion can be achieved [37,39].
Fig. 8. The surface current distributions on the TR layer and the BM layer for polarization conversion mode at (a) 1.84 THz and (b) 2.43 THz, respectively, and (c) the eigenmodes decomposition of x-polarized incident wave.
3.2 Properties of oblique incidence
In the previous sections, the absorption and polarization conversion modes of the MFMS are studied under normal incidence. Here we explore the performances of the proposed MFMS under different incident angles. Figures 9(a) and 9(b) show that the absorption characteristics of the MFMS at oblique incident angles for TE and TM waves respectively. For the incident TE wave, as shown in Fig. 9(a), the broadband absorption peak has blue-shift and the absorption band becomes narrower with the incident angle increases from 0° to 60°; for incident TM wave, the absorption performances slightly influenced for incident angle within 50°, as shown in Fig. 9(b). In addition, Figs. 9(c) and 9(d) show the polarization conversion performance at different incident angles for TE and TM waves. It can be seen that the PCRs are almost steady when the incident angle is less than 25° for both TE and TM wave; when the incident angle is more than 25°, there is an extra polarization conversion peak at higher frequency, it may be higher-order mode response [50]. Therefore, the absorption characteristic of the proposed MFMS is insensitive to the incident angles of TE and TM waves, and a good PCR can also be obtained for incident angle within 25°.
Fig. 9. The absorption spectrums for (a) TE and (b) TM waves and the polarization conversion spectrums for (c) TE and (d) TM waves at different incident angles.
4. Conclusion
We firstly designed a dynamically tunable broadband GMA, whose absorption bandwidth and absorptivity can be adjusted by changing the Fermi energy of graphene. The GMA can achieve excellent broadband absorption as the impedance matching condition is well satisfied. On this basis, a MFMS integrated graphene and photosensitive Si is proposed. By controlling the external DC bias voltage of graphene layers and the intensity of the pump light illumination, the three operating modes can be switched among broadband absorption, broadband linear polarization conversion and broadband circular polarization conversion. The simulation results show that when the MFMS works in absorption mode, the absorptivity is above 90% in the frequency band of 1.74-3.52 THz and relative bandwidth is 67.6%. The absorption characteristic is insensitive to oblique incident angles for TE and TM waves. When the MFMS operates in polarization conversion mode, the incident co-polarized wave can be converted into a cross-polarized wave or the incident LCP/RCP wave can be converted into RCP/LCP wave in the frequency band of 1.54-2.55 THz, the relative bandwidth with more than 90% PCRs reaches 49.3%. The proposed MEMS provides a new strategy for designing tunable multifunctional devices in the THz band, which can integrate multiple functions into a single device. It is expected to be applied in the field of wireless communication.
Appendix: The complex surface conductivity of the graphene
The surface conductivity σgra of graphene is composed of the intraband conductivity σintra and the interband conductivity σinter, which can be acquired by Kubo formula [54]:
The surface conductivity of graphene is related to Fermi level in addition to the EM wave frequency, so one can adjust the surface conductivity of graphene by changing its Fermi level. The graphene Fermi level that varies with the applied bias voltage can be described by the formula [56]:
Funding
National Natural Science Foundation of China (61775126); Natural Science Foundation of Shanxi Province (201801D221164, 201801D121119).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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