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Abstract
We propose a reconfigurable hybrid graphene meta-surface for modulating circularly polarized (CP) waves with dual functionalities of asymmetric transmission (AT) and monodirectional absorption. Such a meta-surface consists of three cascade dielectrics covered with identical metallic resonators and different patterned graphene sheets over the front and the back sides, respectively. The left-handed CP incidences will be transformed into right-handed CP counterparts efficiently with an AT-parameter of 0.8, and the state of transmission will be contrary when the incident CP waves are from the opposite direction. On the other hand, the proposed cascade composite resonator-graphene meta-surface can also function as a super monodirectional absorber to trap the forward incident CP waves at the same frequency range when we simply tune the Fermi energy of graphene. The proposed design should pave the way for building up more advanced meta-devices with multiple functionalities to manipulate CP waves.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Meta-surfaces possessing great capacities of highly efficient polarization conversions, have initiated the quest for tangible applications in different disciplines [1–5]. S.J. Li et al. proposed a low profile, compact, and lightweight coding meta-surface for the wireless communication to convert the linearly polarized (LP) incidence into multi transmissive or reflective circularly polarized (CP) beams [1], demonstrated the programmable control of scattering characteristic of a radiation array [2], and also presented a thin self-feeding Janus meta-surface for manipulating incidences and emitting radiations simultaneously with great power of polarization conversion and radiation-beam steering [3]. Han et al. proposed a chiral meta-surface that can transmit the $x$-polarized incidence to right-handed circularly polarized (RHCP) waves in one direction, and will also be capable of reflecting the left-handed circularly polarized (LHCP) incidence in the opposite direction at the same frequency range [4]. Li et al. designed a three-layer microstructure to realize four band linear to dual-circular polarization conversion of transmissive waves for multiband communication and multifunctional dual-CP antenna systems [5].
Graphene meta-surfaces, in the meanwhile, have been widely applied into the designs of reconfigurable polarization converters and also have extensively employed in the asymmetric transmission (AT) regime, offering different passports for the forward and backward illuminations of different polarized electromagnetic (EM) fields [6–9]. Sorathiya et al. proposed a multi-layer graphene silica-meta-surface based infrared polarizer structure to realize a high polarization conversion rate [6]. Li et al. presented a graphene planar chiral meta-surface with tunable dual-band AT for applications of detectors and polarization-sensitive devices [7]. Huang et al. demonstrated the great potential of graphene-based meta-surfaces and their complementary structures in the terahertz polarization conversion and AT applications [8]. Zhao et al. proposed a controllable AT with perfect polarization conversion using three-layer metal-graphene-metal meta-surfaces in terahertz regime [9]. Amin et al. presented a graphene meta-mirror with significant linear and circular dichroism to tune the polarization states of the reflection through setting different Fermi energies [10]. Masyukov et al. demonstrated a chiral meta-surface with tunable transmission and polarization properties under the illuminations of different optical pumping [11]. These graphene meta-surfaces, capable of transforming the co-LP fields into their cross counterparts or performing the linearly-to-circularly polarized field-conversions efficiently, have brought new applications in sensing [12–15], imaging [16,17], and spectroscopy [18,19] at terahertz frequencies.
However, most of these AT designs solely deal with the conversion of LP waves, where the asymmetric regulations of two different spins of CP waves are rare to perform, as it is difficult to regulate two orthogonal LP components simultaneously with desired performances in the AT of CP waves. Especially, the AT designs are usually not efficiently for the CP fields compared with those of the LP waves. For example, Stephen et al. proposed a chiral metamaterial for broadband AT accompanied with cross-polarization conversion for LP waves and the AT-parameter is greater than 0.9 [20]. On the other hand, multi-functional applications of hybrid graphene meta-surface designs are also expected nowadays in the contemporary wave controlling technologies as closely related interactions between the graphene and the metallic resonators will enhance the prescribed responses [21,22]. Especially, the inherent absorbing capacity of the graphene alone should also enable the hybrid graphene meta-surface to trap the transmitting fields if we can fully explore the functionalities of the composite structures [23–25]. Based on these considerations, we demonstrate a reconfigurable cascaded composite resonator-graphene meta-surface to dynamically switch the AT and the super monodirectional absorption of CP waves. We will show that the LHCP incidences will be transformed into RHCP counterparts efficiently with AT-parameter of 0.8, and the state of transmission will be contrary when the incident CP waves are from the opposite direction. Especially, the proposed cascade composite resonator-graphene meta-surfaces can also function as super monodirectional absorbers to trap the CP waves at the same frequency range when we simply tune the Fermi energy of graphene.
2. Design and modeling
Figure 1(a) schematic demonstrates the proposed cascade resonator-graphene meta-surface under the illumination of CP waves, transforming the forward LHCP fields into the orthogonal components, while rejecting the passport for the forward RHCP incidence. However, when the incident CP waves are from the opposite direction, demonstrated in Fig. 1(b), LHCP fields will be reflected and the RHCP waves, on the other hand, will be given the passport and converted into LHCP fields. In the meanwhile, such a cascade resonator-graphene meta-surface can be switched into a monodirectional absorber when the Fermi energy of graphene is imposed as 0.8 eV as shown in Fig. 1(c), and only traps the forward incidences of CP fields. On the other hand, CP waves from backward direction will be reflected by the meta-surface, as shown in Fig. 1(d). Such a meta-surface consists of three cascade dielectrics covered with identical gold resonators and monolayer patterned graphene sheets over the front and back sides, as shown in Fig. 1(e). The gold resonators consist of a back-to-back C- and L-shaped structure. The graphene patterns in three layers are composed of increasing sized rectangular patches and X-shaped feed lines, forming a pyramidal-like structure. The thicknesses of dielectric substrate and metal are $t=8\mu \text {m}$ and ${{t}_{1}}=0.3\mu \text {m}$ respectively, the period of the unit is $p=70\mu \text {m}$. The structural parameters of resonator meta-surfaces are $d=10\mu \text {m}$, $\text {s}=20\mu \text {m}$, $L=40\mu \text {m}$, ${{L}_{1}}=21\mu \text {m}$, ${{L}_{2}}=25\mu \text {m}$, ${{L}_{3}}=17\mu \text {m}$, $w=10\mu \text {m}$, ${{w}_{\text {1}}}=5\mu \text {m}$, $a=20\mu \text {m}$ and $b=50\mu \text {m}$ as shown in Fig. 1(e).
Fig. 1. Schematic diagram of the cascaded composite resonator-graphene meta-surface. (a) AT with LHCP wave incident from the forward direction, (b) AT with RHCP wave incident from the backward direction, (c) The absorptions of CP waves illuminated from the forward direction, (d) The reflections of CP waves illuminated from the backward direction, (e) Geometric dimensions of the cascaded composite resonator-graphene meta-surfaces, (f) The practical tuning strategy and potential implementation of the cascaded graphene mate-surface consisting of the graphene patches, the dielectric spacer, silica aerogel, polycrystalline silicon layers and gold patches.
The conductivity of graphene can be continuously tuned by manipulating its Fermi energy via chemical doping or electrical gating, and we can thus further manipulate the interactions between the EM fields and the proposed cascade resonator-graphene meta-surfaces. The conductivity $\sigma ={{\sigma }_{\operatorname {int}ra}}+{{\sigma }_{\operatorname {int}er}}$ of graphene structure is characterized by Kubo formula [26–29]:
As shown in Fig. 1(f), the Fermi energy of the graphene meta-surface could be tuned by the electric field biasing structure, and the whole graphene sheet in every layer can be directly connected to the electrodes without the need to design additional feed lines. The DC voltage of Vt (Vi) can thus be applied to the 20 nm thick polycrystalline silicon and the bottom graphene patch array, separated by a 10 nm thick silicon dioxide [30], where the thin polycrystalline silicon is believed to have negligible impacts on the element response [31]. Considering the potential implementation, the polycrystalline silicon layer is first deposited on the substrate using a spin-coating solution [32,33], where another thin insulating layer of substrate will be deposited on it as well. The graphene film grows on the substrate through the plasma-enhanced chemical vapor deposition system, and is patterned by employing electron beam lithography and inductively coupled plasma etching [34–36]. Au film is deposited electrochemically onto nanoporous templates first, and then patterned into the desired C and L shapes by reactive-ion etching. The gold layer is evaporated onto the top of the substrate using e-beam evaporation [37]. Through repeating such a growth and transfer process of microfabrication technology [38], the proposed three-layer graphene mate-surface with desired patterns will be achieved. In addition, the air gap between the adjacent layers can be realized by inserting silica aerogels possessing the merit of optical transparent property with refractive index of 1.01-1.03 [39–41].
The transmission and absorption coefficients can be determined by the following Jones matrix [42,43]:
On the other hand, when different polarized incidences interact with the proposed graphene meta-surface, the absorptivity of LHCP ($A_-$) and RHCP ($A_+$) waves can be defined as [44]
3. Results and discussion
Full wave simulations (CST Microwave Studio) are carried out to verify our proposed design. We mimic the interactions between the EM fields and the proposed cascade resonator-graphene meta-surfaces using Floquet mode analysis with the boundary conditions virtually repeating the modeled structure periodically in x and y directions. We can observe that the RHCP incidence from the forward direction along the –z-axis will not be able to penetrate the device and the transmission in the form of its cross counterpart will also be rejected when the Fermi energy of graphene is imposed as 0 eV, as shown in Fig. 2(a). The currents over the 3 layers of metallic resonators are parallel in the same direction, producing electric resonance between adjacent two layers as the excitation of electric-like dipoles to reflect most of the energy of the incidence [45,46]. Similar situations occur when the LHCP incidences are illuminated from the backward direction, as shown in Fig. 2(b). On the other hand, most of the energy can be converted into their orthogonal states with high efficient transmissions at 2.65 THz, the intensity of electric field excited in metallic resonator layers are very weak and causing inferior scattering between the 3 layer metallic resonators, as shown in Fig. 2(c-d). Clearly, the transmission fully conforms to the principle of optical path reversibility with $T_{-+}^{f}=T_{+-}^{b}$ and $T_{+-}^{f}=T_{-+}^{b}$, which means the polarization conversion efficiency and the direct transmission of CP waves are identical for the counterparts with orthogonal polarization states in opposite directions. Meanwhile, the transmission energy of CP waves of opposite helicities in the same direction are different, leading to the high efficiency AT of CP waves. The proposed cascade resonator-graphene meta-surface achieves excellent AT performance with up to 0.8 AT-parameters when imposed 0 eV Fermi energy over the graphene, as shown in Fig. 3, and the absolute values of AT-parameters from different directions are equal. Certainly, the AT-parameters of two orthogonally CP waves incident from the same direction are numerically opposite to each other.
Fig. 2. The AT of CP waves through the proposed cascade resonator-graphene meta-surface with 0 eV Femi energy imposed over the graphene layer. Transmission coefficients and surface currents with RHCP incidence from forward direction (a) and LHCP incidence from the backward direction (b) respectively. Transmission coefficients and surface currents with LHCP incidence from forward direction (c) and incidence from the backward direction (d).
Fig. 3. AT-parameters of composite resonator-graphene meta-surface with CP illuminations from different directions. (a) The CP waves incident from forward direction, (b) CP waves incident from backward direction.
Figure 4 further demonstrates the absorption characteristics of CP waves from the proposed cascade composite resonator-graphene meta-surfaces when we impose 0.8 eV Fermi energy over the graphene. The transmission and reflection coefficients of the meta-surfaces are both less than -10 dB from 2.6 to 2.8 THz. The energy of the CP waves is localized within the proposed meta-surface with scarce fields transmitting through and reflected back, indicating great absorption of the CP incidences. On the other hand, when the CP waves are illuminated from the backward direction, most of the energy will be directly reflected with rare absorption. As a result, such a cascade composite resonator-graphene meta-surface thus functions as a monodirectional super absorber of CP waves with 96% absorptivity at 2.65 THz, as shown in Fig. 5(a). In the meanwhile, Fig. 5(b) indicates that the absorptions are less than 30% when CP waves are incident from the backward.
Fig. 4. The absorptions of CP waves of the proposed cascade resonator-graphene meta-surfaces with 0.8 eV Femi energy imposed over the graphene layer. Transmission and reflection coefficients as well as the E-fields of CP incidences from the forward (a) and the backward (b) directions respectively.
Fig. 5. Absorptions of CP illuminations from different directions of the composite resonator-graphene meta-surfaces. (a) The CP waves incident from forward direction, (b) CP waves incident from backward direction.
Figure 6 demonstrates the dual functionalities varied with Fermi energy imposed over the graphene. We can observe that the AT-parameter will decrease as the Fermi energy increases, and it becomes almost 0 at 2.65 THz when we impose 0.4 eV Fermi energy and beyond over the graphene. On the other hand, the absorptivity will experience an increase as the Fermi energy goes bigger, and reaches the top with 96% absorption rate at 2.65 THz when 0.8 eV Fermi energy is imposed over the graphene. However, it will have a decline when the Fermi energy continues to turn larger. When we have 1 eV Fermi energy imposed over the graphene, the absorption rate of the proposed cascade composite resonator-graphene meta-surfaces will below 80% at 2.65 THz.
Fig. 6. Dual functionalities varied with Fermi energy imposed over the graphene. (a) AT-parameters, (b) Absorptivity.
Figure 7 explores the impacts of the modeling geometries on the AT-parameters and absorption rate of the proposed cascade composite resonator-graphene meta-surfaces. We can observe that the changes of $L_1$, $L_2$, $L_3$ and $S$ will have different effects on AT-parameters, and the variations of $a$ and $b$ also influence the absorption rate. More specifically, $L_1$ determines the operating frequency of AT, $L_2$ greatly changes the AT-parameters, $L_3$ has no significant effect on the AT-parameters, and $S$ will both tune the working frequency and AT-parameters. On the other hand, $a$ has limited impacts on the absorption rate, and $b$ mainly determines the optimal absorption frequency. By comparing the simulation results, we reach $L_{1}=21$ $\mu \mathrm {m}$, $L_{2}=25$ $\mu \mathrm {m}$, $L_{3}=17$ $\mu \mathrm {m}$, $S=10$ $\mu \mathrm {m}$, $a=20$ $\mu \mathrm {m}$ and $b=50$ $\mu \mathrm {m}$ for the optimized design in this investigation.
Fig. 7. AT-parameters and absorptions varied with structural parameters. AT-parameters varied with $L_{1}$ (a), $L_{2}$ (b), $L_{3}$ (c) and $S$ (d); Absorptivity varied with $a$ (e) and $b$ (f).
Figure 8 demonstrates the AT parameter and absorption of the cascaded composite resonator-graphene meta-surfaces in the absence of graphene or the air gap between the adjacent layers. Without the graphene, the meta-surface can still achieve high AT parameter as shown in Fig. 8(a), but the absorption at the same frequency is only 0.25. Clearly, the three-layer patterned graphene sheets enhance the losses of EM waves and should be the main source to achieve the absorption. Figure 8(b) continues to remove the two air gaps between the adjacent layers of the cascaded composite resonator-graphene meta-surface. Such a meta-surface will lose all the AT performance, but the three layers of pyramid graphene sheets can still achieve a large absorption. Clearly, the air gaps between the adjacent layers of the cascaded composite resonator-graphene meta-surfaces significantly influence the AT parameter and also can produce a slight boost to the absorption capacity.
Fig. 8. Different schematic diagrams of the cascaded composite resonator-graphene meta-surfaces and corresponding AT parameters and absorptions of CP illuminations (a) without graphene, (b) without air space.
We use the three-layer cascaded structure as it achieves a perfect balance between the high AT and great monodirectional absorptivity. When the meta-surface has only one layer of dielectric substrate with metallic resonators and graphene patches attached to its upper and lower surfaces separately as shown in Fig. 9(a), it can hardly generate corresponding diverse current modes for different polarized EM waves, and thus will not achieve AT. Meanwhile, the single-layer element has a very thin profile with limited loss of EM waves, and cannot achieve the function of efficient absorption either. When the meta-surface is two-layer cascaded, the AT parameter increases significantly and the maximum value will reach 0.7 in Fig. 9(b). The corresponding maximum absorption rate at 2.73 THz is 0.75. Figure 9(c) continues to demonstrate the performance of the four-layer cascaded composite resonator-graphene meta-surface. We can observe that neither the AT-parameters nor the absorptivity is improved compared with the three-layer structure. In addition, the maximum AT frequency point has a blue shift, and such a structure can only support the monodirectional absorption of LHCP waves. As a result, we employ three-layer cascaded composite resonator-graphene meta-surfaces for the dual functionalities with switchable AT and monodirectional absorption of CP waves.
Fig. 9. Different layered meta-surfaces and the corresponding AT parameters and absorptions of CP illuminations. The cascaded composite resonator-graphene meta-surfaces with (a) monolayer, (b) two-layer and (c) four-layer structures respectively. 0 eV Fermi energy is imposed over the graphene sheet for the AT and the corresponding best absorption occurs when 0.7, 0.8 and 0.9 eV Fermi energies are imposed over the graphene of the monolayer, two-layer and four-layer structures respectively.
The detailed comparisons with the previous publications concerning meta-surface designs of AT [7,8,29,45,47–49] are demonstrated in Table 1. Reference [7] proposed a 2D chiral patterned graphene meta-surface with dual-AT peaks of 0.019 and 0.052 at the frequency of 35.8 THz and 37 THz respectively. Reference [8] proposed the graphene-based patterns with S-shaped split ring resonator dimers for AT in terahertz region. When the Fermi energy is 0.8 eV, the AT parameter reaches 0.073. Reference [29] proposed a double-layer graphene-based planar chiral meta-surface and possessed 0.17 AT parameter. Reference [45] proposed a bi-layered chiral metamaterial to enhance the AT effects for CP waves with AT-parameter of 0.6. Reference [47] proposed a 2D-chiral twisting meta-array to realize AT of terahertz propagating waves and the AT parameter is 0.08. Reference [48] employed a two-layer meta-surface with dihedral symmetric resonators to achieve 0.56 AT-parameter. Reference [49] relied on three-layer gold resonant rings for the polarization conversion to achieve AT and the AT-parameter is 0.6. Compared with these designs, our proposed cascaded composite resonator-graphene meta-surfaces have a giant AT-parameter of 0.8 to manipulate CP waves. Furthermore, our proposal is also capable of achieving the dynamic conversion of dual-functionalities of AT and monodirectional absorption by simply adjusting Fermi energy imposed over the graphene.
Table 1. COMPARISONS OF ASYMMETRIC TRANSMISSION META-SURFCE 0.8pt
4. Conclusions
In conclusion, we have demonstrated the dynamically tuning the polarizations of EM fields based on the cascade composite resonator-graphene meta-surfaces consisting of three cascade meta-atoms array with graphene sheets attached on the backside. By switching the Fermi energy of graphene between 0 eV and 0.8 eV, an efficient transition between AT and monodirectional absorption of CP waves can be achieved at 2.65 THz. When $\mu _{c}=0$ eV, the AT-parameter can reach 0.8 and absorptivity up to 96% with $\mu _{c}=0.8$ eV. Moreover, both the functionalities can be dynamically modulated by tuning the Fermi energy imposed over the graphene. We expect the proposed design should pave the way for building up more advanced meta-devices with multiple functionalities to manipulate CP waves.
Funding
National Natural Science Foundation of China (61301072, 61671344).
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 maybe obtained from the authors upon reasonable request.
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