1. Introduction

Chirality, meaning that the designed meta-atom cannot overlap its mirror image through geometric transformations, such as DNA strand-like structures [1]. A metamolecule with opposite chiral functions exhibits different responses to various induction modes. At present, chiral structures have been widely used in the design of optical systems, and a series of intrinsic mechanisms of chiral optical interactions have been elucidated [2–4]. In the field of transformation optics, chirality is defined as the difference in transmission or absorption mode in orthogonal channels under polarized beam illumination, which can be intuitively understood as the different response intensities when different modes of polarized light interact with matter [5]. The difference between the imaginary and real parts of the refractive index corresponds to different optical responses, namely circular dichroism (CD) and optical rotation (OA) [6]. In particular, the spin-selective absorption effect based on chiral nanostructures, take advantage of their responsiveness to the surrounding electromagnetic environment, can be used to distinguish enantiomers of biological macromolecules that occur in pairs [7]. However, the weak chiral response in natural materials makes it impossible to realize the aforementioned functions, limiting the further application of basic chirality in multivariate fields. Metasurfaces with subwavelength thicknesses offer fascinating capabilities for manipulating incident waves [8–16]. Numerous interesting applications have been investigated, including anomalous beam refraction [10], vortex beam generator [11], holographic imagers [12,13], etc. With significantly enhanced chiral responses and orders of magnitude higher efficiencies compared to natural materials, metasurfaces are emerging as prime candidates in the spin photonics. Recently, a variety of meta-platforms with spin-selective properties have been reported successively, indicating that the application of metasurfaces provides a new way to manipulate electromagnetic waves at the subwavelength scale [14–16].

Chiral meta-mirrors are metasurface-based exotic spin-selective reflector arrays with two well-defined features, namely, circular polarization preservation and chiral selective absorption [17,18]. By introducing Pancharatnam-Berry (PB) phase, chiral meta-mirrors can independently serve as an alternative to achieve spin-selective phase manipulation of circularly polarized waves [10,11]. It is worth mentioning that THz waves are especially suitable for the design of tunable functional meta-devices due to their hybrid characteristics of microwaves and light waves [19]. In general, when the structural parameters of a metasurface are changed, the varies in its capabilities are always correlated. Therefore, achieving near-independent manipulation of THz waves in different dimensions (frequency, amplitude, phase, and polarization state) remains a great challenge. In particular, the introduction of doped graphene has injected new vitality into the design of meta-mirrors with dynamically tunable properties. The Fermi energy of graphene can be tailored by external bias or chemical doping, and its surface conductivity can be dynamically tuned over a wide range. Not only that, graphene-based designs seem to provide alternative and flexible degrees of freedom more efficiently, i.e., form a combined active-passive modulation scheme (structural parameters and Fermi energy of graphene). But so far, few relevant studies have been reported.

In this work, we propose a chiral meta-mirror to independently manipulate circularly polarized THz waves of different dimensions in both active and passive methods. Shows simulated dual-band high-efficiency reflection for left-handed circularly polarized (LCP) waves at the working frequency, while the reflection of the other spin state is kept smaller than 5% without changing the handedness. It is remarked that the designed graphene-based polarization-selective strategy not only offers a dual-band selective absorption in the CD spectrum but ensures active tunability wavefront shaping functionalities as well. This unique spin-selective functionalities are induced by the total absorption of right-handed circularly polarized (RCP) waves and the efficiency reflection of LCP waves. The proposed design utilized depth-separated bi-layered graphene-arcs to form a vertical chirality, and obtained singular functionality of different wavefront modes. For verification, using spatially rotated meta-atoms, two proof of concept supercells are designed. In contrast to previous designs, our approach to realizing the dual-band chiral functions in one tunable metamirror with a simple structure and definite physics, without introducing chirality-selective building bulks.

2. Structures and methods

Unlike the characteristics of circularly polarized plane waves reflected on ordinary metal mirrors, an artificially designed metasurface with a chiral response operating in reflection mode can absorb one of the circularly polarized components without changing the handedness [20]. In other words, an elaborately parameterized meta-platform can completely consume one of the components and exhibit a strong chiral response. When two twisted graphene-arcs obtain high surface conductivity due to electrical doping, the enhanced anti-bonding mode excited by the chiral metasurface responds to the change of surrounding electromagnetic environment in an amplified manner [21], resulting in a dual-band giant spin-selective CD parameter. The designed chiral meta-atom consists of two C-shaped graphene-arcs with the same parameters and a reflective thin gold film separated by an insulating medium, as shown in Fig. 1(a). Figure 1(b) is a schematic that shows the dual-band chiral spectra of the proposed designed, including enantiomer A and enantiomer B. The structural parameters of a unit cell are shown in Fig. 1, where the periods P = 70 µm. The dimensions of the graphene split-ring resonator are w = 25 µm, and r = 34 µm, respectively. The thicknesses of the MgF₂ spacer and the ground Au layer are t = 20 µm, d = 14 µm and h = 100 nm, respectively. Figure 1(a) shows three structural variables in the designed meta-atom, that is, the split angle of the bilayer graphene-arcs (represented by parameter α), the twist angle of the bilayer graphene-arcs (represented by parameter β) and the orientation angle of the bi-layer graphene-arcs along the z-axis (represented by parameter γ).

 

Fig. 1. Schematic illustration of a bilayer twisted graphene-based chiral meta-mirror with periodic array arrangement, including enantiomer A and enantiomer B.

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Initially, we theoretically analyze the working principle of the proposed design. According to the advanced Jones calculus, the incident and reflected electric fields based on linear polarization can be expressed as [10]:

Here, r_mn (m, n = x, y) represents the reflection coefficient of the m-polarization under the incident n-polarization, including the co-polarization and the cross-polarization component. Where for convenience we have replaced the entries r_mn by A, B, C, D, which from the actual R^lin matrix for linear states. Since the proposed design works in a circularly polarized radiation field, the transformation from Cartesian base to circular base is very necessary. Then, the transformation matrix of the base can be described as

Therefore, the R^circ matrix for circular states is then given by [22]

Here, “+” and “-” indicate that the electric field vector of the plane waves rotates clockwise or counterclockwise when viewed in the +z direction (RCP and LCP waves). For simplify, the definition of the spin direction follows the default setting of the simulation software (CST Microwave Studio). However, compared with the transmission modes, the wave vectors are in opposite directions for transmitted and reflected light, thus the definition of each reflection coefficient in the CST software is different. Consequently, the reflection coefficient of the THz wave propagating in the -z direction can be defined as r_RL = r₊₊, r_LL = r_-+, r_RR = r_+-, r_LR = r_— [23]. The proposed design shows calculated high-efficiency dual-band absorption of 94.7% and 95.5% for LCP waves, while the absorption rate of the other spin state is kept smaller than 30.1% and 20.2% without changing the handedness, respectively. Therefore, the designed meta-mirror can produce a giant dual-band spin-selective chiral response.

In the THz region, the complex frequency-dependent surface conductivity of graphene sheet can be calculated using the well-known Kubo formula and can be described as ${\sigma _g} = {\sigma _{inter}} + {\sigma _{intra}}$. Obviously, the total surface conductivity of graphene is composed of two components, which are contributed by the intra-band and inter-band transitions. As the active tunable component of the proposed design, the surface dynamic conductivity of graphene can be approximately written as follows [24,25],

 

Fig. 2. Pauli blocking principle. (a) Case of the graphene carrier transitions. (b) Real part and (c) imaginary part of the surface conductivity of graphene in low THz band, including inter-band component, intra-band component, and total part.

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By applying the built-in material library conditions of the CST simulation software, the C-shaped graphene arc is modeled as a surface impedance layer with a thickness of 1 nm, which is defined as the product of the graphene electrical conductivity and the tangential electric field on the graphene plane. In addition, the fabrication steps for the experimental demonstration of the proposed method are given in the first section of the Supporting Information.

3. Results and discussions

First, we obtain the circularly polarized reflectivity of the structure in Fig. 1 by numerical simulations. In this case, the Fermi energy of both upper and lower graphene-arcs is fixed at Ef = 1 eV. Figure 2(a) shows the reflectivity of the four circularly polarized components, where, r_-+, r₊₊, r_--, and r_+- are the coefficients of reflection matrix. As shown in Fig. 3(a), there is a large difference between r₊₊ and r_-- in this proposed design, indicating a strong chirality. In detail, the proposed chiral metasurface shows that inefficient reflection of the co-polarized component of the incident RCP wave at the operating frequency of 0.88 THz and 1.53 THz, respectively. By contrast, the proposed design shows an efficient reflection of the co-polarized components of the incident LCP wave, which provides the basis for achieving full phase manipulation. Meanwhile, both cross-polarized components of circularly polarized wave are only about 5% at the frequency of interest. As shown in Fig. 1, the giant chirality of reflection can be easily changed with a mirror transformation of the meta-structure. In order to further investigate the dual-band giant chirality, we calculate the absorptance of the two circularly polarized components. In this work, the absorptance of LCP and RCP waves are described as A_L = 1 - R_LL- R_RL and A_R = 1 - R_RR - R_LR, respectively. As shown by the black and red solid lines in Fig. 2(b), a high absorptance of one circularly polarized wave (i.e., LCP) can be obtained, while the other component (i.e., RCP) can be partially reflected without handedness reversal. In fact, when the Fermi energy of graphene is fixed at 1 eV, the graphene sheet in this meta-atom can be regarded as a lossy material. Thus, the enhanced coupling resonances excited by the composite resonant metasurface respond to the change of surrounding electromagnetic environment in an amplified way, leading to the dramatic phase mutation of scattered waves. In addition, the absorption frequency of the designed chiral metasurface is not sensitive to the incident angle and can work in a wide range of angles (in the xoz plane). When the incident angle is gradually increased from 0° to 30°, the amplitude and frequency range of the dual-band CD spectrum remain unchanged. Moreover, the absorptions in the two states maintain a large contrast (> 50%), even under an incident angle of up to 60°, thereby indicating a robust wide-angle absorption behavior, as shown in Figs. 3(c), (d) and (e).

 

Fig. 3. Circularly polarized reflection spectrum of the chiral metamirror when E_f = 1 eV. (a) The reflectivity of RCP and LCP waves, including co-polarization (r₊₊, r_--) and cross-polarization (r_-+, r_+-) components. Circularly polarized absorption spectrum and CD parameter of the chiral metamirror for RCP and LCP incident waves (b) under normal incidence and (c-e) under oblique incidence

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First, we can further tailor the operating frequency of the dual-band CD spectrum by controlling the variable α, as shown in Fig. 4(a₁). In other words, the resonant frequency can be controlled by simultaneously changing the splitting angle of the bilayer graphene arcs. As shown in Figs. 4(a₂) and (a₃), the first (second) operation frequency can be effectively controlled from 0.57 THz (0.94 THz) to 1.18 THz (1.99 THz) by changing this parameter from 10° to 105° while keeping the CD parameter greater than 0.2. Second, we can also manipulate the working frequency of CD spectrum by introducing another active method, that is, arbitrarily tailoring the Fermi energy of graphene. As shown in Fig. 4(b₁), the simulation results demonstrate that the dual-band CD curves exhibit a noticeable shift as the Fermi energy gradually increases. It can be found that when the Fermi energy of graphene is fixed at 1 eV, the metasurface exhibits a giant dual-band chirality absorption response. When the Fermi energy of graphene gradually decreases, the positions of the two resonance peaks will be red-shifted. Specifically, when the Fermi energy of graphene is equal to 0.3 eV, the CD parameter at the first resonance peak is about 0.2, and at the second resonance peak is about 0.5. In other words, as the Fermi energy of graphene continues to decrease, the interaction between the bilayer chiral graphene metasurface and the incident THz waves gradually weakens, resulting in a continuous decrease in the amplitude of the CD parameter. At the resonance peak of working frequencies, shifting occurs when the Fermi energy of graphene is less than 0.1 eV and gradually disappears.

 

Fig. 4. Full-dimensional near-independent manipulation of circularly polarized waves by combining active and passive modulation modes. (a1-a3) the split angle α of the graphene arc, (b1-b3) the Fermi energy of graphene, (c1-c3) the relaxation time of graphene, (d1-d3) the twist angle β of the bilayer graphene arcs, and (e1-e3) the orientation angle γ of the bi-layer graphene resonator along the z-axis.

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Next, the difference of the magnitude of the CD parameter has a linear function relationship with the relaxation time τ of graphene. In other words, we can manipulate the magnitude of the dual-band spectrum by changing the relaxation time of graphene sheet without affecting the operating frequency, as shown in Fig. 4(c₁). Obviously, the scatter plots depicted in Fig. 4(c₂-c₃) effectively demonstrate our predictions. It is worth noting that the amplitude control range during the manipulation process is 0 to 0.7 at 0.88 THz and 0 to 0.8 at 1.53 THz. In other words, the high modulation depth provides the basis for an intensity-controllable near-field imaging system.

As shown in Fig. 4(d₁), the sign of the CD parameter is inverted as the angle (β) increases, corresponding to a pair of enantiomeric arrangements. Specifically, when the twist angle satisfies β₁ + β₂ = π, enantiomer A and enantiomer B with twist angles β₁ and β₂ are mirror-symmetrical in the xoy plane. Meanwhile, when the twist angle β is changed in the range of 0-180 degrees, the co-polarized circular polarization component at the selected frequency of 1.3 THz maintains a high effective reflectivity. More importantly, the reflected phase will meet the full phase coverage of 0-360 degrees, achieving simultaneous polarization-insensitive and wavefront shaping.

Furthermore, we can also introduce the PB phase principle to achieve chirality-dependent wavefront manipulation, since the meta-platform not only enables spin-selective reflection of incident waves, but also has a phase profile covering the 2π range. It is generally known that the basic principle of PB phase is to generate additional phase factors by rotating anisotropic meta-atoms. Specifically, when the bilayer graphene arc has a rotation angle of γ, an additional phase factor is generated in the co-polarized reflection channel with a magnitude of 2 times the rotation angle. Consequently, we can readily realize the reflected wave with a 2π phase profile by simultaneously rotating the bilayer graphene-arcs from 0 to 180°, as shown in Fig. 3(d₁-d₃). Also, in the aforementioned process, the amplitude of the reflected wave in the co-polarized channel remains almost constant. It can be seen from Fig. 3(e₁) that the difference in reflection amplitude between the LCP and RCP component remains stable. Therefore, choosing the operating frequency of 1.53 THz, Fig. 3(e₂) shows the reflection amplitude of the LCP and RCP components (co-polarized and cross-polarized) of the unit cells “1”- “9” with a phase gradient of 45 degrees. One can clearly see that each meta-atom maintains stable absorption difference of the circularly polarized incident wave. In addition, the LCP component has a perfect linear reflection phase shift, as shown in Fig. 3 (e₃).

Thus, this chiral metasurface adopts a combination of active and passive methods to achieve full-dimensional manipulation of circularly polarized THz waves. Compared with previous works [28,29], our method can not only be used in applications of spin-selective phase manipulation based on THz waves, such as wavefront shaping, but also in the field of chiral detection, and effectively improves the auxiliary degree of freedom of system regulation. Therefore, we further designed and completed a series of theoretical verification processes to prove that our method has a wide range of application possibilities.

Figures 5(a) and  5(b) depict the surface current distributions at the frequencies of the two perfect CD absorption peaks for the illumination of LCP and RCP waves, indicating that the physics underlying of the dual-band chiral response for the proposed design. Since the hybridization coupling theory [1,30], the two-layer twisted graphene-arcs can be regarded as a coupled resonator system, in which the surface plasmon modes of the hybrid meta-structure is produced by hybridization of surface plasmon resonances. Generally, taking the chiral metasurface with E_f = 1 eV as an example, there are two basic plasmonic modes in a hybridization coupling system. One is the bonding mode derived from the symmetrical arrangement and the other is the anti-bonding mode due to anti-symmetric alignment, as shown in Fig. 5(d). One can clearly see from Fig. 5(a) that the induced surface current distributions of the overlapping parts of the two graphene-arcs flows in the same direction. It indicates that the symmetric bonding mode is excited for the incidence of RCP waves. In contrast, under the irradiation of the LCP waves, an anti-bonding mode with opposite surface current directions is generated in the overlapping part of the two graphene-arcs, as shown in Fig. 6(b). The proposed hybrid near-field coupling model is shown in Fig. 6(d). According to the flow direction of the surface current distributions, it can be divided into two classical modes, namely the bonding mode and the anti-bonding mode. Since the anti-symmetric bonding mode has higher energy in the near-field coupled resonator system, the coupling between the upper graphene-arc and the lower graphene-arc is much stronger for the anti-bonding mode, leading a giant absorptive discrepancy for two different circularly polarized waves. Therefore, the giant difference in the absorption under the illumining of LCP and RCP brings about a strong dual-band CD response. On the other hand, when there is only a single graphene arc in the designed chiral nanostructure, the weak chiral response is excited, which proves that the near-field coupling effect in the designed metasurface makes a great contribution to the response to the surrounding electromagnetic environment, as shown in Fig. 6(c).

 

Fig. 5. The physical mechanisms of the dual-band spin-selective absorption in the proposed chiral meta-mirrors. Schematic diagram of the current distribution at the chiral operating frequency (a) under LCP illumination (b) under RCP illumination. (c) Absorption efficiency of a meta-mirror composed of single-layer untwisted graphene arc under different circularly polarized illumination (d) Schematic diagram of the current distribution of bonding and anti-bonding modes.

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Fig. 6. Chiral metasurface for dynamically tunable THz wavefront shaping. (a) Far-field surveillance plots at different frequencies and intensity profiles within different circularly polarized channels. Side views of the electric field distribution at different operating frequencies (b) 0.88 THz, (c) 1.3 THz, (d) 1.53 THz. (e) Far-field mode profiles of chiral metasurfaces with different Fermi energies.

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Without losing universality, as any linear polarization state can be regarded as the superposition of LCP and RCP modes. Therefore, as shown in Fig. 6(a), under x-polarization illuminations on the meta-mirror at the resonance peak of 0.88 and 1.53 THz with chiral-selective characteristics, the RCP component is absorbed with dual-band response while the LCP component is highly reflected. We are able to obtain a pure geometric phase manipulation of eight units scanned across 360° by continuously rotating the bi-layer graphene-arcs simultaneously with an angle step of 22.5° at the operating frequencies of 0.88 THz and 1.53 THz, respectively, as shown in Fig. 4(e). Next, when the LCP wave is perpendicularly illuminated, the meta-atoms with stable absorption amplitudes are selected to build the THz beam deflector. The initial chiral units are arranged in an 8×8 matrix supercell with a gradient phase profile along the x-direction. The abnormal reflection angle θ_r of a metasurface-based reflective array under normal incidence can be calculated by the generalized Snell’s law as follows [31],

Here, λ is the wavelength corresponding to the working frequency, and P is period of the selected meta-atoms. At the first operating frequency of 0.88 THz, due to the existence of the fundamental chirality rule, only the LCP wave can be reflected, and the deflection reflection angle is 37.1°, as shown in Fig. 6(b). Similarly, at the second operating frequency of 1.53 THz, the LCP wave is deflected by a reflection angle of 20.2°, as shown in Fig. 6(d). In contrast, at the achiral resonance frequency of 1.3 THz, the proposed design acts as a spin-independent beam deflector due to the disruption of the underlying chirality principle, and the LCP and RCP waves will experience anomalous reflections with opposite deflection directions, with an angle of 24.1°, as shown in Fig. 6(c). By adding a field monitor during the simulation, the resulting deflection angle of the far-field radiation is consistent with that calculated by the generalized Snell’s law, as shown in Fig. 6(a). On the other hand, by simultaneously tailoring the Fermi energy of the upper and lower graphene arcs, the degree of responsiveness of the proposed design to the surrounding electromagnetic environment can be controlled, thereby effectively manipulating the efficiency of the deflection, as shown in Fig. 6(e). In fact, using the geometric phase profile, the proposed meta-platform can realize a focused beam under the illumination of a circularly polarized wave [32], as illustrated in the second section (Supporting Information).

In addition to wavefront modulation, the proposed design can also be effectively applied to THz near-field imaging under circularly polarized illumination. Without loss of generality, the patterned supercell contains a total of 50×50 meta-atoms, and the imaging plane is chosen to be z = 60 µm. Near-field imaging requires the construction of meta-atoms with different absorptions of incident THz waves in different regions, that is, the two designed metasurfaces have completely opposite CD responses, which can be represented by introducing a pair of enantiomers (A and B). Initially, the meta-atom of enantiomer A is located in the “pentagram” region, while the meta-atom of enantiomer B is placed in the complementary region, and the Fermi energy of the graphene is fixed at 1 eV, as shown in Fig. 7 (a). Obviously, the attendant of spin-selective absorption will produce different regions to respond differently to circularly polarized waves under normal incidence. It can be clearly seen that the near-field profiles of the reflections show a pattern of pentagrams with complementary intensities at 0.88 THz and 1.53 THz, respectively. Also, the imaging quality at the operating frequency of 1.53 THz is slightly better than that at 0.88 THz due to the difference between the dual-band chiral responses. When the Fermi energy of the graphene is set to 0.01 eV, the proposed design can be regarded as an ordinary mirror, i.e., the incident circularly polarized component is reflected with a constant amplitude, so the near-field pattern cannot be observed, as shown in Fig. 7(b), further demonstrating the active tunability of the proposed design. It should be noted that the resolution distance of the near-field digital imaging system is proportional to the number of supercells.

 

Fig. 7. Application of the proposed design in THz near-field imaging (a) Schematic diagram of the initial arrangement of two selected meta-atoms with opposite chirality and pentagram pattern. (b) Near-field patterns at dual operating frequencies under different Fermi energies.

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4. Conclusion

In summary, we propose a platform of bi-layer graphene-based chiral meta-mirrors that can simultaneously achieve giant CD effect and wavefront shaping. Through carefully selected parametric meta-platforms, dual-band CD spectra with spin-selective effects can be obtained. It can effectively reflect circularly polarized waves with polarization changes while absorbing their orthogonal circularly polarized waves. Compared with traditional passive THz meta-devices, we reveal that the designed graphene-based chiral meta-mirror has a combination of active and passive regulation modes. By simply changing the three structural variables of the bilayer graphene-arcs and the two characteristic parameters of graphene, the amplitude, phase, polarization and operating frequency of the incident circularly polarized wave can be arbitrarily tailored, realizing the full-dimensional manipulation of the corresponding spectrum. As a proof-of-concept demonstration, a reflective beam deflector and chiral near-field imaging system are successively designed and numerically simulated, to further exhibit efficient wavefront manipulation and high-performance spin-selective absorption effect. Thus, the proposed ultrathin all-graphene meta-mirrors can provide a wide range of applications in intelligent polarization filtering and imaging systems.