1. Introduction

Optical activity is one of the most important optical effects in 3D chiral materials. Optical activity has attracted much attention due to significant applications in crystallography, spectroscopy, analytical chemistry and optics [1]. Optical activity can behave as circular birefringence (CB) and circular dichroism (CD) in dissipative media. CB is an ability to rotate the polarization state of light, while CD refers to differential transmission or absorption of circularly polarized waves. Although chiral objects are ubiquitous in nature such as DNA, viruses, and amino acids, their responses are quite weak so that chiral optical materials are usually bulky along light propagation direction compared with the wavelength. The advent of metamaterials offers a promising opportunity to realize giant artificial chirality for manipulating the polarization state of light [2–7]. On the one hand, optical activity has been widely observed in 3D-chiral metamaterials [8–13], in which they do not superimpose onto their mirror images. These metamaterials possess intrinsic chirality. On the other hand, the chiral effects can also be reported in intrinsically non-chiral metamaterials [14,15], provided that the whole arrangement formed by such metamaterial together with the wave vector of light cannot be superimposed upon its mirror image. This phenomenon is termed as extrinsic chirality, where two requirements are necessary, i.e., metamolecules without 2-fold rotational symmetry and the oblique incidence [15]. Recently, chiral or achiral metamaterials have developed rapidly to show a powerful polarization manipulation from microwave to optical frequencies [14–26]. For example, chiral and anisotropic metamaterials composed of subwavelength metallic building blocks have been proposed for enhancing CD [16–18] and optical activity [19–22], enabling various potential applications, such as broadband circular polarizers [23], wave plates [24] and chiral sensing [25,26].

Although many chiral and achiral metamaterials have been successfully proposed, the lack of tunability makes them not efficiently and flexibly work in practical applications. Therefore, achieving dynamic manipulation of electromagnetic waves is highly demanded and how to dynamically manipulate the polarization state has become a hot topic in the field of metamaterials. Instead of awkwardly engineered properties by metamaterials' geometrical parameters, a great deal of active materials have been added into chiral metamaterials to achieve dynamic manipulation of the polarization state such as semiconductors [27,28], chalcogenide glass [29,30], VO₂ [31], indium-tin oxide [32], and especially graphene [33–36]. Graphene is a two-dimension material consisting of one monolayer of carbon atoms arranged in a honeycomb lattice. Its sheet conductivity can be continuously tuned within a broad frequency range by changing the Fermi energy levels via chemical or electrostatic doping, which enables excellent electrical and optical properties including high transparency, fast electrical modulation and on-chip integration [37,38]. Therefore, graphene has been recently applied to realize tunable optical properties and photonic devices from polarization conversion [33], wave plate [34], anomalous refraction [35,36], optical modulation and detection [38], biosensing [39] to broadband fiber polarizer [40], plasmonic antenna [41,42] and perfect absorber [43]. Several metamaterials with patterned graphene or graphene layer have been investigated to achieve intrinsic and extrinsic 2D chirality showing asymmetric transmission [44–46]. For polarization manipulation using intrinsic 3D chirality, chiral metamaterial has been demonstrated to electrically modulate circularly polarized waves, in which the hybrid metamaterial is constructed by conjugated double-Z chiral meta-molecules with integrated graphene layer [47]. Another hybrid chiral metamaterial consisting of gold U-shaped resonators and graphene grating has been reported to exhibit tunable mid-infrared CD with ~10% intensity [48]. Besides graphene, optical activity in monolayer black phosphorus has been reported due to extrinsic chirality, in which CD can be tuned from 6.5% to 14.7% at the incident angle of 79° by controlling the Fermi level of black phosphorus through chemical or electrostatic doping [49]. To our best knowledge, extrinsically chiral metamaterial allows the presence of strong chiroptical response [14], thus graphene achiral metamaterial will be expected to generate a strong and tunable chiral phenomenon.

In this work, we propose graphene achiral metamaterial and theoretically investigate chiroptical responses arising from extrinsic 3D-chirality in mid-infrared regime. The achiral metamaterial consists of cascaded metallic split ring apertures and complementary graphene rings that are patterned on a dielectric layer. The strong extrinsic chiroptical responses are only allowed in the metamaterial for oblique incidence and the integrated graphene can dynamically modulate extrinsic chirality by changing its Fermi level. The angular dependences of the extrinsic chiroptical responses are investigated as well. The proposed metamaterial scheme is of importance to realize active polarization modulator, biosensor and chiral detection.

2. Theoretical model

The achiral metamaterial is composed of three stacked layers, in which the top layer is gold split ring aperture resonators, the middle layer is structured graphene that is complementary to gold split ring aperture, and the lower layer is a dielectric substrate. The schematic diagram of the metamaterial with all geometric parameters is depicted in Fig. 1. The metallic split ring resonators are etched from a gold layer with the thickness t_a = 50nm and the detailed dimensions are given below, p = 2000 nm, r = 850 nm, w = 150 nm, α = 160°, β = 140°. The open angles α and β are different. Herein, the incident waves propagate along the -z direction while the periodic boundary conditions are set along x and y directions. We numerically investigate the chiroptical response of graphene achiral metamaterials in the frequency range of 40-65 THz by use of the commercial software CST. In our simulation, the right-handed (RCP, +) and left-hand (LCP, -) circularly polarized waves are incident upon the metamaterial. The gold and graphene resonators lack two-fold rotational symmetry, thus the proposed hybrid achiral metamaterial will show extrinsic chirality with resonant optical activity when the tilted angle occurs around the symmetric axis of the metamaterial. At normal incidence, there is no extrinsic chirality. Therefore, the angle of incidence is set as 45° in the initial study. The patterned graphene is an array of asymmetrically split ring resonators that are an inverse design of the gold split ring apertures. The thickness of the graphene t_g is 1 nm. The dielectric layer’s permittivity is 2.25 and its thickness t_s = 200 nm. The gold is set as Drude model with the plasma frequency ω_p = 1.37 × 10¹⁶ S⁻¹ and the damping constant ω_c = 4.08 × 10¹³ S⁻¹ [50]. The conductivity of the monolayer graphene can be described by the Kubo formula [51,52]. The surface conductivity includes two terms: σ_g = σ_intra + σ_inter. σ_intra means the intraband electron-photon scattering, which can be described as:

 

Fig. 1 Schematic views of the graphene achiral metamaterial (a) The stereogram view of a unit cell. (b) The front view of a unit cell. (c) The whole view of the graphene metamaterial. The circularly polarized wave propagates along -z direction. The patterned graphene can be tuned by electrostatic doping, illustrated by panel c.

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3. Results and discussions

The reflection matrix $E_k^r=r_{kj}{E}_j^{inc}$ relates the reflected wave E^r to the incident wave $E^{inc}$ in terms of RCP and LCP waves. The same formula can be applied in the transmission. The reflection and transmission coefficients in terms of the power are given by $R_{kj}={\left|r_{kj}\right|}^2$ and $T_{kj}={\left|t_{kj}\right|}^2.$ The phase of reflection and transmission will be described as arg r_+-, arg r_-+ and arg t_–, and arg t₊₊, respectively. The extrinsic chirality of the achiral metamaterial is achieved by the tilted angle around the symmetric axis of the metamaterial.

The chiroptical response of the graphene achiral metamaterial is shown in Fig. 2, in which the angle of incidence is θ = 45$°$ and the Fermi energy level of graphene E_f is set as 0.7eV. Here, reflection and transmission induced CDs can be expressed as $\Delta \text{R}=R_{+-}-R_{-+}$ and $\Delta \text{T}=T_{--}-T_{++},$ corresponding to the reflection and transmission differences of RCP and LCP waves. The distinct reflection levels $R_{+-}\ne R_{-+}$ can be obviously seen from Fig. 2(a). The maximal difference of R_+- and R_-+ happens at around 50 THz, and the reflective contrast exceeds 70%. Figure 2(b) shows the simulation results in the transmission mode, which indicates that the maximal difference of the transmission is about 40% at around 51 THz. At about 52.5 THz, the reflection and transmission CDs are vanished according to Figs. 2(a) and 2(b). The circular birefringence can be obtained from the phase difference. The circular birefringence in the reflection mode is defined as $\Delta {\varphi }_{\text{r}}=(\text{arg}{r}_{+-}-\text{arg}{r}_{-+})/2$, while in the transmission mode it is defined as follows $\Delta {\varphi }_{\text{t}}=(\text{arg}{t}_{--}-\text{arg}{t}_{++})/2$. Figures 2(c) and 2(d) show the existence of the circular birefringence. As illustrated in Fig. 2(c), it can be noted that the maximum specular circular birefringence is about 40°. In addition, the maximum circular birefringence of the transmission can reach 50° according to Fig. 2(d).

 

Fig. 2 (a) Reflection spectra, (b) transmission spectra, (c) reflection phase and (d) transmission phase of circularly polarized waves for θ = 45$°$ and E_f = 0.7eV.

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Graphene offers an advantage to dynamically tune the electromagnetic response of the metamaterial. We can modulate the extrinsic chirality of the graphene achiral metamaterial by changing the Fermi energy level. Figure 3 shows the optical properties in the achiral metamaterial for different Fermi energy levels. The peaks of all spectra will be blue shifted when the achiral graphene is added into the metamaterial. Meanwhile, the CD peak values of reflection and transmission are almost kept unchanged according to Figs. 3(a) and 3(b). It is easily concluded that the achiral metamaterial will own the nature of extrinsic chirality no matter there is a graphene or not. The CD peak values in the reflection and transmission will reach about 0.5 and 0.3 without graphene at θ = 45°. Figure 3(c) shows that the CB in the reflection can increase 5° with integrated graphene. While the peak amplitudes of the CB in the transmission slightly decrease after adding graphene in Fig. 3(d).

 

Fig. 3 The tunable extrinsic chirality of the graphene achiral metamaterial. (a)-(b) The reflection and transmission induced CD spectra. (c)-(d) reflection and transmission circular birefringence spectra. (e)-(f) the absorption spectra of RCP and LCP waves at θ = 45° for different Fermi energy levels of graphene.

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Here, we calculate the absorption A_L of the LCP wave as the formula$A_L=1-R_{--}-R_{\text{+}-}-T_{--}-T_{+-}$and the absorption A_R of the RCP wave can be described as $A_R=1-R_{++}-R_{-+}-T_{-+}-T_{++}.$ In Figs. 3(e) and 3(f), it is noted that the A_L and A_R change slightly after adding graphene to the metamaterials. As the Fermi level increases, the peak absorption of LCP and RCP waves will be actively modulated. Both of the absorption spectra shift blue while the absorption values almost remain unchanged. Importantly, there is a large absorption difference of the LCP and RCP waves and as a result the tunable extrinsic chirality occurs in the hybrid achiral metamaterial at oblique incidence.

In order to fully understand the property of the hybrid achiral metamaterial, next the angular dependence of the extrinsic chirality is investigated, in which the Fermi level is fixed at 0.7eV. As shown in Figs. 4(a)-4(d), the extrinsic chirality are vanished with zero CD and CB for both reflection and transmission when the circular polarized waves are normally incident and the optical activity will be more pronounced by increasing the incident angle θ. The CD of the reflection and transmission could reach 80% when the angle of incidence θ is nearly equal to 80°. At about 52.5 THz, the CD values of both reflection and transmission approaches zero, but the rotatory power CB of reflection and transmission can reach about 40° (see Fig. 4c) and 60° (see Fig. 4d), in which it is well known as a pure circular birefringence. This results are consistent with Fig. 2. As seen from Fig. 4(e), the absorption A_L in the achiral metamaterial can reach 40% at θ = 80° and the absorption peak occurs at around 48 THz. The absorption A_R of the RCP is much less than one of the LCP within a wide range of incident angles in Fig. 4(f). Therefore, the proposed hybrid achiral metamaterial will yield strong extrinsic chirality with large CB and CD values within a wide angle range for both reflection and transmission modes and are more flexible to the polarization detection of chiral molecules.

 

Fig. 4 The angular dependence of extrinsic chirality in the graphene achiral metamaterial. (a)-(b) The reflection and transmission CD spectra. (c)-(d) reflection and transmission CB spectra. (e)-(f) the absorption of LCP and RCP waves. The graphene Fermi energy is 0.7eV and the angles of incidence θ vary.

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4. Conclusion

In conclusion, we have studied tunable extrinsic chirality of both reflected and transmitted waves in graphene achiral metamaterial for a wide range of incident angles. The patterned graphene is exactly complementary to the metallic structure. The strong extrinsic chiroptical responses of the metamaterial are allowed at oblique incidence and the integrated graphene can dynamically modulate CD and CB spectra by changing its Fermi level. The peaks of the chiroptical responses will show a blue shift with increasing the Fermi level of the patterned graphene. The maximal CD values of reflection and transmission can reach 80% and 50%, respectively. The maximal CB values (rotatory power) of reflection and transmission can reach 80° and 60°, respectively. The proposed graphene achiral metamaterial offers a strong and tunable extrinsic chiroptical response for both reflection and transmission simultaneously and therefore provides more flexible opportunities to realize chiral sensing and polarization manipulation.