1. Introduction

Chirality occurs in natural chiral molecules lacking mirror symmetry, such as cholesteric liquid crystals, sugars, proteins, DNA, viruses and amino acids [1]. Consequently, optical activity known as 3D-chiral effect has been proven highly important in analytical chemistry and molecular biology [2]. Meanwhile, 2D chirality linked to the effect of asymmetric transmission also exists in natural planar chiral materials [3]. However, neither a 2D- nor a 3D- chiroptical effect is conspicuous in natural materials. Either effect can only be detected once strong phase differences between right circularly polarized (RCP) and left circularly polarized (LCP) light accumulate over a long optical path.

Since the advent of nanotechnology, much stronger 3D-chiral responses associated with circular dichroism (CD) [4] and optical activity [5] as well as 2D-chiral responses related to circular conversion dichroism (CCD) [6] and asymmetric transmission [7] have been elicited both from chiral metamaterials (MMs) [8] and achiral MMs [4]. However, fabrication of intrinsically 3D chiral MMs, such as helix [9] and twisted bi-layer configurations [10] in the high frequency region, is still fraught with difficulties. Therefore, 2D planar chiral MMs and achiral MMs, also known as chiral metasurfaces (CMS) [11–14] and achiral metasurfaces (AMS) [15,16], have lately been proposed to achieve a strong chirality in the optical region because they are relatively easy to fabricate. Nonetheless, despite the strong chirality of the MMs, their fixed resonance constitutes serious limitations [17].

Tuning circular polarization can significantly improve detection sensitivity when exploring the chirality of a material, hence the importance of that technique in biosensing [18]. Recently, promising approaches of acquiring controllably chiral responses using MMs have been highly promoted. For example, optical activity in MMs has been actively tuned through external stimuli, such as electrostatic actuation [18], heat [19] or photoexcitation [20–22]; it can also be passively tuned by tilting the MMs against the incident beam [23] or by changing the geometry of the resonance element [24]. Very recently, tunable chiral MMs integrated with active semiconductors have been demonstrated at terahertz (THz) frequencies [9, 20–22], however little research has been done on actively tuning chiral responses from MMs at higher frequencies. That is because the semiconductors do not sustain high densities of injected free electrons outside the THz frequency range, especially from the visible to mid-infrared (MIR) regions [25]. Although it has been shown that chiroptical response can be modulated in the near-infrared (NIR) region by introducing twisted plasmonic metamaterials [24], the relative strength of different circularly polarized waves and the operating spectra cannot be tuned without changing the geometry of the resonance element. Furthermore, among all the techniques for tuning circular polarization, voltage control turns out to be one of the easiest ways in terms of practical operations. Thus, an effective method for actively controlling the chiroptical effect at higher frequencies such as the MIR region, using voltage-controlled planar metamaterials with much simpler geometry is desirable and necessary for practical applications. In this work, we show that even a simple metasurface with Au patches integrated by a single graphene layer enables a pronouncedly tunable CCD in the M-IR region, where the 2D-chiroptcial response is tuned using voltage-biased graphene. This voltage-controlled tunable 2D chirality occurs in the simple metasurface design that is ideally suitable for well-established planar manufacturing technologies with a known high fabrication tolerance, opening up an avenue to polarization control devices in the MIR region and may have an impact in a variety of novel devices and applications, beyond circular polarization manipulation and control.

Graphene is an atom-thick level sheet with two-dimensionally arranged carbon atoms forming a honeycomb lattice [26]. It is a viable candidate for tunable MMs with much unexplored potential since its carrier mobility and conductivity can be continuously modulated over a wide frequency range from THz to optical regimes. The ultrathin graphene also has the advantage of being compatible with planar MMs and appropriate for compact modulators. Therefore, graphene-enabled tunable MMs have attracted considerable attention and have been demonstrated by electrically or optically controlling the graphene’s Fermi level [27–33]. Importantly, the ability to create tunability in chiral MMs using graphene has been demonstrated in both theory [34] and by experiments [35,36], showing that graphene-based MMs are gaining traction in the field of circular polarization control.

Here, we demonstrate the theory of tuning the spectra of a giant CCD can be tuned by using a metal-backed AMS embedded with a graphene film in the M-IR regime. The proposed AMS consists of a 2D reflectarray of Au squares separated from a continuous Au film by a GaAs dielectric layer, where the Au squares occupy the sites of a rectangular lattice. This structure can be called 'metasurface' since its planar reflectarray of Au squares exhibits subwavelength periodicity and negligible thicknesses as compared to the incident wavelength [37,38].

Under oblique incidence, the rectangular reflectarray provides a giant CCD (namely, a large difference between the left-to-right and right-to-left circularly polarized reflectance conversion efficiencies) if it is tilted around any in-plane axis that does not coincide with one of the array's lines of mirror symmetry of the metasurface pattern. The giant CCD attributes to the strong electric and magnetic resonances in the metal-backed AMS [39]. It is because the chirality is characterized by electric and magnetic dipolar moments, and enhancing chirality spectroscopy entails manipulation of both electric and magnetic fields of light [40,41]. By integrating graphene layer with the metal-backed AMS, one can effectively tune the spectra of the CCD via biasing the Fermi level of graphene using external voltage stimuli. The proposed graphene-coupled, voltage-controlled AMS with reduced dimensionality and complexity is of tremendously potential applications in metallic nanostructures and ultrathin active devices. It may be integrated within today’s nanophotonic systems and finds diverse functionalities, like biomolecule sensing, switches, circular polarization transformers, and modulators.

2. Structure and design

Figure 1(a) shows the AMS consisting of two Au layers spaced by a 40nm thick GaAs dielectric interlayer coupled with a 0.5nm thick graphene sheet in the middle. The top metal layer is a 40nm thick Au disk array, where the pitches along the x and y directions are L_x = 400nm and L_y = 800nm. The side length of Au square is d = 200nm. The bottom Au layer has a thickness of 80nm, preventing the transmission of the incident light hence leading to a nearly zero transmittance [39]. Particularly, the strong electric and magnetic resonances in the tri-layers structure may introduce a big difference in the reflectance for RCP and LCP waves under off-normal incidence. The top view of the unit cell is shown in Fig. 1(b), while Fig. 1(c) shows the incident wavevector k, the vector normal to the surface n, and the two primitive lattice vectors (a and b) in red. The incident angle θ is measured between k and n. φ is the rotation angle between the parallel (to the x–y plane) component of k and y-axis. The structure is suspended in a vacuum. A simple Drude model is used for the dielectric constant of Au, ${\epsilon }_m\left(\omega \right)=1-\frac{{\omega }_p^2}{[\omega (\omega +i{\omega }_c)]}$ where ${\omega }_p=1.37\times {10}^{16}Hz$ is the plasma frequency and ${\omega }_c=4.08\times {10}^{13}Hz$ is the scattering frequency for Au [42].The dielectric constant of GaAs in the MIR regime is 10.89 [43]. The simulation is performed by commercial finite integration package CST MICROWAVE STUDIO^®. By applying a voltage between the graphene and bottom Au mirror shown in Fig. 1(c), the carrier density and the position of the Fermi level in the graphene can be dynamically modulated and thus tuning CCD spectra. Here, a 0.5nm thick graphene film has an effective permittivity described by ${\epsilon }_{eff}=1+\frac{i{\sigma }_g}{\omega {\epsilon }_{0}t}$, where σ_g is the conductivity of graphene, ${\epsilon }_0$the permittivity of vacuum, and t = 0.5 nm [30–32]. According to the Kubo formula [44,45], conductivity of graphene (σ_g = σ_intra + σ_inter) consists of intraband conductivity (${\sigma }_{intra}=\frac{i{e}^2}{\pi \hslash }\underset{0}{\overset{\infty }{{\displaystyle \int }}}\frac{ϵ}{\omega -2i\Gamma }\left(\frac{\partial f_d\left(ϵ\right)}{\partial ϵ}-\frac{\partial f_d\left(-ϵ\right)}{\partial ϵ}\right)dϵ$) and interband conductivity (${\sigma }_{inter}=\frac{i{e}^2}{\pi \hslash }\underset{0}{\overset{\infty }{{\displaystyle \int }}}\frac{f_d\left(ϵ\right)-f_d(-ϵ)}{\omega -2i\Gamma -{(2ϵ/\hslash )}^2/(\omega -2i\Gamma )}dϵ$), where e is electron charge, ħ the reduced Planck’s constant, Γ the phenomenological scattering rate, $f_d\left(ϵ\right)={(1+e^{(ϵ-E_F)/(k_{B}T)})}^{-1}$ the Fermi–Dirac distribution, k_B the Boltzmann constant, T the temperature, and E_F the Fermi energy of graphene determined by the carrier density$n_s=\frac{1}{\pi {\hslash }^2{v}_F^2}\underset{0}{\overset{\infty }{{\displaystyle \int }}}[f_d\left(ϵ\right)-f_d(ϵ+2E_F)]ϵdϵ$ where Fermi velocity is $v_F\approx 9.5\times {10}^5\text{m}/\text{s}$. Here, we set the environmental temperature at T = 300K, and the phenomenological scattering rate atΓ = 2 THz. Figure 1(d) shows the ${\epsilon }_{eff}$of graphene at different E_F for the MIR spectral range. By modulating E_F, it is possible to continuously adjust ${\epsilon }_{eff}$, where a blue-shift of the ${\epsilon }_{eff}$spectra is obtained by increasing the E_F. This proves that ${\epsilon }_{eff}$is very sensitive to the bias Fermi level in the MIR region from 1500 to 3000 nm, hence having a potential application in the field of tunable optical metadevices and ultrafast electro-optical modulation.

 

Fig. 1 (a) Schematic of graphene-integrated AMS. The thicknesses of the Au squares, GaAs spacer, graphene and Au mirror is 40, 40, 0.5 and 80 nm, respectively. (b) Illustration of AMS's rectangular lattice pattern, where L_x = 400nm, L_y = 800nm and d = 200nm. (c) Demonstration of k, n, a, b, θ and φ, marked in red. (d) Effective permittivity of graphene (${\epsilon }_{eff}$) for Fermi energies of graphene (E_F) of 0.26, 0.30, and 0.42 eV.

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3. Results and discussion

$r_{ij}$ is the complex circular reflection matrix that connects the reflected field vector $E_i$ and the incident field vector $E_j^0$ by $E_i=r_{ij}{E}_j^0$, where ‘i’ and ‘j’ are symbols for RCP ( + ) and LCP (-) components [46]. $R_{ij}={\left|r_{ij}\right|}^2$represents the intensities of the corresponding reflected and converted components for RCP and LCP incident waves. The total reflectance through the AMS is expressed as $R_j=R_{jj}+R_{ij}$, where $R_j$ is the total reflectance of the structure when the incident wave has polarization j. Although this metal-backed AMS has a near-zero transmittance, one may alternatively utilize the reflectance spectra for the possible applications of the chiroptical response. The diagonal terms$r_{++}$and $r_{--}$of $r_{ij}$ are used to detect the 3D chirality which is linked to the circular dichroism (CD):$\Delta R^{3D}={\left|r_{++}\right|}^2-{\left|r{}_{--}\right|}^2=R_{++}-R_{--}$, where $R_{++}$ and $R_{--}$ are direct reflectance of circular polarization. Similarly, 2D chirality is measured by the off-diagonal terms $r_{-+}$and $r_{+-}$of $r_{ij}$ which is related to the circular conversion dichroism (CCD):$\Delta R^{2D}={\left|r_{-+}\right|}^2-{\left|r{}_{+-}\right|}^2=R_{-+}-R_{+-}$, where $R_{-+}$ stands for left-to-right polarized conversion efficiencies and $R_{+}{}_{-}$ stands for right-to-left polarized conversion efficiencies in reflectance [4,6]. To obtain a reference reflectance spectra, we first investigated the chiroptical response of the AMS without bias voltage, (E_F = 0 eV) for RCP and LCP incidence with θ = φ = 45°, L_x = 400nm and L_y = 800nm, as shown in Fig. 2(a)-2(b). Figure 2(a) shows that the diagonal elements of the reflectance matrix: $R_{+ +}$and $R_{- -}$coincide with each other, indicating the absence of 3D chirality ($CD=R_{+ +}-R_{- -}=0$). Figure 2(b) shows the off-diagonal elements $R_{- +}$ and $R_{+ -}$ both possess one main peak whereas have the largest difference ($CCD= R_{- +}-R_{+ - }=0.23$) at 𝛌 = 2152nm. Therefore, this AMS has an extrinsically 2D chirality with a giant CCD, arising from the mutual orientation of non-chiral elements and the direction of light propagation [6]. Here, $R_{+ +}$,$R_{- -}$,$R_{- +}$, $R_{+ - }$correspond to right-to-right, left-to-left, left-to-right and right-to-left polarized reflectance conversion efficiencies.

 

Fig. 2 The spectra of (a) $R_{++ }$ and $R_{- - }$; (b)$R_{- + }$ and $R_{+-}$with L_x = 400 nm and L_y = 800 nm at θ = φ = 45°, E_F = 0 eV; (c) CCD for φ = θ = 45° at different L_y/L_x with L_x = 400 nm and E_F = 0 eV ; (d) CCD for θ = 45° with different φ at L_x = 400 nm, L_y = 800 nm and E_F = 0 eV; (e) CCD for φ = 45° with different θ at L_x = 400 nm, L_y = 800 nm and E_F = 0 eV; (f) CCD for E_F = 0,0.26, 0.3 and 0.42 eV.(g) Peak positions vs E_F .(h) CCD spectra of the AMS without and with graphene sheet (E_F = 0 eV) for θ = φ = 45°.

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The CCD spectra with different L_y/L_x for fixed L_x = 400nm and θ = φ = 45° are shown in Fig. 2(c), where the CCD is nearly zero for a square array of the Au squares (L_x = L_y = 400nm) since the plane of incidence falls on a line of mirror symmetry of the structure. The value of CCD is gradually increased with L_y / L_x. Even so, for larger values of L_y / L_x (L_y / L_x > 2) the CCD is decreased, owing to reduced coupling of neighboring Au squares along the y direction, which is induced by the diluted rectangular lattice. Figure 2(d) shows the CCD spectra for different φ with θ = 45°. The shape and spectral region of the CCD curves are independent with φ. The CCD achieves the maximum value at φ = 45°, but vanishes for φ = 0° and 90° as the anisotropic axis of the structure is in the incident plane hence leading to a mirror plane of the experimental geometry. Moreover, opposite rotation angles ( ± φ) result in opposite signs of CCD corresponding to two enantiomeric arrangements.

By fixing φ = 45°, Fig. 2(e) shows that CCD's value can be tuned via tilting the structure from θ = 0° to 60° and obtain the maximum for θ = 45°. Furthermore, the CCD spectra are not reversed when θ is opposite, showing that the metal-backed AMS provides an extrinsically 2D chirality [47]. Extrinsic 3D chirality appears when what shows in the experiment is different from its mirror image. That condition is met when the metamaterial and incident direction satisfies the conditions of oblique incidence and there is no 2-fold rotational symmetry and no mirror line in the plane of the incidence [47]. Extrinsic 3D chirality, i.e. circular dichroism and circular birefringence, is reversed for opposite angles of incidence and vanishes in structures with 2-fold rotational symmetry [4]. However as in the case of extrinsic 2D chirality, the chiroptical responses are the same here for opposite angles of incidence (θ) and occur in a structure with 2-fold rotational symmetry. Here, the opposite angles of θ are indistinguishable (namely identical experiments result from waves incident at angles θ and -θ) and thus leading to the same 2D-chiral effect (CCD). This agrees with the definition of enantiomeric configurations for the 2D-chiral effect [6].

Graphene-based MMs have received much attention due to their fast and broad tenability [27–33]. Fermi level in graphene can be fast adjusted using an FET structure [28], where an E_F change of 0.1 eV can be achieved with a bias voltage of a few volts. This would modulate the resonance frequency of the MMs. Figure 2(f) shows that CCD spectral peak exhibits a clear red-shift of the resonance wavelengths of 10 and 34 nm for small variations of corresponding E_F of 0.04 and 0.12 eV respectively, whereas the peak values of the CCD at various E_F are almost invariant. The red-shift of the CCD spectra is due to the change of${\epsilon }_{eff}$in graphene for different E_F. Figure 2(g) shows the relationship of peak positions (resonance wavelengths) with respect to E_F for the numerical simulations. It is clear that varying E_F allows direct control over the chiroptical resonance throughout the MIR regime. This may enable highly sensitive detection of a material’s chirality with circular polarization modulation spectroscopy [18, 48]. Figure 2(h) displays the CCD spectra of the AMS without and with graphene sheet (E_F = 0 eV) for θ = φ = 45°. It shows that the resonance wavelength of the CCD spectra of the bare AMS is red-shifted by coupling a free of bias voltage graphene layer to the AMS. Importantly, our paradigm provides a wide tuning range of the CCD spectra in the MIR region from 1500 to 3000 nm, and may be more efficient compared to those recently proposed tunable chiral and achiral MMs through a control of incident angle, structural geometry or material properties [17–24].

In Fig. 3(a), we present two CCD spectra with normal (θ = φ = 0°) and oblique (θ = φ = 45°) incidences for L_x = 400nm and L_y = 800nm with E_F = 0 eV. For θ = φ = 0°, CCD is absent in the structure across the whole wavelength range. Figure 3(b)-3(c) shows the simulation snapshots of the total electric field intensity $E=\sqrt{{\left|E_x\right|}^2+{\left|E_y\right|}^2+{\left|E_z\right|}^2}$ at 𝛌 = 2152 nm on the Au square array-air interface under RCP and LCP normal incidences (θ = φ = 0°) where no CCD is obtained, and for θ = φ = 45° where a substantial CCD response is observed. The incident total electric field $E_j^0$ has the amplitude of 1 V/m. The E field distributions on the Au square array-air interface are normalized to the maximum intensity of total E field at θ = φ = 0°. For θ = φ = 0°, Fig. 3(b) shows that the E field patterns for the RCP and LCP incidences are exact mirror images of each other. The difference of these field patterns is cancelled, resulting in a zero CCD. For θ = φ = 45°, Fig. 3(c) shows that the field patterns are significantly different between the LCP and RCP light. Moreover, the field pattern appears asymmetric over the nanodisks array under the oblique incidence since the time of the pulse propagating through different regions of the structure is unequal. This also explains how the oblique incidence causes the asymmetric reflectance of the two circular polarizations shown in Fig. 2(b). Different circularly polarized light gives rise to the phase of the various resonance modes that cause constructive or deconstructive interferences of the modes at the Au squares. This results in a significant difference in the backward scattering of the RCP and LCP lights.

 

Fig. 3 (a) Simulated CCD spectra at normal (θ = φ = 0°) and oblique (θ = φ = 45°) incidences with E_F = 0 eV. (b-c) Snapshots of total E field distribution at the Au squares array-air interface during light propagation through the metasurface at λ = 2152 nm and E_F = 0 eV. The response to RCP light is displayed on the left and the response to the LCP light is displayed on the right. The incident total electric field $E_j^0$ has the amplitude of 1 V/m. The E field distributions on the Au squares array-air interface are normalized to the maximum intensity of E field at θ = φ = 0°. (b) Total E field distributions on perpendicular incidence (θ = φ = 0°), showing patterns with mirror symmetry for the two circular polarizations.(c) The asymmetric field distributions in the case of oblique incidence (θ = φ = 45°).

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In Fig. 4(a), we present the CCD spectra at several E_F = 0.26, 0.30 and 0.42 eV for θ = φ = 45°. As can be seen, the resonance wavelength of the CDD spectra red-shifts as the E_F increases, whereas the maximum value of the CCD is relatively immune to E_F. Figure 4(b)-4(d) show the E field distributions with RCP and LCP waves at 𝛌 = 2170, 2180 and 2214 nm corresponding to E_F = 0.26, 0.3 and 0.42 eV, where the field patterns are very different between RCP and LCP oblique incidence, indicating a significant chiroptical response.

 

Fig. 4 (a) Simulated CCD spectra at oblique (θ = φ = 45°) incidences with E_F = 0.26, 0.30 and 0.42 eV. (b-d) Snapshots of total E field distribution at the Au squares array-air interface during light propagation through the metasurface at oblique incidence (θ = φ = 45°). The response to RCP light is displayed on the left and the response to the LCP light is displayed on the right. The incident total electric field $E_j^0$ has the amplitude of 1 V/m. The E field distributions on the Au squares array-air interface are normalized to the maximum intensity of E field at θ = φ = 0°. (b) Total E field distributions at E_F = 0.26 eV and 𝛌 = 2170 nm. (c) Total E field distributions at E_F = 0.30 eV and 𝛌 = 2180 nm. (d) Total E field distributions at E_F = 0.42 eV and 𝛌 = 2214 nm.

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4. Conclusion

In conclusion, a large CCD in the MIR region can be achieved using a highly symmetric AMS with a rectangular reflectarray of Au squares. This extrinsically 2D chirality is induced by the mutual orientation of the AMS and the oblique incident wave. The AMS can be combined with an ultrathin graphene sheet to obtain a prominent tuning capability of the huge CCD. The simple geometry of the AMS allows for its easy fabrication for the MIR region from 1500 to 3000 nm.