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Maximum chirality of THz metasurfaces with quasi-bound states in the continuum

Baoku Wang, Fei Yan, Xingguang Liu, Weimin Sun, and Li Li

Open Access Open Access

Abstract

Metasurfaces hold great promise for terahertz (THz) chiral-optical devices. Here, we proposed a chiral THz metasurface with quasi-bound state in the continuum (BIC) for maximum chirality. By exploiting structural perturbations of the dipole displacement and the diverging angle for the THz metasurface, the symmetry-protected BIC transforms into quasi-BIC. The critical coupling condition is satisfied by the introduction of graphene, enabling the theoretical maximum absorption of the quasi-BIC. Subsequently, the perturbations are balanced to obtain maximum chirality. The numerical simulations show that the THz metasurface exhibits strong linear chirality with the circular dichroism (CD) of 0.99 at the quasi-BIC. Additionally, the chiral third harmonic generation (THG) is achieved, characterized by high efficiency up to 19% and strong THG-CD as high as 0.99. It is expected that the THz metasurfaces has great potential for applications in chiral sensing and imaging.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Terahertz (THz) waves unfold unparalleled opportunities for a myriad of pivotal applications, including ultrafast computing [1], quantum sensing [2], and wireless communications [3]. Metasurfaces, artificially designed subwavelength structures, are utilized for the manipulation of THz waves due to their particular electromagnetic properties. Various THz metasurfaces were presented, facilitating captivating optical phenomena including metalens [4,5], vortex beam generation [6,7], hologram [8,9], and wavefront controlling [10,11]. In particular, metasurfaces have provided an interesting platform for investigating and exploring THz chiral optical effect. The chirality of the metasurfaces can be quantified by circular dichroism (CD), defined as the absorption difference between right circularly polarized (RCP) and left circularly polarized (LCP) waves. In contrast to three-dimensional natural materials or metamaterials, metasurfaces demonstrate their superiority not only in compactness and simplicity of fabrication but also in significantly enhancing CD, offering a new way to achieve more complex manipulation of THz waves at subwavelength scale. Chiral metasurfaces can provide diverse functionalities in THz region including biomolecular sensing [12], polarization control [13,14] and nonlinear imaging [15], which are highly intriguing for practical applications.

Recently, bound states in the continuum (BICs) have been introduced into the metasurface system to enhance optical chiral response [16–18]. Initially suggested in quantum mechanics, BICs have been extended to diverse fields, including acoustics, fluid mechanics, and electromagnetic waves [19]. BICs are regarded as resonance modes with zero leakage and zero linewidth because the energy in the resonant cavity is completely captured without leakage into the continuous. By introducing structural perturbations such as breaking the out-of-plane/in-plane inversion symmetry or varying illumination symmetry, BICs supported metasurface becomes quasi-BICs with ultrahigh Q-factors, causing significant chiral response [16–18,20–23]. In particular, strong nonlinear CD is also obtained for planar quasi-BIC metasurfaces [22]. However, the strong linear and nonlinear chirality cannot be ensured simultaneously. The largest linear CD is caused by MD mode, while the largest nonlinear CD is dominated by ED mode, which are obtained under the different structural parameters. Exploring metasurface in the THz region with both strong linear chirality and nonlinear chirality is still a basic challenge.

In this paper, we propose a chiral metasurface with symmetry-protected BIC for maximum chirality in THz regime. The quasi-BIC is observed by exploiting structural perturbations including the dipole displacement and the diverging angle. The addition of a monolayer graphene into the metasurface allows the critical coupling conditions to be satisfied, leading to the theoretical maximum absorption of the quasi-BIC. Subsequently, the maximum chirality is obtained by balancing the perturbations. The linear chiral response with CD of 0.99 is achieved. In addition, due to the robust third-order nonlinear susceptibility of graphene, the THz metasurfaces demonstrate the ability to obtain nonlinear chirality. The third harmonic generation (THG) conversion efficiency of 19% and THG-CD up to 0.99 is attained. The findings hold significant promise for THz chiral sensing and imaging.

2. Results and discussions

The unit cell of the proposed metasurface without graphene is illustrated Fig. 1. The structural parameters include the period of square lattice p = 16.92 µm, the bars with cross section a × b (a = 2.97 µm, b = 2.52 µm) and lengths L = 8.46 µm. The refractive indices of silicon and silica are 3.48 and 1.5, respectively. The numerical simulation including linear and nonlinear using finite element method (FEM). The proposed metasurface without graphene is a representative structure for the symmetry-protected BIC. To understand the BIC supported by metasurface, we first perform the analysis of the band structure and Q-factor in the case of identically placed and parallel bars. From the band structure and Q-factor shown in Fig. 2, a BIC at Г point can be observed in THz region, characterized by electric dipoles as shown in the inset of Fig. 2(b). The symmetry-protected BIC can transform into a quasi-BIC through introducing asymmetric perturbations, achieved by turning a bar 90° around the y-axis to attain an out-of-plane asymmetric structure, while keeping the tops of the bars in the same horizontal plane (see section 1 in Supplement 1). The asymmetry factor consists of height difference and level difference. Here we denote the asymmetry factor by the height difference Δh = a − b (a is fixed 2.97 µm) to simplify. Under transverse magnetic-polarized wave irradiation, the transmission spectra for the height difference Δh = 0.4 µm is shown in Fig. 2(c), revealing the quasi-BIC resonance with an asymmetric Fano line shape. It can be illustrated by normalized Fano profile within the coupled-mode theory framework [24]. The fitted transmission curve is shown in Fig. 2(c), where it coincides well with the Fano resonance curve. Moreover, the radiation rate of the quasi-BIC can be derived as γ = 0.0109 THz, and the corresponding Q-factor is 6355. To further confirm the BIC, the transmission spectra for different height difference Δh is calculated, as shown in Fig. 2(d), which is multiple 0-1 transmission plots stacking together rather than the range extending to 0-6. As anticipated for BICs-driven systems, in the symmetric case Δh = 0, the BIC is identifiable by the vanishing resonance in the transmission spectra, as shown by the black curve. As the height difference Δh increases, the quasi-BIC engages in energy exchange with the external modes, resulting in sharp resonances. The radiation and linewidth of quasi-BIC resonance can be directly controlled by the height difference Δh.

 figure: Fig. 1.

Fig. 1. Schematic of the metasurface without graphene, (a) metasurface with symmetry structure, (b) breaking out of plane symmetry by turning one bar 90° around the y-axis.

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 figure: Fig. 2.

Fig. 2. (a) Band structure of near the Г point for metasurface with symmetry structure. (b) Corresponding Q-factors of the eigenmode in the k space in the vicinity of the Г point. Inset shows the electric-field distribution and surface current distribution. (c) Transmission spectra at the height difference Δh = 0.4 µm and (d) height difference Δh from 0 to 0.5 µm for metasurface with breaking out-of-plane symmetry.

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The absorption of the dielectric metasurface is inherently limited, leading to a weak CD expressing the difference in absorption between circular polarizations. The monolayer graphene is introduced into metasurfaces at the top of the bars to tune the absorption for maximum chirality. In the THz range, the linear conductivity of graphene is calculated using the Drude-like model [25],

$$\sigma = \frac{{{e^2}{E_F}}}{{\pi {\hbar ^2}}}\frac{i}{{\omega + i{\tau ^{ - 1}}}},$$
where ℏ is the reduced Planck’s constant, τ = 2 ps is the carrier relaxation time, e is the electron charge, and EF = 0.2 eV is the Fermi level. The linear conductivity is a complex number, where the real part indicates the loss of graphene. Graphene as the only lossy material in the proposed structure determines the dissipative loss rate δ.

In the temporal coupled-mode theory (CMT), the dynamic equations of the system with a single-mode optical resonator coupled with two identical ports can be written as [26–28]

$$\frac{{da}}{{dt}} = ({i{\omega_0} - \gamma - \delta } )a + {M^T}|{{s_ + }} \rangle ,$$
$$|{{s_ - }} \rangle = C|{{s_ + }} \rangle + Ma,$$
where a is the resonance amplitude of single mode, ω0 is the resonance frequency, γ is the radiation loss rate, and δ is the dissipative loss rate. |s + 〉 = [s1+, s1+]T and |s−〉 = [s1−, s1−]T are the amplitudes of incident and outgoing waves. C is the usually unitary and symmetric matrix describing the scattering process, between the two ports without the resonator. M is the coupling matrix expressing the coupling between ports and resonance. Based on the energy conservation and time reversibility argument, the relations M†M = 2γ and CM* = −M can be obtained. The amplitude of the resonant mode under the incident wave amplitude |s + 〉 can be expressed as
$$a = \frac{{{M^T}|{{s_ + }} \rangle }}{{i({\omega - {\omega_0}} )+ ({\gamma + \delta } )}}.$$

The light absorption at the frequency ω can be calculated by the following equation

$$A = \frac{{2\delta \gamma }}{{{{({\omega - {\omega_0}} )}^2} + {{({\delta + \gamma } )}^2}}}.$$

It is discernible that the absorption conforms to the Breit-Wigner distribution, and the equation anticipates a symmetrical Lorentzian curve delineated by three parameters, ω0, γ, and δ. At the resonant frequency ω = ω0, the absorption achieves the maximum, and its peak A0 is given by the ratio between the radiation loss rate γ and the dissipative loss rate δ,

$${A_0} = \frac{{2\delta \gamma }}{{{{({\delta + \gamma } )}^2}}}.$$

When the critical coupling condition (γ = δ) is met, the theoretically maximum absorption for the single-mode two-port system is A0 = 0.5. In our structures with inversion symmetry, its momentum space contains the symmetry-protected BIC shown in Fig. 1(a). For ideal BIC, the radiation channel is completely forbidden, regarded as a resonance with infinite lifetime and zero leakage γ = 0. By introducing perturbations to break the structural symmetry, as shown in Fig. 1(b), a quasi-BIC with infinitesimal radiation leakage γ > 0 is constructed, displaying a leak mode with asymmetric Fano line shape. γ can be computed analytically using the summation of the radiation from each port and the incoming and outgoing waves [29,30]

$$\gamma = c({{{|{{D_x}} |}^2} + {{|{{D_y}} |}^2}} )$$
$${D_{x,y}} ={-} \frac{{{k_0}}}{{\sqrt {2{S_0}} }}\left( {{p_{x,y}} \mp \frac{1}{c}{m_{y,x}} + \frac{{i{k_0}}}{6}{Q_{xz,yz}}} \right),$$
where k0 = ω0/c, S0 is the unit cell area, Dx,y is the coupling amplitude, and p, m, and Q represent the electric dipole moment, magnetic dipole moment, and electric quadrupole moment per unit cell. When the structural symmetry is breaking by turning one bar, the unit cell remains with the symmetry of mirror transformation (y) → (−y). Therefore, the electric field components Ex and Ey are odd and even functions concerning the symmetry, leading to Dx = 0. Moreover, both mx and Qyz in Eq. (8) are zero due to Ey (−z) = Ey (z). After above simplifications, the radiation rate γ can be written as
$$\gamma = \frac{{ck_0^2}}{{2{S_0}}}{|{{p_y}} |^2},$$
where py indicates the net electric dipole moment of the asymmetric resonator, which is related to the height difference Δh of the resonator, expressed as py ∝ ± Δhp0, p0 is the electric dipole moment of corresponding symmetry resonator. The radiation rate δ for the quasi-BIC is given as the following expression regarding the height difference Δh
$$\gamma \propto \varDelta {h^2}.$$
The radiation rate can be determined by the height difference Δh of the metasurface structure.

Keeping graphene Fermi level EF = 0.2 eV as a constant, with the dissipative loss rate δ remaining unchanged, the radiation rate γ be modulated by the height difference Δh to meet the critical coupling condition, which leads to the theoretical maximum absorption of 0.5. The absorption spectra of the proposed metasurface with the height difference Δh from 0.2 to 0.6 µm is shown in Fig. 3(a). The absorption of the quasi-BIC resonance shows an increasing and decreasing process, reaching the theoretical maximum absorption of 0.5 when the height difference Δh = 0.4 µm, where the values of the radiation rate γ and dissipative loss rate δ are equal. The absorption of the quasi-BIC as a function of the height difference Δh is depicted in Fig. 3(b). For unequal values of the radiation rate γ and the dissipation loss rate δ, the absorption is less than 0.5, and especially decreases as the difference between their values increases. This phenomenon is consistent with our expectation, the quasi-BIC with theoretical maximum absorption of 0.5 is realized, further enhancing light-matter interactions in THz metasurface system.

 figure: Fig. 3.

Fig. 3. (a) Absorption spectra of the proposed metasurface with different height difference Δh after introducing graphene into our structure. (b) Absorption of quasi-BIC as a function of the height difference Δh.

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 figure: Fig. 4.

Fig. 4. (a) Graphene metasurface with turning one bar out of plane. (b) Graphene metasurface with turning one bar out of plane and rotating the bars in of plane.

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For an incident wave polarized along unit vectors e, the coupling parameter me of the eigenstates can be expressed as

$${m_{\textbf e}} \propto \int\limits_V {{\textbf J}({\textbf r} )} \cdot {\textbf e}{e^{ikz}}dV ={-} i\omega ({{{\textbf p}_1} \cdot {\textbf e}{e^{ik{z_1}}} + {{\textbf p}_2} \cdot {\textbf e}{e^{ik{z_2}}}} ),$$
where V represent the unit cell volume, k is the light wavenumber, J(r) represent the displacement current. p1,2 represent the electric dipole moments of the bars 1 and 2, and z1,2 represent their effective z-coordinates. The coupling coefficients ${m^{\prime}_{\textbf e}}$ for waves incident onto the backside of the metasurface are calculated through similar integrals, accounting for the reversed propagation direction (eikz→e-ikz). The transmission from an incident wave (polarized along unit vector i) to an outgoing wave (polarized along unit vector j) can be given by the following formula
$${T_{{\textbf {ji}}}} = {|{{t_{{\textbf {ji}}}}} |^2} = {\left|{{\tau_c}{\delta_{{\textbf {ji}}}} - \frac{{{m_{\textbf i}}{{m^{\prime}}_{\textbf j}}}}{{i({\omega - {\omega_0}} )- ({\gamma + \delta } )}}} \right|^2},$$
where τc represents a coefficient of background transmission that conserves polarization, and δji represents the Kronecker delta symbol.

When the bars are identically placed and parallel, the eigenstate dipoles are strictly antiparallel, p1 = − p2. Additionally, with z1 = z2, the eigenstate is entirely shielded from all normally incident plane waves, as indicated by me = 0, irrespective of the direction vector e. Turning one bar introduces unequal coordinates z1 ≠ z2, as shown in Fig. 4(a), leading to a nonzero coupling parameter given by Eq. (11), even if p1 = − p2. And the total dipole moment of the proposed metasurface is induced by the displacement of the bar mass center along the z-axis. The coupling parameters between the quasi-BIC and the normal incident wave along the bar (γ-direction) polarization can be evaluated as [16,31]

$${m_\gamma } \propto {{\textbf p}_1} \cdot {{\textbf e}_\gamma } + {{\textbf p}_2} \cdot {{\textbf e}_\gamma }{e^{ikd}} = |{{{\textbf p}_1}} |({1 - {e^{ikd}}} ),$$
where d is the relative shift of the bar centers of mass, determined by Δh.

The remaining mirror symmetry of the proposed metasurface is broken by rotating the bars in plane by a diverging angle θ. The electric dipoles p1 and p2 of the bars no longer antiparallel, and their respective effective z-coordinates z1 ≠ z2, as shown in Fig. 4(b), bring a three-dimensional chirality. Under the circularly polarized waves normal incidence, the coupling parameters in Eq. (13) can be described as

$${m_{L,R}} \propto \sin ({\theta \pm {{kd} / 2}} ),$$
where L, R are the left circularly polarized (LCP) and the right circularly polarized (RCP) waves.

When the perturbations of the dipole displacement and the diverging angle are balanced (θ = kd/2), the quasi BIC efficiently couples to LCP wave with mL∝sin(2θ), while remaining completely isolated from the RCP wave with mR = 0. For the proposed metasurfaces that satisfy the critical coupling conditions, the absorption of the LCP is approaching the theoretical maximum of 0.5 at the quasi-BIC, while that of the RCP is close to 0, allowing for maximum chirality. Notably, this design approach based on lossless system is also applicable in the lossy system, leading to the shift in the maximum chirality condition θ = kd/2 + c (with c is a constant), accompanied by frequency shifts and value changes in CD. The CD is defined as the normalized absorption difference under RCP and LCP waves incidence to quantify the chirality, which is expressed as

$$CD = \frac{{{A_L} - {A_R}}}{{{A_L} + {A_R}}}$$
where AR, xcL are the absorption of the RCP and LCP waves.

When high difference Δh = 0.4 µm and diverging angle θ = 4°, the chiral metasurface with the lossy system attains its maximum chirality. These parameters are fixed in all the following simulations, unless otherwise explained. The transmission spectra for the chiral metasurface are depicted in Fig. 5(a), where Tij represents the transmittance of output polarization i from the input polarization j (i, j∈{R, L}; R and L are RCP and LCP waves). The cross-polarized transmission TLR and TRL for RCP and LCP waves remains consistent, while the co-polarized transmission TRR and TLL for RCP and LCP exhibit distinct different. In accordance by the CMT phenomenology, the metasurface suppressed the most transmission of the LCP wave at quasi-BIC but transmit the RCP wave. The corresponding absorption spectra and CD is calculated as shown in Fig. 5(b). The RCP and LCP absorption of chiral metasurfaces show significant difference. The absorption of LCP and RCP waves are 0.46 and 0.002 at quasi-BIC, the CD can be up to 0.99. It implies that the chirality of the metasurface is significantly enhanced, even obtaining the maximum chirality, with the CD approaching 1. The quasi-BIC supported the proposed metasurface exhibits strong absorption of LCP wave and maximal CD. This is favorable for the enhancement of nonlinear chirality at THz frequencies.

 figure: Fig. 5.

Fig. 5. (a) Transmission spectra under RCP and LCP incidences. (b) Corresponding absorption spectra of RCP and LCP and CD spectra.

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Experimental evidence confirms that graphene exhibits the robust third-order nonlinear susceptibility at THz frequencies, arising from intraband electron transitions and the resonant nature of the light-graphene interactions. The expression for the third-order nonlinear conductivity of graphene is presented by the following formula [32,33]

$${\sigma ^{(3)}} = \frac{{i{\sigma _0}{{({\hbar {v_F}e} )}^2}}}{{48\pi {{({\hbar \omega } )}^4}}}T\left( {\frac{{\hbar \omega }}{{2{E_F}}}} \right),$$
where σ0 = e2/4ℏ, T(x) = 17 G(x) − 64 G(2x) + 45 G(3x), G(x) = In|(1 + x)/(1 − x)| + iπθ(|x| − 1), θ(z) is the Heaviside step function. The nonlinear current density is derived by applying the linear electric field as the source to produce the nonlinear response, calculated as follows [34,35]
$$J = \sigma {E_{\textrm{TH}}} + {\sigma ^{(3)}}E_{\textrm{FF}}^3,$$
where EFF is the electric fields at the fundamental frequency and ETH is the electric fields at the third harmonic frequency. The input power at fundamental frequency is denoted by PFF, and the THG output power is denoted by PTH, calculated through the integration of the power outflow at the third harmonic frequency. The THG conversion efficiency is defined as η = PTH/PFF [36,37] to represent the power conversion between the fundamental frequency and third harmonic frequency. The THG-CD is defined as the normalized THG difference between RCP and LCP waves, expressed as THG-CD = (PTHL-PTHR)/(PTHL + PTHR).

Figure 6(a) shows the THG output power under RCP and LCP incidences under the pumping intensity of 50 kW/cm2, exhibiting distinct peaks at 11.17 THz. The THG output power under RCP incidence is lower than that under LCP incidence by seven orders of magnitude at the quasi-BIC. This indicates a distinct chiral behavior in THG process between RCP and LCP waves. The THG-CD between the LCP and RCP can be up to 0.99 at the quasi-BIC, as shown by the green curve in Fig. 6, revealing a clear contrast in THG output power between two incident circular polarizations. Figure 6(b) and (c) show corresponding electric-field-enhancement distributions and surface current distributions for the quasi-BIC along graphene surface under RCP and LCP incidence. The electric fields under RCP and LCP incidence are enhanced about 5 and 80 times, respectively, and exhibits significant differences, further revealing the reason for the enhanced THG-CD for the quasi-BIC. Moreover, the surface current distribution indicates that the quasi-BIC is induced by electric dipoles. The exploration of chirality for the quasi-BIC resonance, induced by the diverging angle θ, demonstrates variations in both linear and nonlinear chirality. Figure 7(a) illustrates the LCP absorption and CD for quasi-BIC as a function of the deriving angle θ from 0° to 8°. The absorption for LCP wave is better than 0.45 when the diverging angle θ from 2° to 5°, approaching the case of satisfying the critical coupling condition. Notably, through tuning the graphene Fermi level, it is possible to meet the critical coupling condition again, obtaining the theoretical maximum absorption of 0.5 for LCP wave. When the diverging angle θ = 0°, the CD is just below than 0.02, the metasurface is achiral. As the diverging angle θ increases, the CD increases and decreases, achieving a maximum of 0.99 at the diverging angle θ of 4°. This is consistent with the existence of a CD maximum as expected by the CMT. Figure 7(b) depicts the THG output power for LCP wave and THG-CD as a function of the deriving angle θ. With the diverging angle θ increasing, the THG output power for LCP wave shows the identical trend with absorption shown in Fig. 7(a), and reaches the maximum value when the diverging angle θ = 3°. The LCP THG output power is enhanced by the theoretical maximum absorption of the quasi-BIC. The THG-CD reaches the maximum value of 0.99 at diverging angle θ from 2° to 8°.

 figure: Fig. 6.

Fig. 6. (a) THG output power of the chiral metasurfaces and the corresponding nonlinear THG-CD under pumping intensity I = 50 kW/cm2. (b) and (c) electric-field-enhancement distributions and surface current distributions for the quasi-BIC along graphene surface under RCP and LCP incidence.

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 figure: Fig. 7.

Fig. 7. Influence of deriving angle on linear and nonlinear chirality. (a) Absorption under LCP incidence and CD for linear chirality. (b) THG output power and THG-CD for nonlinear chirality.

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Figure 8 shows the THG conversion efficiency of LCP waves and the corresponding THG-CD for the quasi-BIC versus the intensity of the incident wave. The fundamental frequency for the chiral metasurface is fixed at 11.17 THz, aligned with the resonance frequency of the quasi-BIC. The THG conversion efficiency is significantly improved with increasing the incident intensity, reaching 19% under the incident intensity of 50 kW/cm2. Because theoretical maximum absorption at the quasi BIC under LCP wave incidence is obtains by satisfying the critical coupling condition, significantly enhancing the interaction of light with nonlinear matter. It is worth noting that the saturation effect will occur when the incident intensity is beyond a certain value [38,39] (see more details in Section S2 of the Supplement 1). The inset in Fig. 8 reveals a quadratic dependence with a slope of approximately 2, indicating the THG nonlinear process. The achieved THG conversion efficiency of 19% under the incident intensity of 50 kW/cm2 is much higher than that of previously reported nonlinear graphene metasurfaces and gratings [33,35,38,40] (seeing Table 1). Moreover, Fig. 8 displays that THG-CD is not affected by the incident intensity, remaining constant of 0.99. Combining high nonlinear efficiency and strong nonlinear CD, the extremely strong nonlinear chirality is achieved. Compared with previously reported chiral metasurfaces [17,18,22,41,42], the proposed chiral THz metasurface can simultaneously achieve maximum linear and nonlinear chirality, as shown in Table 1. It validates the efficacy of designing metasurface to achieve strong chirality by the theoretical maximum absorption and balancing perturbations.

 figure: Fig. 8.

Fig. 8. LCP THG conversion efficiency and THG-CD dependence of the incident intensity at 11.17 THz. The inset is corresponding log–log plot for LCP THG conversion efficiency.

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Tables Icon

Table 1. Comparisons among chiral or nonlinear metasurface

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Finally, we analyzed the manufacturing feasibility of the designed metasurface. A multi-step nanofabrication method combining a multi-step electron beam lithography process and a multi-step deposition process is experimentally demonstrated to achieve metasurface structures with different heights [18]. Moreover, large-area graphene sheet growth directly by CVD method [43]. The structural dimensions of the designed metasurfaces are on the order of micrometers, and the manufacturing tolerances (mainly caused by lateral alignment accuracy [18]) are about 1%, with negligible impact on the optical performance.

3. Conclusion

In summary, we study the THz quasi-BIC metasurface for maximum chirality. For the THz metasurface without graphene, the dipole displacement and the diverging angle is exploited as structural perturbations, revealing the symmetry-protected BIC transition to a quasi BIC. By incorporating the monolayer graphene into the metasurface, the theoretical maximum absorption of the quasi BIC is achieved due to fulfillment of the critical coupling conditions. Then, the extremely strong chirality is obtained by balancing the perturbations. The linear chiral response with the CD of 0.99 occurs at the quasi BIC. Additionally, the nonlinear chirality is effectively enhanced, including the high efficiency of 19% and strong THG-CD of 0.99. This result renders the designed metasurface as a promising candidate for applications in THz chiral sensing and imaging.

Funding

Fundamental Research Funds for the Central Universities (2023FRFK06002, AUGA5710012622); National Natural Science Foundation of China (12304417).

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 may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

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Supplement 1       Supplementary document forMaximum chirality of THz metasurfaces with quasi-bound states in the continuum-519234

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)
Fig. 1.
Fig. 1. Schematic of the metasurface without graphene, (a) metasurface with symmetry structure, (b) breaking out of plane symmetry by turning one bar 90° around the y-axis.

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Fig. 2.
Fig. 2. (a) Band structure of near the Г point for metasurface with symmetry structure. (b) Corresponding Q-factors of the eigenmode in the k space in the vicinity of the Г point. Inset shows the electric-field distribution and surface current distribution. (c) Transmission spectra at the height difference Δh = 0.4 µm and (d) height difference Δh from 0 to 0.5 µm for metasurface with breaking out-of-plane symmetry.

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Fig. 3.
Fig. 3. (a) Absorption spectra of the proposed metasurface with different height difference Δh after introducing graphene into our structure. (b) Absorption of quasi-BIC as a function of the height difference Δh.

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Fig. 4.
Fig. 4. (a) Graphene metasurface with turning one bar out of plane. (b) Graphene metasurface with turning one bar out of plane and rotating the bars in of plane.

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Fig. 5.
Fig. 5. (a) Transmission spectra under RCP and LCP incidences. (b) Corresponding absorption spectra of RCP and LCP and CD spectra.

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Fig. 6.
Fig. 6. (a) THG output power of the chiral metasurfaces and the corresponding nonlinear THG-CD under pumping intensity I = 50 kW/cm2. (b) and (c) electric-field-enhancement distributions and surface current distributions for the quasi-BIC along graphene surface under RCP and LCP incidence.

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Fig. 7.
Fig. 7. Influence of deriving angle on linear and nonlinear chirality. (a) Absorption under LCP incidence and CD for linear chirality. (b) THG output power and THG-CD for nonlinear chirality.

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Fig. 8.
Fig. 8. LCP THG conversion efficiency and THG-CD dependence of the incident intensity at 11.17 THz. The inset is corresponding log–log plot for LCP THG conversion efficiency.

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Tables (1)

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Table 1. Comparisons among chiral or nonlinear metasurface

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Equations (17)

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σ = e 2 E F π ℏ 2 i ω + i τ − 1 ,
d a d t = ( i ω 0 − γ − δ ) a + M T | s + ⟩ ,
| s − ⟩ = C | s + ⟩ + M a ,
a = M T | s + ⟩ i ( ω − ω 0 ) + ( γ + δ ) .
A = 2 δ γ ( ω − ω 0 ) 2 + ( δ + γ ) 2 .
A 0 = 2 δ γ ( δ + γ ) 2 .
γ = c ( | D x | 2 + | D y | 2 )
D x , y = − k 0 2 S 0 ( p x , y ∓ 1 c m y , x + i k 0 6 Q x z , y z ) ,
γ = c k 0 2 2 S 0 | p y | 2 ,
γ ∝ Δ h 2 .
m e ∝ ∫ V J ( r ) ⋅ e e i k z d V = − i ω ( p 1 ⋅ e e i k z 1 + p 2 ⋅ e e i k z 2 ) ,
T ji = | t ji | 2 = | τ c δ ji − m i m ′ j i ( ω − ω 0 ) − ( γ + δ ) | 2 ,
m γ ∝ p 1 ⋅ e γ + p 2 ⋅ e γ e i k d = | p 1 | ( 1 − e i k d ) ,
m L , R ∝ sin ⁡ ( θ ± k d / 2 ) ,
C D = A L − A R A L + A R
σ ( 3 ) = i σ 0 ( ℏ v F e ) 2 48 π ( ℏ ω ) 4 T ( ℏ ω 2 E F ) ,
J = σ E TH + σ ( 3 ) E FF 3 ,
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