† Corresponding author. E-mail:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11174051, 11374049, and 11204139), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131283), and the Fundamental Research Funds for the Central Universities, China.

The obvious circular dichroism (CD) and optical activity can be obtained based on the chiral metamaterial due to the plasmon-enhanced effect, which is very attractive for future compact devices with enhanced capabilities of light manipulation. In this paper, we propose a dual-chiral metamaterial composed of bilayer asymmetric split ring resonators (ASRR) that are in mirror-symmetry shape. It is demonstrated that the CD can get enhancement in the terahertz regime. Moreover, the CD can be further improved by modulating the asymmetry of ASRR. The enhanced CD effect in the terahertz regime has great potential applications in sensing, biomedical imaging, and molecular recognition.

Although there are various chiral materials in nature, the chirality-associated optical phenomena are usually very weak. Artificial chiral metamaterials have exhibited lots of optical properties in recent years,^{[1–4]} including plasmon-enhanced circular dichroism (CD) and optical activity, which exhibit potential applications in physics, biology, and chemistry.^{[5–7]} This is because artificial metamaterials associated with many novel optical properties^{[8–12]} can lead to strong couplings between electric and magnetic responses attributed to their peculiar geometric structures as well as their unit sizes much smaller than the wavelength of radiation.^{[13–18]} Utilizing these strong electromagnetic couplings in chiral geometric structures, the strong CD and optical activity can occur.^{[19–26]} Recently, Kuwata-Gonokami *et al.* have demonstrated that the giant optical activity could exist in two-dimensional gratings consisting of chiral gold nanostructures with subwavelength features.^{[19]} Decker *et al*. have shown that the obvious CD can be produced by a double-layer chiral planar magnetic metamaterial at near-infrared wavelengths.^{[21]} Kwon *et al.* obtained the strong CD and optical activity through adopting a genetic algorithm in a similar bistratal planar chiral metamaterial in the near-infrared regime.^{[22]} Cao *et al*. realized an obvious CD and optical activity through a chiral metamaterial which is integrated with Ge_{2}Sb_{2}Te_{5} phase-change material in the mid-infrared regime.^{[24]} Gansel *et al*. investigated the three-dimensional (3D)-chiral gold helix which can be used as a broadband circular polarizer.^{[27]} However, to obtain the optimum CD through adjusting the structure of chiral metamaterial is limited to the sign and magnitude of the CD rather than the frequency response. Plum *et al*. have investigated that the optical activity can be excited in an extrinsically chiral metamaterial.^{[28,29]} Singh *et al.* have shown that the sign and magnitude of CD can be tuned by the asymmetric factor of the metamaterial at normal incidence, but these were produced by planar achiral metamaterials.^{[30]}

In this work, we investigated the optimum CD in a chiral metamaterial composed of a 3D-extrinsically-chiral unit cell. This unit cell has a dual-chiral characteristic, which means that both the entire configuration and the component structures are chiral. By adjusting the asymmetry of structure, we realized the further improved CD in the terahertz regime, which falls between the microwaves and far-infrared domain and has unique application potentials. Since the discovery of terahertz proposed by Fleming in 1974, the research of terahertz has made great progress. It has various potential applications in technological domains, such as security detection, sensing, biomedical imaging, and molecular recognition.^{[31–33]} Currently, there are few papers about improving CD in THz region. In particular, the large CD in THz is very useful for the molecular recognition, highly efficient terahertz polarization rotators, and vibration sensor.^{[30]} Consequently, the development of metamaterials with large CD in THz region is very important.

Let us first consider the theoretical analysis of the electromagnetic propagation through a certain slab of uniform chiral medium when a plane wave comes in along the +*z* direction, with the electric field *ω*, *k*, and *I _{j}* represent the frequency, wave vector, and amplitudes, respectively. The transmitted light is then given by

*T*

_{lin}, which relates the generally complex amplitudes of the incident field to that of the transmitted field, can be described as

In the case of a circular polarization, the *T*

*t*is the linear transmission coefficient, + and − denote the right-handed circularly polarized wave (RCP) and the left-handed circularly polarized wave (LCP), respectively. In this way, the transmission matrix

_{ij}*T*= |

_{ij}*t*|

_{ij}^{2}correspond to transmission and circular polarization conversion in terms of power. Therefore, the total transmissions of RCP and LCP are

*T*

_{+}=

*T*

_{++}+

*T*

_{−+}and

*T*

_{−}=

*T*

_{−−}+

*T*

_{+−}, respectively.

Circular dichroism is defined as CD = |*A*_{+}| − |*A*_{−}|, where the circular-polarization absorbances of RCP and LCP are *A*_{+} and *A*_{−}, given by *A*_{+} = 1 − |*R*_{+}| − |*T*_{+}| and *A*_{−} = 1 − |*R*_{−}| − |*T*_{−}|, respectively. Meanwhile, *R*_{+} and *R*_{−} are the circular polarization reflections for RCP and LCP, respectively. In general, the reflections for RCP and LCP are identical through the metamaterials, and thus the circular dichroism is also defined as CD = |*A*_{+}| − |*A*_{−}| = |*T*_{+}| − |*T*_{−}|.

To investigate the transmission characteristics of the metamaterial, we have used full-wave numerical simulations by a commercial package based on the finite-element method (FEM).^{[34]} We consider the right-handed circularly polarized wave (RCP, +) and left-handed circularly polarized wave (LCP, −) to illuminate our proposed structures along the +*z* direction. Figure *ε* = 2.1). The introduced chiral resonator consists of a square two-gap asymmetric split ring resonator (ASRR) with the geometric parameters as follows: The length of the side *a* = 60 μm, the shifted distance of the asymmetric gap *d* = 10 μm, aluminium width *w* = 6 μm, gap width *g* = 3 μm, and aluminium thickness is 0.2 μm. The in-plane unit size of the periodic metamaterial is 75 μm × 75 μm.

Figure

The transmission spectra for different structures normally illuminated by circularly polarized terahertz waves are presented in Fig. *T*_{++} = *T*_{−−} and *T*_{−+} = *T*_{+−}. Utilizing the equation CD = |*T*_{+}| − |*T*_{−}|, thus there is almost no CD phenomenon as shown in Fig. *T*_{++} ≠ *T*_{−−} but *T*_{−+} = *T*_{+−} at 0.87 THz and 1.16 THz in Fig. *T*_{+}| − |*T*_{−}|, as well as *T*_{−+} = *T*_{+−} and *T*_{++} ≠ *T*_{−−} in the dual-chiral metamaterials, it is obvious that the circular dichroism CD = |*T*_{++}| − |*T*_{−−}|. Figure *T*_{++} ≠ *T*_{−−}, while *T*_{−+} = *T*_{+−} at 1.00 THz and 1.20 THz. Intriguingly, the difference between *T*_{++} and *T*_{−−} is obviously enlarged. The corresponding CDs are about 0.45 and 0.5 in Fig.

Generally, for a linear light normally travelling through the medium, there is another characteristic for a chiral structure, that is, the rotation of the polarization angle *θ*. This is a useful effect conventionally known as optical activity. For the proposed dual-chiral metamaterials, the polarization rotation angle *θ* of the transmitted light is given by *θ* = (arg*t*_{++} − arg*t*_{−−})/2, where *t*_{++} and *t*_{−−} denote the complex transmitted coefficients of RCP and LCP, respectively, while arg represents the phase angle. The ellipticity of the transmitted wave that is connected to the power transmittance *T*_{+} and *T*_{−} by

In the above text, we have obtained the improvement of CD through the rotation operation from SBM to ASBM. We consider changing the value of the parameter *d* of the ASBM. As illustrated in Figs. *d* in the ASBM. This starts from achiral metamaterial (*d* = 0 μm), where no CD phenomenon appears [Fig. *d* ≠ 0), two distinct CD phenomena (CD1 and CD2) emerge. Moreover, these two CDs can be tuned with the increase of *d* [Figs. *d* increasing, and reach the maximum, about 0.5 and 0.55 at *d* = 15 μm. Therefore, it is verified that the CDs in our dual-chiral metamaterial can be further improved through operating the asymmetry (*d* ≠ 0) in the ASBM.

We also studied the forward and backward surface current distributions at the frequencies where CD happens for the ASBM (*d* = 15 μm) in Fig. ^{[21,35]} thus a stronger CD1 (0.5) happens. Figure

In summary, we obtained a large CD effect in the THz region through a dual-chiral metamaterial based on two chiral asymmetric split ring resonators excited by normally incident light. It is found that the CD can be improved by adjusting the asymmetry between the two ASRRs in the terahertz regime. In addition, the underlying mechanism for the enhanced CD is discussed in terms of the induced dual magnetic-dipole response, attributed to the strong coupling between the forward and backward resonant structures of the bilayer geometry. This significant CD effect in the proposed dual-chiral metamaterial is very useful for sensing, biomedical imaging, and molecular recognition.

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