Optical chirality breaking in a bilayered chiral metamaterial

Jianxing Zhao; Yuegang Fu; Zhiying Liu; Jianhong Zhou

doi:10.1364/OE.25.023051

1.Introduction

Metamaterials, exhibiting many new properties such as negative refraction index [1–3], perfect lens [4] and invisible cloaks [5], have attracted growing attention in the scientific communities in recent years. Chiral metamaterials that cannot be superimposed onto their mirror images can also possess giant gyrotropy [6,7], circular or elliptical dichroism [8–10], and strong optical activity [11–13]. As a remarkable characteristic of chiral metamaterials, asymmetric transmission effect is reciprocal and arises from polarization conversion dichroism. Since Fedotov et al [14] firstly observed asymmetric transmission effect in planar chiral metamaterials, lots of sophisticated models have been reported on planar metamaterials to achieve asymmetric transmission in microwave [15–23], THz [24] and even optical [25–33] frequency regions. This property can be used in potential design of photonic devices such as isolators and circulators.

Moreover, metamaterials are also designed to mimic the electromagnetically induced transparency (EIT) effect, which is a quantum interference effect that reduces light absorption over a narrow spectral region in a coherently driven atomic system [34,35]. The plasmonic analogue of EIT has been theoretically and experimentally observed in metamaterials by introducing Fano resonances within an absorption band [36–39]. By optimization, the EIT-like effect allows for a very narrow transparency resonance in the absorption spectrum, which is highly desirable for sensing applications [40,41].

In this paper, we numerically investigate an optical chirality breaking effect in a bilayered chiral metamaterial, consisting of periodic metallic arrays of two L-shaped structures and a nanorod twisted on both sides of a dielectric slab, by using the finite-difference time-domain (FDTD) method. The simulated results show that the optical chirality of asymmetric transmission effect can be broken by the introduction of the nanorods, resulting in a narrow symmetric transmission window. The plasmonic mode properties show that the mechanism of the optical chirality breaking effect is originated from the EIT-like effect due to the coupling between the nanorods and L-shaped structures. The optical chirality breaking window can be modulated by adjusting the geometric parameters of the nanorods. Our design can provide a new way of manipulating the polarization of light or developing plasmonic sensing applications.

2.Theoretical modeling

Figure 1 illustrates our proposed periodic chiral metamaterial. The unit cell consists of two metallic layers parallel to the x-y plane sandwiching a dielectric layer, as shown in Fig. 1(a), each metallic layer consists of two identical L-shaped structures (with a rotation about the z axis by $180 °$ ) and a nanorod (divided from the middle and assigned on both sides of the two L-shaped structures). The resonant structure in each metallic layer has the same geometric pattern, except that the structure in the back layer has been rotated clockwise about the z axis with $90 °$ and then flipped along the x axis regarding that in the front layer. In the simulation model, the dielectric layer is made of silica with a permittivity of 2.1 and a thickness of $t = 40 n m$ . The metallic structure is made of silver with a thickness of $h = 40 n m$ , and is modeled by the experimentally determined dielectric function [42]. The periodicity of the nano chiral structure is $p = 220 n m$ , and the other parameters shown in Fig. 1(c) are, $a = 160 n m$ , $g = 40 n m$ , $w = 40 n m$ , $l = 100 n m$ and $r = 10 n m$ .

Fig. 1 Schematic of the bilayered chiral metamaterial. (a) The unit cell of the chiral metamaterial. (b) and (c) Front and back layers of the unit cell.

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To numerically investigate the optical chiral properties of the metamaterial, three-dimensional (3D) finite-difference time-domain (FDTD) method is used to calculate the asymmetric transmission and plasmonic mode distributions. Periodic boundary conditions are applied in x and y directions, and PML absorbing boundary condition is applied in both the z directions. In order to investigate the optical chirality of metamaterials, $T$ matrix [27] is used to describe the polarization properties of the complex amplitudes of the incident to the transmitted field. For linear base (indicated with subscript $l i n$ ), $T$ matrix is described as

(\begin{matrix} t_{x} \\ t_{y} \end{matrix}) = (\begin{matrix} T_{x x} & T_{x y} \\ T_{y x} & T_{y y} \end{matrix}) = (\begin{matrix} i_{x} \\ i_{y} \end{matrix}) = T_{l i n}^{f} (\begin{matrix} i_{x} \\ i_{y} \end{matrix}),

where indices x and y correspond to the polarization states of the transmitted and the incident lights,

f

indicates the forward (-z direction) propagation. Due to the symmetry property of the proposed metamaterial structure,

T

matrix has some special properties, i.e.,

T_{x x} = T_{y y}

and

T_{x y} \neq T_{y x}

[43], which means that, the total transmission for x-polarized light equals to that of y-polarized light propagating along the opposite direction [18]. The asymmetric transmission is characterized by the asymmetric transmission parameter

Δ

, which is defined as the difference between the transmittances in the two opposite propagation directions [27]

Δ_{l i n}^{x} = {| T_{y x} |}^{2} - {| T_{x y} |}^{2} = - Δ_{l i n}^{y} .

For the proposed structure, the optical chirality of asymmetric transmission effect is for linear polarization only [16,18,19,20,28,29].

3.Results and discussion

Figure 2(a) shows the asymmetric transmission parameter $Δ$ in our interested pass band. At around 743nm wavelength, $Δ$ is near zero, which means that the transmissions for x-polarization and y-polarization along the -z direction are the same (as shown in Fig. 2(b)) and no asymmetric transmission occurs. Moreover, from Fig. 2(c), at wavelength range, the cross-polarization transmission coefficients $| T_{x y} |$ and $| T_{y x} |$ both drop sharply to near zero and the co-polarization transmission coefficients $| T_{x x} |$ and $| T_{y y} |$ increase to about 0.8, and no polarization conversion occurs. While at other wavelengths, strong asymmetric transmission with polarization conversion is presented like that those reported in literatures [18,19,28]. From Fig. 2, we can see that strong asymmetric transmission effect is presented at around 639nm and 875nm wavelengths, and a narrow symmetric transmission window with an equal transmittance of about 0.65 is obtained at around 743nm wavelength. Optical chirality is broken in transmission window for the chiral metamaterial. We attribute the optical chirality breaking effect to the plasmonic analogue of EIT.

Fig. 2 (a) Asymmetric transmission parameter $Δ$ for x- and y-polarized lights. (b) Total transmission spectra for x- and y-polarized excitations. (c) Moduli of the $T$ components.

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In order to reveal the physical mechanism of the optical chirality breaking effect, we analyze the interaction between the structure and external light by presenting the electric field distributions of the metamaterial at 743nm wavelength. Due to the symmetry property of the metamaterial, x- and y-polarized lights for forward propagation are considered to demonstrate the interaction between the front layer and the back layer for convenience. Figures 3(a) and 3(b) show the electric field distributions of the front layer and the back layer of the structure for y-polarized incident light. We also show in Figs. 3(c) and 3(d) the electric field distributions without nanorod, where the field is mainly localized in the two L-shaped structures. For the structure with nanorod, we can find that the light energy is mainly stored around the nanorods along the y direction in the back layer, and the field in the two L-shaped structures is very weak, which indicates that the suppression of the optical chirality occurs in the back layer.

Fig. 3 Electric field distributions for y-polarized light propagating along the -z direction at 743nm wavelength. (a) and (b) Front and back layers with nanorod. (c) and (d) Front and back layers without nanorod.

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As a comparison, we also investigate the optical chirality of the same structure without nanorods as shown in Fig. 4. There is no zero value of asymmetric transmission parameter $Δ$ found at around 743nm wavelength, and no symmetric transmission window exists. From Fig. 4(d), we also find that the cross-polarization transmission coefficient $| T_{x y} |$ is always larger than zero, which means that y-polarized incident light can be converted into x-polarized state. Thus strong optical chirality of asymmetric transmission with polarization conversion is presented, which is the same as literatures reported [18,19,28]. After introducing the nanorods, the optical chirality breaking window appears at around 743nm wavelength. Comparing Fig. 4(d) with Fig. 2(c), both the cross-polarization transmission coefficients $| T_{x y} |$ and $| T_{y x} |$ approach zero at that wavelength due to the introduction of the nanorods and the co-polarization transmission coefficients $| T_{x x} |$ and $| T_{y y} |$ increase sharply. Therefore, the total contributions to the transmission come from $| T_{x x} |$ or $| T_{y y} |$ . It is interesting that even the introduction of the nanorods do not break the symmetry property of the structure, the optical chirality is broken.

Fig. 4 (a) Fragment of the metamaterial without nanorods. (b) Asymmetric transmission parameter $Δ$ for x- and y-polarized lights. (c) Total transmission spectra for x- and y-polarized excitations. (d) Moduli of the $T$ components.

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To further investigate the impact of the nanorods on the optical chirality, we analyze the transmission characteristics of the front layer and the back layer separately by using the y-polarized light excitation, i.e., one layer is removed when analyzing the other one, and all the other geometric parameters remain unchanged.

The total transmission spectra of the two single layers are shown in Figs. 5(a) and 5(b). As a comparison, we also show in Figs. 5(a) and 5(b) as red dashed lines the transmission spectra for single layer without nanorods. Without nanorods, each layer exhibits a broad transmission dip due to the mode resonant loss. However, when the nanorods are introduced, a transmission peak appears within each transmission dip at around 760nm wavelength.

Fig. 5 (a) and (b) Total transmission spectra for the single front and the single back layers with the illumination of y-polarized light. Black solid and red dashed lines correspond to the transmission spectra for the metamaterial with and without nanorods, respectively. (c) and (d) Moduli of the $T$ components of the single back layer without and with nanorods. Insets show the electric field distributions of the metamaterial with nanorods at the transmission peak wavelength.

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We interpret the above phenomenon in terms of the plasmonic analogue of EIT [36–41]. In the proposed metamaterial, coherently coupled bright and dark modes are generated in the unit cell of each layer. For the chiral layer without nanorods, the spectrally broad bright mode is directly coupled to the external light. When the nanorods are introduced, due to the near-field coupling, a spectrally narrow dark mode is excited and coupled back to the bright mode, leading to a destructive interference and a suppressed state in the radiative chiral structure with a much weaker electric field. The insets in Figs. 5(a) and 5(b) show the electric field distributions at the transmission peak wavelength for each layer, where destructive interference leads to a weak electric field in the center chiral structure while the coupling between the center chiral structure and the nanorods is strong. The linewidth of these EIT-like profiles is solely limited by intrinsic Drude loss of the metal. Thus the chiral structure induced field is suppressed in each layer due to the EIT-like effect.

In order to investigate the impact of the EIT-like effect on the optical chirality, we also calculate the $T$ matrix coefficients of the back layer without nanorods and with nanorods as shown in Figs. 5(c) and 5(d), respectively. Due to the symmetry of the two layers, for the front layer, the $| T_{x x} |$ and $| T_{y y} |$ interchange with each other and the $| T_{x y} |$ and $| T_{y x} |$ remain the same. For the chiral structure without nanorods, the cross-polarization transmission coefficients $| T_{x y} |$ and $| T_{y x} |$ are always larger than zero, indicating the optical chirality exists in the whole pass band. When the nanorods are introduced, the cross-polarization transmission coefficients $| T_{x y} |$ and $| T_{y x} |$ both drop to near zero at the transmission peak wavelength, where the co-polarization transmission coefficients $| T_{x x} |$ and $| T_{y y} |$ both present a peak value, and the optical chirality of the chiral metamaterial breaks. Therefore, the transparency window and the optical chirality breaking simultaneously arise due to the EIT-like effect by introducing the nanorods.

It is worth noting that, only the bilayered metamaterial presents asymmetric transmission effect in the resonance pass band, the single layers cannot give birth to the polarization conversion dichroism and the asymmetric transmission parameters $Δ$ equal to zero. For our proposed bilayered metamaterial with the nanorods introduced, a narrow window with $Δ = 0$ arises in the resonance pass band, and the polarization conversion simultaneously disappears. As analyzed above, due to the EIT-like effect, each single layer presents an optical chirality breaking and transparency window in the chiral pass band, and the plasmonic modes at the transparency peak wavelength shown by the insets of Figs. 5(a) and 5(b) agree well with that of the bilayered metamterial at the optical chirality breaking wavelength shown in Figs. 3(a) and 3(b). Therefore, we attribute the optical chirality breaking effect of the bilayered metamaterial to the EIT-like effect as well. The center chiral structure induced spectrally broad bright mode resonance results in a background asymmetric transmission pass band, and the coupling between the spectrally narrow dark mode and the bright mode results in an optical chirality breaking and symmetric transmission window in the asymmetric transmission pass band, which is in agree with the results shown in Fig. 2.

For sensing application, figure of merit (FOM), which is defined as the sensitivity value divided by the resonance linewidth at half-maximum [41], is introduced to evaluate the sensing ability of the proposed structure. In our case, by using water and 25% aqueous glucose solution as the dielectric environments [41], the sensitivity of the EIT-like feature in the chirality breaking window is $\approx 480 n m / R I U$ , and the full-width half-maximum (in water) is $\approx 78.5 n m$ , which lead the FOM to reach about 6.1. We also consider how the rod length affect the optical chirality breaking effect. Figure 6 shows the calculated asymmetric transmission parameters $Δ_{l i n}^{y}$ for different rod lengths. When the length $l$ increases from 80nm to 140nm, the optical chirality breaking window undergoes a redshift within the resonance pass band due to the redshift of the nanorods induced dark mode. Thus an important factor for modulating the symmetric transmission window in the strong asymmetric transmission pass band is provided. In addition, the asymmetric transmission can be modulated as well by changing the geometric parameters of the chiral metallic structure [28,29,32].

Fig. 6 The dependence of the asymmetric transmission parameter $Δ_{l i n}^{y}$ on the rod length $l$ of the bilayered chiral metamaterial.

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4. Conclusion

In summary, we reported the numerical observation of an optical chirality breaking effect in a chiral metamaterial by using finite-difference time-domain (FDTD) method. The simulated results show that zero asymmetric transmission pass band can be achieved in chiral metamaterial due to the plasmonic analogue of EIT caused by coupling between the nanorods and L-shaped structures. The optical chirality breaking window can be modulated by changing the rod length. Our findings are beneficial in designing new polarization controlled devices or developing new plasmonic sensing methods.

Funding

National Natural Science Foundation of China (NSFC) (11474041, 11474037); “111” Project of China (D17017).

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Optical chirality breaking in a bilayered chiral metamaterial

Abstract

1.Introduction

2.Theoretical modeling

3.Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (2)

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