Moir\'{e} Metasurface with Triple-Band Near-Perfect Chirality

Bokun Lyu(吕博昆), Haojie Li(李昊杰), Qianwen Jia(贾倩文), Guoxia Yang(杨国霞),\\ Fengzhao Cao(曹凤朝), Dahe Liu(刘大禾), and Jinwei Shi(石锦卫)$^{\hyperlink{s}{*}}$

doi:10.1088/0256-307X/40/5/054202

⇦Chinese Physics Letters, 2023, Vol. 40, No. 5, Article code 054202⇨ Moiré Metasurface with Triple-Band Near-Perfect Chirality Bokun Lyu (吕博昆), Haojie Li (李昊杰), Qianwen Jia (贾倩文), Guoxia Yang (杨国霞), Fengzhao Cao (曹凤朝), Dahe Liu (刘大禾), and Jinwei Shi (石锦卫)* Affiliations Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China Received 9 February 2023; accepted manuscript online 8 April 2023; published online 1 May 2023 ^*Corresponding author. Email: shijinwei@bnu.edu.cn Citation Text: Lyu B K, Li H J, Jia Q W et al. 2023 Chin. Phys. Lett. 40 054202 Abstract Chiral metasurfaces have been proven to possess great potential in chiroptical applications. However, the multiband chiral metasurface with near-perfect circular dichroism has not been well studied. Also, the widely used bilayer metasurface usually suffers from the interlayer alignment and weak resonance. Here, we propose a twisted Moiré metasurface which can support three chiral bands with near-unity circular dichroism. The Moiré metasurface can remove the restriction of interlayer alignment, while maintaining a strong monolayer resonance. The two chiral bands in the forward direction can be described by two coupled-oscillator models. The third chiral band is achieved by tuning the interlayer chiral mode on resonance with the intralayer mode, to eliminate the parallel and converted components simultaneously. Finally, we study the robustness and tunability of the triple-layer Moiré metasurface in momentum space. This work provides a universal method to achieve three near-unity circular dichroism bands in one metasurface, which can promote applications of chiral metasurfaces in multiband optical communication, chiral drug separation, sensing, optical encryption, chiral laser, nonlinear and quantum optics, etc.

DOI:10.1088/0256-307X/40/5/054202 © 2023 Chinese Physics Society Article Text When an object cannot overlap with its mirror image via the rotation or translation operations, it is considered to have chirality. Materials with strong chirality are widely used in various fields, such as molecular detection,[1-3] drug research,[4] and analytical chemistry.[5] However, chirality of natural materials is very weak due to mismatch between size of material unit cell and wavelength of incident light. Artificial structures with strong chiral properties are consistently explored. To date, artificial structures with large chirality have been developed with a variety of materials,[6,7] and chirality can be tuned by a variety of means, such as phase transition,[8] film curvature,[9] and incident angle.[10] Plasmonic chiral metamaterials and metasurfaces made of metals have received extensive attention due to their enhanced near-field optical response. Two-dimensional chiral arrays of various shaped chiral meta-atoms have been widely studied because of their simple fabrication methods, such as L-shaped resonators,[11,12] G-shaped resonators,[13] and windmill shape with triple or quadruple axis of rotation symmetry.[14,15] The three-dimensional (3D) chiral metasurface usually obtains a larger chiral response due to the stronger electromagnetic coupling effect, whereas the fabrication process is complex and requires 3D etching techniques, such as spiral structure.[16,17] Other research groups have used ion beam irradiation to simplify fabrication of 3D structures,[18,19] or deep learning to replace tedious process of structural optimization.[20,21] Multiband polarization selective element is of great interest in multifunctional integrated devices. However, the previous works usually focused on achieving a large chiral response in a single frequency band,[12,22-26] or to achieve the opposite chiral response in adjacent bands.[27] The research of multiband chirality in one metasurface is basically located in mid-infrared,[28] terahertz,[29,30] and microwave regions.[22,27] The study of multiband chirality with near-unity circular dichroism (CD) in telecom band has not been reported. The typical bilayer structure requires strict interlayer alignment,[3] which is an important reason of hindering the further development of multiband chiral devices. In this Letter, we successfully manipulate the optical chiral response of a triple-layer twisted Moiré metasurface to achieve near-perfect circular dichroism in three desired bands simultaneously by symmetry breaking. Using Moiré metasurface to construct multiband chiral device has two advantages. Firstly, Moiré metasurface is robust to misalignment, which can greatly reduce the requirement for fabrication accuracy. Secondly, it can generate a stronger chirality than the well-aligned metasurface because it can maintain strong intralayer resonance, which provides a new route to design multiband polarization selective device. The coupled-oscillator model and channel analysis method are used to analyze the chiral original of the different enantiomer under normal incidence and verified by simulation. Then we construct a twisted Moiré metasurface composed of three gold nanoarrays of various size, which can achieve near-perfect CD in three near-infrared bands simultaneously (centered at 980 nm, 1170 nm, and 1550 nm). We find that the chirality response of this Moiré metasurface can be partially explained by the superposition of two effective bilayer metasurfaces. However, the third band in the backward direction can only be obtained by considering three layers together. Finally, we explore the anisotropy chirality of the twisted triple-layer Moiré metasurface in full momentum space, and find the energy bands localized differently in different directions of the superlattice. The Moiré metasurface is composed of three gold nanoarray layers, with the same lattice constant and different sizes of metal atoms, as shown in Fig. 1. The light is incident normally on the metasurface along +$z$ direction. The sizes of each layer are: bottom layer L$_{1}$: 235 nm (length) $\times 60$ nm (width) $\times 60$ nm (thickness), middle layer L$_{2}$: $\mathrm{275\,nm\times 60\,nm\times 60\,nm}$, and top layer L$_{3}$: $\mathrm{195\,nm\times 75\,nm\times 80\,nm}$. The lattice direction of L$_{2}$ has a twisted angle of 43.6$^{\circ}$ relative to L$_{1}$, which is a Pythagorean angle, and at this angle the Moiré superlattice is translationally symmetric,[31-33] (see Fig. S1 in the Supplementary Materials). The Moiré pitch of 1610.5 nm defines a square Moiré unit cell. The spacer between L$_{1}$ and L$_{2}$ is 60-nm-thick SiO$_{2}$. The L$_{3}$ lattice is perpendicular to L$_{2}$, with a 30-nm-thick SiO$_{2}$ spacer between them (i.e., 150 nm to L$_{1}$). There are two forward transmission bands (LCP, left-handed circularly polarized) and one backward transmission band (RCP, right-handed circularly polarized) at normal incidence.

Fig. 1. Schematic illustration of the chiral coupling in a triple-layer Moiré metasurface. (a) The proposed twisted Moiré metasurface is constituted by three layers of gold nanorod arrays. The pitch of every square lattice array layer is fixed at 300 nm. The sizes of each layer are: bottom layer L$_{1}$: 235 nm (length) $\times 60$ nm (width) $\times 60$ nm (thickness), middle layer L$_{2}$: $\mathrm{275\,nm\times 60\,nm\times 60\,nm}$, and top layer L$_{3}$: $\mathrm{195\,nm\times 75\,nm\times 80\,nm}$. The forward normal-incidence direction is $+z$, and the lattices of L$_{2}$ and L$_{3}$ have a $+43.6^{\circ}$ twisting angle with respect to L$_{1}$. The spacer between L$_{1}$ and L$_{2}$ is 60 nm, between L$_{1}$ and L$_{3}$ is 150 nm. (b) The three layers can form three coupled oscillators, and two of them have specific chirality. By further tuning the parameters, triple-band near-unity chirality can be achieved at telecom band, with two bands in the forward direction, and one band in the backward direction.

Each monolayer gold nanorods are $C_{2}$-symmetric and highly anisotropic, which has no chirality. They can have chirality only when they are chirally coupled. Essentially, to analyze the eigenmodes, these three layers should be considered as a whole. However, from the view of a simplified model, the three layers can form three Moiré pattern metasurfaces (L$_{1}$–L$_{2}$/L$_{2}$–L$_{3}$/L$_{1}$–L$_{3}$), correspond to three groups of coupled modes. The layers L$_{2}$ and L$_{3}$ are perpendicular to each other, so the mode group L$_{2}$–L$_{3}$ is achiral, and in the following, only chiral mode groups L$_{1}$–L$_{2}$ and L$_{1}$–L$_{3}$ are considered. These two mode groups are shown in Fig. 1(b). Usually, the strong chiral coupling between the two layers can be described by the dipole Coulomb interaction,[34] or the Born–Kuhn model.[30] Here, we use a coupled-oscillator model to depict the proposed metasurface. The key difference of it from the other bilayer models such as the Born–Kuhn model and center-aligned model[3,35] is that each oscillator here corresponds to a Moiré dipole. A Moiré dipole is defined as the effective dipole of each layer within one Moiré unit cell. Therefore, Moiré dipole can inherit the advantages of Moiré metasurface. Firstly, it is more robust to the translation error. Secondly, it can maintain the gap resonance of each layer, which is of great importance to realize the third CD band. The schematic diagram of different mode groups formed by the three layers can be found in Fig. S2. The RCP and LCP light beams can couple to antibonding and bonding modes (states), respectively. We use commercial software Lumerical FDTD to simulate the Moiré metasurface. The simulation results of the two bilayer metasurfaces with forward incidence are shown in Figs. 2(a), 2(b) and 2(d), 2(e). The maximal CD in the forward direction obtained from simulation is greater than 0.98, which is in the bonding state at 1550 nm of L$_{1}$–L$_{2}$ group. Another CD peak reaches 0.97, which corresponds to the antibonding state at 980 nm of L$_{1}$–L$_{3}$ group. In Figs. 2(g)–2(h), we also calculate the transmittance spectra of all the polarization components of the two bilayer metasurfaces. First, we can see that each component corresponds to one transmission channel, and the channels in the forward and backward directions have a one-to-one correspondence. For example, the parallel-component channels follow $T_{\rm frr}=T_{\rm brr}$, but the converted-component channels $T_{\rm flr}=T_{\rm brl}$, etc. This is in consistent with the reciprocity theory. For the asymmetric structure, the CD and transmission difference between forward and backward incidences are mainly caused by the converted-component channels such as $T_{\rm flr}=T_{\rm brl}$. Take the L$_{1}$–L$_{2}$ structure as an example, the backward transmittance at 1030 nm is determined by $T_{\rm brr}$ and $T_{\rm blr}=T_{\rm frl}$, while for the forward transmission, the dominant channels follow $T_{\rm frr}=T_{\rm brr}$ and $T_{\rm flr}=T_{\rm brl}$. We can see that $T_{\rm blr}$ and $T_{\rm flr}$ are obviously nonzero, which is the main reason why there is only one near-unity CD peak of L$_{1}$–L$_{2}$ metasurface at both forward and backward incidence.

Fig. 2. Simulation results of the bilayer and triple-layer Moiré metasurfaces in Fig. 1 under forward normal incidence. [(a), (b), (d), (e), (g), (h)] Full-wave simulations of CD spectra [(a), (b)], total transmittance spectra [(d), (e)], and transmission component spectra [(g), (h)] of the two bilayer Moiré metasurfaces in the forward direction. [(c), (f), (i)] Full-wave simulations of CD spectra (c), total transmittance spectra (f), and transmission component spectra (i) of the triple-layer Moiré metasurface in the forward direction. The dashed black lines in (a)–(c) represent the transmittance difference. The dotted green lines in each panel highlight the maximal CD and minimal transmittance. Subscripts f and b indicate the forward and backward incidence, r and l denote RCP and LCP; for example, $T_{\rm flr}$ represents the LCP component transmittance of RCP light incident in the forward direction.

Next, we discuss the origin of the parallel and converted components. The transmission minimum of parallel components stems from the interlayer chiral resonance of the metasurface. Still take the L$_{1}$–L$_{2}$ structure as an example, the minimum of $T_{\rm fll}$ at 1550 nm is caused by the bonding state resonance [Fig. S2(b)], which absorbs the LCP light strongly. Similarly, the minimum of $T_{\rm frr}$ at 1030 nm is caused by the antibonding state, which absorbs the RCP light strongly. The converted component is affected firstly by the interlayer chiral resonance of the metasurface, and when there is no interlayer chiral resonance, it is determined secondly by the resonance of each monolayer (see Fig. S3 for reference). For example, the $T_{\rm frl}$ at 1550 nm is weak, because both the LCP resonance of the bilayer and the linear resonance of layer L$_{2}$ can absorb it greatly. The $T_{\rm flr}$ at 1550 nm is obvious and equal to $T_{\rm frr}$ approximately because there is no RCP resonance in the bilayer at 1550 nm, while the strong linear resonance of L$_{2}$ can lead to nonzero $T_{\rm frr}$, $T_{\rm flr}$, and $T_{\rm frr}\approx T_{\rm flr}$. The same components at 1030 nm can be understood in a similar way. In Figs. 2(c), 2(f), and 2(i), we can still find the two states with CD greater than 0.95 at nearly the same two wavelengths in the triple-layer Moiré metasurface, and both of them stems from LCP transmission of the two bilayer metasurfaces. In this way, we successfully realize two near-unity CD peaks in the forward direction. However, the triple-layer metasurface does not guaranty triple near-unity CD bands. Actually, as can be seen in Fig. 2 that in the forward direction, we can realize only two bands. To obtain the third band, we consider the backward incidence. However, the simple bilayer models in Fig. S2 cannot be used now because the two mode groups can affect each other in the backward direction, and the three layers need to be considered together, as shown in the bottom of Fig. 1(b). It is not easy to analyze the modal interaction directly in the backward direction. Thanks to the reciprocity theory, we can obtain this information by analyzing the forward field distribution, which is much easier. Again, we take the L$_{1}$–L$_{2}$ mode group as an example, to see the impact of layer L$_{3}$ on it. The field distributions of the two resonant wavelengths of L$_{1}$–L$_{2}$ structure obtained at the position of L$_{3}$ are shown in Fig. 3. It can be seen that the field of the bonding state is much stronger and mainly located inside the gap, while that of the anti-bonding state is mainly located outside it. Since layer L$_{3}$ is perpendicular to L$_{2}$, the residual transmission of bonding state is not much affected by L$_{3}$, but that of the anti-bonding state will be greatly modified, because the field is mostly parallel to L$_{3}$. The same argument also applies to L$_{1}$–L$_{3}$ mode group. Therefore, based on reciprocity theory, when RCP light is incident on the triple-layer metasurface in the backward direction, the result will be completely different from the direct superposition of the two bilayer metasurfaces. Based on the analysis of bilayer metasurface, to obtain the third near-unity CD band, both the parallel and converted components should be eliminated from the transmitted light. Therefore, the chiral (by all layers) and linear resonance (by output layer) should be tuned close enough. In the backward direction, the Hamiltonian of the triple-layer metasurface is \begin{align} H=\left( { \begin{array}{*{20}c} \omega_{1} & g_{12} & g_{13}\\ g_{21} & \omega_{2} & 0\\ g_{31} & 0 & \omega_{3}\\ \end{array} } \right), \tag {1} \end{align} where $\omega_{1}$, $\omega_{2}$, and $\omega _{3}$ represent the resonant frequencies of the three layers, and $g_{12}= g_{21}$, $g_{13}= g_{31}$ are the chiral coupling strength between the layers. The chiral coupling between L$_{2}$ and L$_{3}$ is set to 0, because they are perpendicular to each other, and under the same polarization, the detuning between them is pretty big (see Fig. S3).

Fig. 3. Simulation results of electric field intensity of L$_{1}$–L$_{2}$ Moiré pattern at the position of L$_{3}$. (a) The electric field intensity at 1550 nm under forward LCP incidence. The local electric field distributes mainly inside the gap along the long-axis direction of L$_{2}$ nanorods. (b) The electric field intensity at 1030 nm under forward RCP incidence, and the local electric field distributes mainly along the short-axis direction of L$_{2}$ nanorods. The black dashed lines represent the long axis of L$_{3}$ nanorods in the triple-layer metasurface, which is perpendicular to L$_{2}$.

Fig. 4. Simulation results of the bilayer and triple-layer Moiré metasurfaces under backward normal incidence. Full-wave simulations of CD spectra [(a), (b)], transmittance spectra [(d), (e)], and transmission component spectra [(g), (h)] of the two bilayer Moiré metasurfaces in the backward direction. Full-wave simulations of CD spectra (c), transmittance spectra (f), and transmission component spectra (i) of the triple-layer Moiré metasurface in the backward direction. The dashed black curves in (a)–(c) represent the transmittance difference. The vertical dashed green lines in all panels highlight the maximal CD and minimal transmission.

One of the eigenvalues (interlayer chiral resonance) should be equal to $\omega_{1}$ (intralayer linear resonance) to achieve a minimal transmission, and the result is included in Section 3 of the Supplementary Materials. This is the condition to realize the third CD band in the backward direction. Obviously, for given $\omega_{1}$, $\omega_{2}$, and $\omega _{3}$, the key to meet this condition is to tune the coupling strength. To do so, we calculate the results of metasurfaces with different L$_{3}$ positions, and the results are shown in Fig. S4. It can be seen that, besides the resonance positions of the L$_{1}$–L$_{3}$ group, the channels $T_{\rm brr}$, $T_{\rm brl}$ and $T_{\rm blr}$ are also greatly changed. The optimized distance from L$_{3}$ to L$_{1}$ is 150 nm, which corresponds to a 30 nm spacer between L$_{2}$ and L$_{3}$, and the best results are shown in Fig. 4, in which $T_{\rm brr} \sim T_{\rm blr} \sim 0$, and a near-unity CD is formed at 1170 nm in the backward direction. Notably, only twisted Moiré metasurface can maintain the strong intralayer linear resonance, while the twisted center-aligned metasurface[36] cannot maintain such a strong and stable linear resonance because the gap resonance is destroyed during twisting. Therefore, we propose a universal method to obtain triple near-unity CD peaks in one metasurface, which can be extended to any frequency band easily.

Fig. 5. Simulations results in momentum space of a triple-layer Moiré metasurface. (a) Schematic diagram of directions in momentum space. (b)–(e) Full field simulation of angle-resolved CD spectra obtained in $G_{1}$ direction (b) and $G_{2}$ direction (c) at forward incident, and that obtained in $G_{1}$ direction (d) and in $G_{2}$ direction (e) at backward incidence.

Finally, we further analyze the chirality in momentum space to study the robustness and tunability of the device. We first simulate the angle-resolved CD spectra, as shown in Fig. 5, the corresponding angle-resolved transmittance spectra are shown in Figs. S5 and S6. As indicated in Fig. 5(a), $G_{1}$ and $G_{2}$ are two directions of a Moiré superlattice in momentum space. At forward incidence, the CD band at 980 nm in the $G_{1}$ direction and the CD band at 1550 nm in the $G_{2}$ direction are localized, which are robust to the incident direction. The CD band at 1550 nm in the $G_{1}$ direction and the CD band at 970 nm in the $G_{2}$ direction are nonlocalized. At backward incidence, the CD band at 1170 nm in the $G_{2}$ direction has better angular tunability than $G_{1}$ direction. This result gives us the knowledge how to tune the CD band of the triple-layer metasurface. The robustness of the Moiré metasurface is also checked by introducing a misalignment between the layers. The results are shown in Fig. S7. We can see that the misalignment of L$_{1}$ has negligible impact on the final result. The deviation of L$_{2}$ or L$_{3}$ slightly shifts the CD peak, which can be compensated by tuning the incident angle, as just discussed. Importantly, the CD value is still close to unity, unaffected by the deviation. Compared with the well-aligned metasurface,[2,36] we have proven that Moiré metasurface is more robust to interlayer misalignment. In conclusion, we have successfully achieved near-perfect circular dichroism in three desired bands simultaneously in one triple-layer twisted Moiré metasurface. The CD of bilayer metasurface is analyzed by the coupled-oscillator model with the channel analysis method. Then we construct a twisted Moiré metasurface composed of three gold nanoarrays of various sizes, which can achieve near-perfect CD in three near-infrared bands simultaneously (centered at 980 nm, 1170 nm, and 1550 nm). Loss is a big issue in metallic metasurface. The benefit of using metal is that it also has stronger interlayer coupling compared with dielectric metasurface, which is important for the chiral band formation. Also, the loss can enhance the resonant absorption, leading to a larger transmission contrast. The efficiencies (transmission of a chiral light) of the three bands are: at 980 nm $T_{\rm R}=0.24$, at 1170 nm $T_{\rm L}=0.43$, at 1550 nm $T_{\rm R}=0.64$, all greater than those in Ref. [37] (reflectance $\sim 0.1$). On the other hand, the loss of metal is less important when the metasurface is extended to mid-IR, THz or microwave region. The chirality response of this Moiré metasurface in the forward direction can be understood by the superposition of two effective bilayer metasurfaces. However, the mechanism of the third band in the backward direction can only be obtained by considering three layers together, and by eliminating both the parallel and converted components simultaneously at a given wavelength. Finally, we study the robustness and tunability of the triple-layer Moiré metasurface in momentum space. This work clarifies the origin of CD in twisted Moiré metasurface, and proposes a universal method to achieve three near-unity CD bands in one metasurface, which can promote both understanding and applications of chiral metasurface in multiband optical communication, chiral drug separation, sensing, optical encryption, multicolor chiral laser, multi resonance nonlinear, and quantum optics, etc. The idea proposed here can also be extended to other frequency band easily, such as mid-IR, THz, and microwave bands. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12174031, 91950108, and 11774035). 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