A. Structural designs

For the ease of structural engineering, here, Freeth’s Nephroid spiral curve is used to construct the air slits that form the 2D nano-kirigami patterns in a free-standing gold nanofilm. As shown in Fig. 1(a), the slit curve is defined by a polar equation, i.e., ρ=a(1+2⁡sinθ/2) with the unit of μm, where a = 0.162. Here, θ is a parameter that can be flexibly selected with θ1 and θ2 as the starting and ending radians, respectively, based on the desired curvature [see the left panel of Fig. 1(a)]. By utilizing the nano-kirigami principle, the 2D precursors with C3 symmetry arranged in the hexagonal lattice could be transformed into 3D meta-molecules with different levels of deformation [Fig. 1(b)]. The C3 symmetry guarantees the CD response entirely arising from the structural chirality rather than anisotropy. To quantitively evaluate the chiral effects of these meta-molecules, a CD is defined as CD = ARCP − ALCP, where ARCP and ALCP denote the absorption for RCP and LCP incidence, respectively. Due to the C3 symmetry of the structures, the reflection under the normal incidence of RCP light and LCP light is identical, i.e., RRCP = RLCP.3838. T. Naeem, A. S. Rana, M. Zubair, T. Tauqeer, and M. Q. Mehmood, Opt. Mater. Express 10(12), 3342 (2020). https://doi.org/10.1364/ome.411113 In such a case, by applying ARCP∕LCP = 1− RRCP∕LCP − TRCP∕LCP, the CD can then be calculated through the formula of CD = TLCP − TRCP, where TLCP and TRCP denote the transmission for LCP and RCP incidence, respectively.

B. CD reversal by tailoring the plasmonic slit length

Flexible CD engineering is first explored by changing the plasmonic slit length. As shown in Fig. 1(b), the maximum stereo height of 3D chiral meta-molecules with different θ2 is all kept at 500 nm, and the hexagonal lattice period is kept as p = 1.2 µm. It can be seen that the handedness of the 3D chiral meta-molecules is right-handed (RH), and the nearly indistinguishable differences among the meta-molecules are governed by θ2. Interestingly, it is found in Fig. 1(c) that the transmission spectra of the meta-molecules show sharp dips near the lattice period under the excitation of circularly polarized light, which is a clear signature of chiral SLRs. It should be noted that the SLRs can also be identified by controlling the spacing between the units while keeping the meta-molecules unchanged (see Fig. S1 in the supplementary material). Such chiral SLRs are formed by the coupling between the single-particle LSPR mode (scatterings from electric quadrupole moments) and the Rayleigh anomalies (see Fig. S2 in the supplementary material).Importantly, it is found that at the SLR wavelengths, tiny structural changes can alter the phase distributions dramatically. As illustrated in Fig. 1(d), ϕx and ϕy are the phase distributions of Ex and Ey of the eigenmode (the x and y components of the electric field are shown in Fig. S3 in the supplementary material), respectively. When the region is far away from the meta-molecule, the phase distributions of the radiated field of SLR resemble that of the plane wave. In the far-field region, the radiated field of SLR propagating in the positive z direction can be expressed asErz=E0xeiϕ0xE0yeiϕ0ye−ikz.(1)Here, E0x/0y and ϕ0x/0y are the amplitude and initial phases, respectively. In such a case, the handedness of SLR is determined by the sign of Δϕ (Δϕ = ϕ0y − ϕ0x). When θ2 = 3.2, one can obtain Δϕ = 0.367π, and thus, the handedness of the SLR is RH, which is consistent with the handedness of the chiral meta-molecule in Fig. 1(c). When θ2 is decreased to 3, the Δϕ is equal to 0.986π. Unexpectedly, the value of Δϕ changes to −0.473π for θ2 = 2.8, which leads to the handedness of SLR becoming left-handed (LH). Figure 1(e) plots the evolution of Δϕ with θ2. It can be seen that the Δϕ changes from (0, π) to (−π, 0) as the θ2 decreased from 3.2 to 2.8. In such a case, the inversion of SLR handedness is readily achieved without changing the structural handedness.For incident excitation along the z direction, the transmitted wave can be viewed as the superposition of the achiral background transmitted wave and the excitation of SLR, which is defined asTRCP=|t−tE0x−iE0yeiΔϕ|2, TLCP=|t−tE0x+iE0yeiΔϕ|2.(2)Here, t is the achiral background transmission and is real. Consequently, one can get the CD value asCD=4t21−E0xE0y⁡sinΔϕ.(3)Thus, the sign of CD is highly in accordance with the handedness of the SLR.From the above analysis, it can be inferred that the slit length (related to θ2) determines the value of Δϕ, which controls the SLR handedness and finally the sign of the CD. With this in consideration, we further analyze the transmission spectra in Fig. 1(c) to investigate the chiroptical responses and reveal the deeper physics. In the case of θ2 = 3.2, the transmission spectrum shows a typical chiral Fano asymmetric line shape due to the interferences between two pathways [see Eq. (2)]. Since the chiral SLR is RH for θ2 = 3.2, the transmission of RCP light is less than that of LCP light around the resonance. When θ2 is decreased to 3.0, the transmission of RCP light is almost equal to that of LCP light near the resonance due to the weak chirality of SLR. As θ2 is decreased to 2.8, the transmission spectrum under LCP excitation shows the obvious Fano line shape, while the transmission spectrum of RCP light shows that no resonance is excited. This is because the radiation field of SLR is almost from LCP light for θ2 = 2.8. Thus, here, the chiral SLRs are formed through the chiral light–matter interaction via exciting chiral Fano resonance. To quantitatively analyze such flexible CD engineering, the CD spectra under different θ2 are plotted in Fig. 1(f). It can be seen that near the SLR wavelengths, the positive CD peak with a value of 0.44 is transformed into a negative CD dip with a value of −0.66 when the curve length L merely decreases by less than 0.2 µm. It should be noted that in this specific design, the rotational orientation of the unit cell can also slightly change the resonant wavelength of SLR (see Fig. S4 of the supplementary material). The results in Fig. 1(f) show that the bisignate circular dichroism can be obtained once the sign of the circular dichroism at a wavelength close to the lattice period is reversed. The reason for the bisignate circular dichroism is due to the different chiroptical responses in the short and long wavelength regions that originate from chiral SLRs and LSPRs, respectively.3939. C.-Y. Ji, S. Chen, Y. Han, X. Liu, J. Liu, J. Li, and Y. Yao, Nano Lett. 21(16), 6828 (2021). https://doi.org/10.1021/acs.nanolett.1c01802 Here, the bisignate circular dichroism is based on the absorption effect [see Fig. 1(f)], which is different from the mechanism of non-absorption effects.4040. H. Ren and M. Gu, Laser Photonics Rev. 12(5), 1700255 (2018). https://doi.org/10.1002/lpor.201700255 In such a way, the flexible CD engineering is realized via minor structural changes by tuning the chiral SLRs.Here, the sign reversal of the circular dichroism can also be understood from the perspective of the chiral competition mechanism of the bi-chiral meta-molecule array. The handedness of the meta-molecules formed by intercellular twisted arms can be LH (see Fig. S5 in the supplementary material), with which the hexagonal lattice array can be hybridized into RH and LH units, respectively. As a result, the final handedness of the SLR is determined by the competitive relationship between the RH and LH units. Since the competition is very sensitive to structural configurations, the sign reversal of CD can be realized under minor structural changes.

C. CD reversal by controlling the deformation area

Since the SLR wavelength is determined by λSLR = neff × p (neff is the effective refractive index of the mode), the chiral SLRs, in principle, can be tuned by varying neff through controlling the deformable configurations without varying the slit lengths and lattice period. To test this idea, a FIB-based irradiation strategy called hole-shaped Boolean irradiation is used for structural deformations, as shown in Fig. 2(a). Here, the hole-shaped Boolean irradiation refers to the fact that there are certain regions that are not illuminated within a regular irradiation area, similar to the subtraction of the Boolean. This can obtain meta-molecules with central flat disks of different sizes to tune the chiral SLR, as illustrated in Fig. 2(b). Specifically, the colorful dotted circle with different radius R in the inset of Fig. 2(c) represents the boundary of the irradiated and non-irradiated regions. This means that the inner circular region (rR) in the hexagonal lattice represents the non-irradiated area, while the remaining region (r > R) is the irradiated one. Therefore, the central part of the meta-molecule remains flat, while the arms are selectively upward deformed [see Fig. 2(a)]. As shown in Fig. 2(b), the central disk becomes larger and the arms become twister as the radius R increases when the maximum heights of the simulated 3D meta-molecules remain unchanged at 400 nm.The results in Fig. 2(c) show that the Δϕ changes from (0, π) to (−π, 0) as R increases to 0.3 µm. In such a case, the handedness of the SLR is changed from RH to LH due to the structural perturbations controlled by Boolean irradiation. The results in Fig. 2(d) show that the positive CD peak evolves into a negative CD dip at the same wavelength when R is increased from 0.1 to 0.3 µm and the CD spectra exhibit opposite profiles. This can also be attributed to the chiral competition determined by SLR. Accordingly, the normalized surface electric field distributions at the corresponding wavelengths of CD peaks/dips exhibit dramatic differences in Fig. 2(e). The intensity of the electric field excited by RCP light is greater than that of LCP light in the case of R = 0.1 µm, which denotes a larger absorption and a smaller transmission of RCP light, resulting in a positive CD peak. In comparison, the case is precisely contrary when R = 0.3 µm. Moreover, it can be seen that the region of the intensified electric field moves gradually from the center to the edge of the lattice as the enlargement of the central disk. Therefore, it is proved that the chiral SLRs are extremely sensitive to deformations, and the hole-shaped Boolean irradiation provides another scheme to realize flexible CD sign reversal, while the geometric chirality of the meta-molecule keeps unchanged.

D. Effect of the asymmetric environment on chiral SLR

It has been shown that the asymmetric environment can affect the SLRs for arrays of relatively short nanoparticles under normal incidence due to the mismatch of refractive index between substrate and superstrate, while SLRs can be observed for tall nanostructures.32,3532. E. Ponomareva, K. Volk, P. Mulvaney, and M. Karg, Langmuir 36(45), 13601 (2020). https://doi.org/10.1021/acs.langmuir.0c0243035. V. G. Kravets, A. V. Kabashin, W. L. Barnes, and A. N. Grigorenko, Chem. Rev. 118(12), 5912 (2018). https://doi.org/10.1021/acs.chemrev.8b00243 However, it has not been well investigated on chiral meta-molecules whether the asymmetric environment has a significant effect on chiral SLR in the same way. Considering the flexible chiral SLRs in our meta-molecules, the chiral meta-molecules are further designed on a silica substrate, while the superstrate is air, as shown in Fig. 3(a). The asymmetric environment is thus formed due to the refractive index mismatch between silica and air. Compared with the results in Fig. 1(c), the linewidth of the transmission spectra in Fig. 3(a) becomes much wider, and the resonance dip is very shallow. The intensity of CD peak/dip in Fig. 3(b) also becomes weaker, and the linewidth of the CD spectrum becomes much wider, clearly demonstrating the suppression of chiral SLR by the asymmetric environment. The electric field distributions along the surfaces of the meta-molecule arrays also verify the dramatic differences induced by the substrate effects, as plotted in Figs. 3(c)–3(d). It has been shown that when the refractive indices are re-matched, the chiral SLRs can again be observed (see Fig. S6 of the supplementary material).

E. Experimental demonstrations

For experimental demonstrations, the proposed meta-molecule arrays with θ2 = 3.2 and θ2 = 2.8 are fabricated by using the FIB-based nano-kirigami method, as shown in Fig. 4. To minimize the fabrication imperfections, the lattice period is scaled up to 1.4 µm, and the revealed physical mechanisms are valid. Specifically, the chiral meta-molecules sitting on silica substrates are fabricated in three major steps: first, the 2D precursors on a solid Au/silica film are fabricated by high-dose FIB milling; second, the meta-molecules are locally suspended after wet etching of silica below the etched slits; finally, the 2D to 3D transformation is obtained by relatively low-dose FIB irradiation, as illustrated in Fig. 4(a) (see more details in Sec. ). For the chiral meta-molecules in free-standing gold nanofilms, the 2D precursors are first fabricated in a gold film by FIB milling. Subsequently, global FIB irradiation is applied, and the 3D chiral meta-molecule arrays with a maximum deformation height of about 500 nm are directly realized, as illustrated in Fig. 4(b) (see more details in Sec. ). As shown in the scanning electron microscopy (SEM) images in Figs. 4(c)–4(f), high-quality 2D and 3D meta-molecules are successfully fabricated in both cases.For optical characterizations, the transmission spectra of the fabricated 3D meta-molecule arrays are measured under the normal incident LCP and RCP light with a home-built optical system (see more details in Sec. ). The results in Fig. 5(a) clearly show that for the free-standing meta-molecules, the RCP transmission is relatively lower at the wavelength of 1560 nm for θ2 = 3.2, indicating that the interaction of RCP with the chiral meta-molecule array is stronger than that of LCP. In comparison, the interaction of RCP with the chiral meta-molecule array is relatively weaker than that of LCP near the wavelength of 1490 nm for θ2 = 2.8, although the two structures look very similar. To quantitatively characterize the chiral responses, the CD spectra of both arrays are plotted in Fig. 5(b). It can be seen that the positive CD peak and negative CD dip with the values of 0.3 and −0.2 are experimentally achieved for θ2 = 3.2 and θ2 = 2.8, respectively, successfully verifying the predication of CD reversal by simply varying the slit length through changing the value of θ2. Such experimental measurements agree well with the simulation results in Figs. 5(c)–5(d) except that the measured peak/dip wavelengths are slightly larger than those of the simulation results. The simulated/measured Q-factors of the meta-molecule arrays for θ2 = 3.2 and θ2 = 2.8 are 11.3/7.6 and 33.7/22, respectively. The difference between simulations and experiments might be caused by the implantation of Ga+ ions during FIB irradiations, which causes the change in the refractive index and absorption properties of the films. Another reason might be the structural difference between ideal simulations and realistic experiments, for example, the imperfect preparation and surface roughness. Since the slit length of the 2D meta-molecule array with θ2 = 2.8 is shorter than that of θ2 = 3.2, a higher dose of FIB irradiation is required to reach the same height for the array with θ2 = 2.8. Thus, there are more Ga+ implanted in the case of θ2 = 2.8. In such a case, the side effects caused by Ga+ implantation for θ2 = 2.8 are more obvious than those with θ2 = 3.2. That is why the difference between the experimental and simulated spectra for θ2 = 2.8 is larger than that with θ2 = 3.2, see Figs. 5(a) and 5(c). Such a difference could be reduced by enlarging the sample size and thus shifting the operation wavelength toward the long wavelength band.The transmission and CD spectra of meta-molecules on a silica substrate are also measured and plotted in Figs. 5(e)–5(f). It can be clearly seen that both the transmission and CD spectra show broadband spectral characteristics, without clear peaks or dips. Such experimental observations provide solid evidence that the asymmetric environment plays a vital influence on the generation of chiral SLRs and the subsequent CD responses.