Metasurfaces, with artificially designed ultrathin and compact optical elements, enable versatile manipulation of the amplitude, phase, and polarization of light waves. While most of the metasurfaces are static and passive, here we propose a reprogrammable metasurface based on the state-of-art electromechanical nano-kirigami, which allows for independent manipulation of pixels at visible wavelengths through mechanical deformation of the nanostructures. By incorporating electrostatic forces between the top suspended gold nano-architectures and bottom silicon substrate, out-of-plane deformation of each pixel and the associated phase retardation are independently controlled by applying single voltage to variable pixels or exerting programmable voltage distribution on identical pixels. As a proof-of-concept demonstration, the metasurfaces are digitally controlled and a series of tunable metasurface holograms such as 3D dynamic display and ultrathin planar lenses are achieved at visible wavelengths. The proposed electromechanical metasurface provides a new methodology to explore versatile reconfigurable and programmable functionalities that may lead to advances in a variety of applications such as hologram, 3D displays, data storage, spatial light modulations, and information processing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
On-chip reconfigurable manipulation of light at nanoscale is one of the most important challenges faced by urgent applications such as photonic metamaterials and metasurfaces. For example, by patterning subwavelength optical elements at the interface, metasurfaces [1–3] are able to control over the full characteristics of electromagnetic (EM) waves with versatile applications from flat lens and mirrors [4–6], polarization control [7,8], vortex light generation , detection , holograms displays [11,12] to surface wave couplings , communication system , quantum light control , etc. While most of the studied optical metasurfaces are passive and static, recent advances on dynamic/tunable metasurfaces have explored a new freedom of light manipulation by adopting reconfiguration schemes such as electrical bias [16–20], mechanical strain , thermal effect , liquid crystals , phase-change materials , chemical and structural approaches [25,26], etc. Among these attempts, two types of strategies are recognized, i.e. the modulation of the refractive index of the involved media and the engineering of the physical boundaries of the structural interfaces. While the former one is limited to few material options, the latter strategy can be applied to broad material varieties by introducing dramatic spatial changes through mechanically displacing the structural unit, which is favorable for implementation in practical device applications. For instance, the recent integration of optical metasurfaces with microelectromechanical systems (MEMS)  and spatial light modulators (SLM)  devices has exhibited promising functionalities towards realistic applications. Nevertheless, the pixelated reconfiguration of metasurface itself without additional and complex combinations remains challenging.
Meanwhile, the state-of-the-art nano-kirigami/origami methods have been recently demonstrated as a facile method for the flexible fabrication of 3D micro-/nanostructures [29–31], enabling novel optical characteristics such as giant optical chirality [32,33], elastic wide-angle gratings , stereo metasurfaces , etc. More importantly, the deformable configuration of nano-kirigami structures can be aroused by employing external stimuli such as pneumatic pressure , mechanical compression , electronic bias , etc., paving an avenue towards the development of tunable photonic metadevices. Especially, the use of electrical bias as the trigger in reconfigurable nano-kirigami metasurfaces has been proved capable to develop electromechanical metasurfaces at optical wavelengths , but the feasibility of pixelated operation remains unexplored.
In this article, we propose a scheme for electromechanically reprogrammable metasurfaces based on a nano-kirigami deformation principle. By incorporating electrostatic forces between the top suspended gold nano-architectures and bottom silicon substrate, out-of-plane structural deformation of each pixel and the associated phase retardation are independently controlled by applying single or addressable biased voltages across the Au/SiO2/Si chip. As a result, the metasurfaces are digitally controlled and a series of tunable metasurface holograms such as 3D dynamic display and ultrathin planar lenses are achieved at visible wavelengths. The proposed digitization of metasurfaces could build up a novel platform for versatile light manipulation and diverse tunable ultrathin metadevices at nanoscale.
2. Results and discussions
2.1 Proposal of electromechanically reconfigurable metasurfaces
The unit cell pattern of proposed electromechanically reprogrammable metasurfaces is composed of two combined Archimedean spirals in a gold nanofilm, and arranged in a square lattice with a separation of 2 µm, as schematically shown in Fig. 1(a). The Archimedean spiral curves can be described as r(θ) = 220 × θ, where r is the distance to the spiral center and θ is the azimuthal angle (from 2π to maximum 4.25π in this article, θ = 2π+Δθ, where Δθ is varied within [0, 1.76π] in Fig. 1(a)), respectively. To realize the electromechanical and pixelated out-of-plane deformations, a SiO2/Si substrate coated by a 60-nm-thick gold film is applied based on an on-chip and electromechanically reconfigurable nano-kirigami method , in which the predesigned 2D spirals can be patterned by electron-beam lithography (EBL) and subsequent ion-beam etching (IBE), followed by a wet-etching processes to suspend the top gold nanostructures. As shown in Fig. 1(b), the 2D nano-kirigami pattern suspended above SiO2 pillars can be deformed into 3D geometry by attractive electrostatic force when a proper voltage is applied. Such a transformation is reversible by switching on and off the voltage and can be utilized to dynamically modulate the optical properties of the metasurfaces, providing a simple scheme for reconfigurable spatial displacement. Since the reflection phase is dependent on the deformation height of the central plates (see below analysis), the induced shift in optical phase (Δϕ) can thus be controlled by the introduced electrostatic force. It should be noted that there is positive feedback between the attractive electrostatic force and the deformation of predesigned spiral patterns, i.e. the reduced gap between nanostructures and Si substrate in turn increases the attractive force when the suspended parts are pulled downward by the electrostatic force. Once the applied voltage exceeds the critical voltage (named pull-in voltage), the system becomes unstable and the deformation increases dramatically. Therefore, in following simulations, the applied voltage is controlled below the pull-in voltage.
Furthermore, by varying structural parameters (for example the range of azimuthal angle Δθ) of the nano-kirigami pattern, nanostructures with different morphologies can reach different deformation height (Δh) under the same voltage, as shown in Fig. 1(c) and 1(d). For example, under the same voltage, spirals with small Δθ are more difficult to achieve large deformations for efficient phase modulation than the spirals with large Δθ. In such a case, the optical characteristics, especially the reflection optical phase, can be designed by varying the azimuthal angle of the spirals. Based on this characteristic, two strategies can be adopted to achieve the electromechanically reconfigurable metasurfaces. The first one is to construct metasurfaces with different pixels, in which the phase retardation Δϕ is controlled by the designed value of Δθ and the deformations are triggered by the same voltage. The second scheme employs the same unit cell in each pixel, in which different voltages are adopted to achieve pixelated phase retardation.
2.2 Electromechanically reconfigurable metasurfaces under single-voltage control
Figure 1(e) and 1(f) illustrate a reconfigurable nano-kirigami metasurface before and after the deformation by switching off and on a single voltage. Specifically, in Fig. 2(a), the deformation height of the central plate of the unit cell and corresponding phase shift at three wavelengths as a function of Δθ are plotted, which is calculated by using the finite element software COMSOL when a single voltage of 10.4 v is directly applied to the unit cell. It can be seen that the deformed height increases continuously with the azimuth angle. The maximum out-of-plane deformation height of the Archimedean spirals is about 230 nm when Δθ = 2.25π, and the phase shift compared with the undeformed region is Δϕ = 1.73π (as can be expected by Δϕ = 2πneffh/λ, where neff is the effective refractive index of the medium and λ is the operating wavelength 532 nm). It should be mentioned that the formula mentioned above does not count the influence from the suspended arms. Nevertheless, it can be simply utilized to efficiently construct the structural patterns, with which the deviation is negligible (see the following reconstructed hologram images). Importantly, the phase difference can change from 0 to nearly 2π at visible wavelength region, as shown in the right of Fig. 2(a), which is sufficient for the gradient phase control. To construct a metasurface, eight spiral antennas are selected to cover the 2π phase difference with eight steps (with eight different azimuth angles), as plotted in Fig. 2(b). Furthermore, the reflection efficiency keeps almost constant with the azimuthal angle, providing an ideal scheme for encoding a phase-only hologram. To this aim, Fig. 2(c) illustrates the sketch of a proposed dynamic holographic hologram with the Archimedean spirals of different azimuthal angles. For a brief demonstration, the metasurface is designed with 32 × 32 cells in a square lattice, resulting in an overall size of 64 µm × 64 µm. To obtain the corresponding phase profiles for reconstructed target objects, for example an Archimedean spiral pattern, a modified Gerchberg-Saxton (GS) algorithm  in the Fresnel diffraction range in a computer-generated hologram (CGH) is utilized. The wavelength in G-S algorithm here is 532 nm, and the reconstructed image from the simulated metahologram is an Archimedean spiral pattern under x-polarized incidence. During the simulations, perfectly matched layer absorbing boundary condition and periodic boundary condition are applied with Si substrate and the edges of the metasurface, respectively, with published material parameters (Gold-CRC, SiO2-Palik, and Silicon-Palik) . During the hologram simulations, the whole arrays are simulated for the holographic images. Since the working wavelength (532 nm) is smaller than the size of modulation spirals, the presence of the multi-order diffraction and zero-order diffraction speckle are inevitable. Nevertheless, here we merely test the feasibility of the digitization of metasurfaces by electromechanical reconfiguration, although the signal noise ratio and the quality of the reconstructed image directly from the phase profiles of hologram might be unsatisfactory. In order to get clear hologram image, an additional phase shift along the y axis is encoded into the CGH to enable the CGH reconstruction component away from the zero-order diffraction. The phase shift introduces gradient phase change to the original CGH so that the reconstructed images will be projected with a reflection angle, which can suppress the feedback of the zero-order diffraction beam so as to improve the quality of the reconstructed image. As the numerical Fresnel reconstruction image of the metasurface, Fig. 2(d) plots the far-field intensity distribution at 1 mm away from the metasurface under a bias voltage of 10.4 v, showing well reconstructed images. It should be mentioned that here the holographic display is polarization insensitive since only the central plate of the spiral structures contributes to the phase construction, while the twisted arms are treated as a random noise in far-field imaging. At the same time, the resolution of the reconstructed images is determined by the pixel number of the metasurface according to the G-S algorithm, with which the quality of the images can be improved by increasing the unit number.
Such a scheme can also be employed for dynamic beam steering, as schematically illustrated in Fig. 3(a). In this case, eight selected antennas in Fig. 2(b) are adopted to build up the phase profiles required for reflective beam focusing with focal length f = 800 µm at 532 nm with applied voltage of 10.4 v. Specifically, to focus an incident plane wave beam, the ultrathin metasurface is designed with spatially varied phase shift. The spatial phase profile along the radial direction can be calculated by3(b), as a template to be filled with designed antennas to form the reconfigurable metalens after a phase discretization to eight steps.
For a proof-of-concept demonstration, the designed metalens is built up by 80 × 80 pixels with a periodicity of 2 µm in x-y (z = 0) plane. As shown in Fig. 3(c), the calculated discrete phase profiles at z = 0 and corresponding intensity at z = 800 µm under three selected bias voltages are depicted, revealing that the light can be simply reflected or focused at the predetermined positions (here corresponding to f = 800 µm) before and after the voltages are applied. For example, due to the flat surface of 2D units before applying voltage, the metasurface can be treated as a reflective mirror at V = 0 v. With the gradual increase of the applied voltage, the deformation of the nanostructures occurs. As a result, the height of the central part and phase retardation are also increased, and the metasurface finally achieve the predesigned phase profiles for focusing function at the voltage of 10.4 v, as plotted in the bottom of Fig. 3(c).
The full-field theoretical intensity profiles of the light at a wavelength of 532 nm behind the metalens in the x-y and x-z plane are displayed in Fig. 3(d) and (e), showing the enhancement of focusing effect with the increase of the voltage and a bright spot in the focal plane at 800 µm under 10.4 v. As shown by the intensity profiles plotted in Fig. 3(c), the sidelobes around the focal point can be greatly suppressed by increasing the applied voltage, which can be further improved by the enhancement of space-bandwidth product though miniaturizing the unit size, as well as the increase of effective reflective area though increasing the ratio of deformable part in the unit cell (reducing the ineffective reflective area on the deformed arms). Therefore, the simulation results in Fig. 3(d) and (e) clearly prove the feasibility of dynamic switching between mirror reflecting and beam focusing, indicating that our scheme can be extended to realize reconfigurable switching between targeted optical functions.
2.3 Programmable metasurfaces based on pixelated voltage control
As the second scheme of digitalized metasurfaces, identical unit cells are employed to construct the initial 2D patterns and the deformation of each pixel (together with the induced phase retardation) is independently controlled by the pixelated predesigned input voltage. Here, we apply the nanostructure in Fig. 1(a) as the unit cell of the coding metasurface and the azimuthal angle is kept constant in this platform. We choose θ = 4.25π to meet the design demand and the simulated deformation height of the nanopattern is shown in Fig. 4(a).
When the applied voltage increases linearly from 0 to 10.5 v, the deformation height is exponentially increased from 0 to 256 nm, reaching a maximum of 256 nm and a phase retardation of −1.92π (532 nm) at 10.5 v. To construct the metasurfaces, eight values of bias voltage are selected to cover the 2π phase range with a step of π/4 under uniform reflection efficiency, as shown in Fig. 4(b). Note that the continuity of the input voltage makes it possible for continuous deformation and phase modulation of the nanostructure rather than discrete sampling. Figure 4(c) illustrates a sketch of the proposed dynamic holograph imaging with the reprogrammable metasurface under certain voltage distribution. In order to get the phase profile for holographic display, a phase-only off-axis CGH of a windmill-like nanopattern and other patterns (with pixel dimension of 2 µm × 2 µm and pixel number of 32 × 32) are designed according to the modified GS algorithm in Fresnel range, and additionally reconstructed beam steering is also encoded by imposing a gradient phase shift to separate the reconstruction beam from the zero order diffraction. Each unit element is encoded with the pre-calculated voltage with respect to each pixel on the metasurface interface, and the eight-level independent DC voltage distribution is used to deform the unit cell for to realized eight predesigned phase shift for the reconstruction of the holographic image. In such a case, by digitalizing the distribution of the voltage in a high speed, dynamic switching between different holographic images can be successfully visualized. To test this functionality, the phase profiles of several holograms for the reconstructed images are numerically calculated, and the corresponding voltage distribution are encoded, as plotted in the first column of Fig. 4(d). In the specific numerical simulations, the holograms are illuminated by a 532 nm normal incidence wave, and the holographic image is monitored at z = 1 mm. As shown in the second column of Fig. 4(d), three types of reconstructed images (“smile”, “windmill”, “star”) are clearly shown from the same metasurface by simply programing the applied voltage distributions. Such uniform design of the unit cell greatly simplifies the fabrication complexity and the flexibility of the digitalized voltage control with high-speed response makes electromechanical metasurface promising for other dynamic optical and photonic applications.
In summary, we have demonstrated an electromechanically reprogrammable nano-kirigami metasurface to achieve pixelated out-of-plane deformations towards digitalized phase control. The digital metasurfaces with independent manipulation function of addressable pixels at visible wavelengths have been proved to be able to achieve dynamic holographic display and beam steering by simply controlling the input DC voltage. Both strategies of variable pixel patterns controlled by a single voltage and identical pixel patterns controlled by programmable voltage distribution are successfully demonstrated. It should be mentioned that due to the complex 3D deformed geometries and to increase the simulation efficiency, we only employed 32 × 32 cells in the numerical simulations for image reconstruction, of which the principle can be applied to holograms with more pixels. For future experimental explorations, the pixelated voltage applied to each spiral unit could be achieved by utilizing the multi-line addressing method that has been successfully commercialized in pixel-level controlled OLED (Organic Light-Emitting Diode) displays. Such a platform enables diverse dynamic optical and photonic reconfiguration in the visible wavelength range, and is highly extendible to other configuration designs, material platforms and wavelength regions. This work may pave a new avenue for active metasurface and dynamic manipulation of light at nanoscale, which could lead to advanced device applications with multitasking and rewritable optical functionalities.
National Natural Science Foundation of China (61675227, 61975014, 61975016, 62035003); National Key Research and Development Program of China (2017YFA0303800); Science and Technology Planning Project of Guangdong Province (2020B010190001); Beijing Municipal Natural Science Foundation (1212013, Z190006).
The authors thank Analysis & Testing Center at Beijing Institute of Technology for assistance in FIB facilities and useful discussions.
The authors declare no conflicts of interest.
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.
1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
2. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
3. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
4. S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018). [CrossRef]
5. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012). [CrossRef]
6. C. Tong, T. Shiwei, Z. Bin, W. Guangming, J. Wenye, Q. Chao, W. Zuojia, L. Erping, and C. Hongsheng, “Ultrawideband chromatic aberration-free meta-mirrors,” Adv. Photonics 3(1), 016001 (2020). [CrossRef]
7. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
8. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef]
9. P. Yu, J. Li, X. Li, G. Schutz, M. Hirscher, S. Zhang, and N. Liu, “Generation of Switchable Singular Beams with Dynamic Metasurfaces,” ACS Nano 13(6), 7100–7106 (2019). [CrossRef]
10. N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365(6448), eaax1839 (2019). [CrossRef]
11. H. Gao, Y. Wang, X. Fan, B. Jiao, T. Li, C. Shang, C. Zeng, L. Deng, W. Xiong, J. Xia, and M. Hong, “Dynamic 3D meta-holography in visible range with large frame number and high frame rate,” Sci. Adv. 6(28), eaba8595 (2020). [CrossRef]
12. G. Zheng, H. Muhlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
13. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef]
14. P. Xie, G.-M. Wang, H.-P. Li, Y.-W. Wang, and B. Zong, “Wideband RCS Reduction of High Gain Fabry-Perot Antenna Employing a Receiver-Transmitter Metasurface,” Prog. Electromagn. Res. 169, 103–115 (2020). [CrossRef]
15. T. Stav, A. Faerman, E. Maguid, D. Oren, V. Kleiner, E. Hasman, and M. Segev, “Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials,” Science 361(6407), 1101–1104 (2018). [CrossRef]
16. J. Li, P. Yu, S. Zhang, and N. Liu, “Electrically-controlled digital metasurface device for light projection displays,” Nat. Commun. 11(1), 3574 (2020). [CrossRef]
17. B. Zeng, Z. Huang, A. Singh, Y. Yao, A. K. Azad, A. D. Mohite, A. J. Taylor, D. R. Smith, and H. T. Chen, “Hybrid graphene metasurfaces for high-speed mid-infrared light modulation and single-pixel imaging,” Light: Sci. Appl. 7(1), 51 (2018). [CrossRef]
18. X. Zhao, J. Schalch, J. Zhang, H. R. Seren, G. Duan, R. D. Averitt, and X. Zhang, “Electromechanically tunable metasurface transmission waveplate at terahertz frequencies,” Optica 5(3), 303–310 (2018). [CrossRef]
19. L. Cong, P. Pitchappa, C. Lee, and R. Singh, “Active phase transition via loss engineering in a terahertz MEMS metamaterial,” Adv. Mater. 29(26), 1700733 (2017). [CrossRef]
20. X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016). [CrossRef]
21. S. C. Malek, H. S. Ee, and R. Agarwal, “Strain Multiplexed Metasurface Holograms on a Stretchable Substrate,” Nano Lett. 17(6), 3641–3645 (2017). [CrossRef]
22. A. Komar, R. Paniagua-Domínguez, A. Miroshnichenko, Y. F. Yu, Y. S. Kivshar, A. I. Kuznetsov, and D. Neshev, “Dynamic Beam Switching by Liquid Crystal Tunable Dielectric Metasurfaces,” ACS Photonics 5(5), 1742–1748 (2018). [CrossRef]
23. C. Zou, A. Komar, S. Fasold, J. Bohn, A. A. Muravsky, A. A. Murauski, T. Pertsch, D. N. Neshev, and I. Staude, “Electrically Tunable Transparent Displays for Visible Light Based on Dielectric Metasurfaces,” ACS Photonics 6(6), 1533–1540 (2019). [CrossRef]
24. S. Abdollahramezani, O. Hemmatyar, M. Taghinejad, H. Taghinejad, Y. Kiarashinejad, M. Zandehshahvar, T. Fan, S. Deshmukh, A. A. Eftekhar, W. Cai, E. Pop, M. A. El-Sayed, and A. Adibi, “Dynamic Hybrid Metasurfaces,” Nano Lett. 21(3), 1238–1245 (2021). [CrossRef]
25. J. Li, Y. Chen, Y. Hu, H. Duan, and N. Liu, “Magnesium-Based Metasurfaces for Dual-Function Switching between Dynamic Holography and Dynamic Color Display,” ACS Nano 14(7), 7892–7898 (2020). [CrossRef]
26. J. Li, S. Kamin, G. Zheng, F. Neubrech, S. Zhang, and N. Liu, “Addressable metasurfaces for dynamic holography and optical information encryption,” Sci. Adv. 4(6), eaar6768 (2018). [CrossRef]
27. J. Rogers, Y. Huang, O. G. Schmidt, and D. H. Gracias, “Origami MEMS and NEMS,” MRS Bull. 41(2), 123–129 (2016). [CrossRef]
28. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011). [CrossRef]
29. M. K. Blees, A. W. Barnard, P. A. Rose, S. P. Roberts, K. L. McGill, P. Y. Huang, A. R. Ruyack, J. W. Kevek, B. Kobrin, D. A. Muller, and P. L. McEuen, “Graphene kirigami,” Nature 524(7564), 204–207 (2015). [CrossRef]
30. Y. S. Guan, Z. Zhang, Y. Tang, J. Yin, and S. Ren, “Kirigami-Inspired Nanoconfined Polymer Conducting Nanosheets with 2000% Stretchability,” Adv. Mater. 30(20), 1706390 (2018). [CrossRef]
31. J. Li and Z. Liu, “Focused-ion-beam-based nano-kirigami: From art to photonics,” Nanophotonics 7(10), 1637–1650 (2018). [CrossRef]
32. Z. Liu, H. Du, J. Li, L. Lu, Z. Y. Li, and N. X. Fang, “Nano-kirigami with giant optical chirality,” Sci. Adv. 4(7), eaat4436 (2018). [CrossRef]
33. W. J. Choi, G. Cheng, Z. Huang, S. Zhang, T. B. Norris, and N. A. Kotov, “Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators,” Nat. Mater. 18(8), 820–826 (2019). [CrossRef]
34. L. Xu, X. Wang, Y. Kim, T. C. Shyu, J. Lyu, and N. A. Kotov, “Kirigami Nanocomposites as Wide-Angle Diffraction Gratings,” ACS Nano 10(6), 6156–6162 (2016). [CrossRef]
35. Z. Liu, J. Li, Z. Liu, W. Li, J. Li, C. Gu, and Z. Y. Li, “Fano resonance Rabi splitting of surface plasmons,” Sci. Rep. 7(1), 8010 (2017). [CrossRef]
36. S. Chen, W. Wei, Z. Liu, X. Liu, S. Feng, H. Guo, and J. Li, “Reconfigurable nano-kirigami metasurfaces by pneumatic pressure,” Photonics Res. 8(7), 1177–1182 (2020). [CrossRef]
37. Z. Liu, Y. Xu, C. Y. Ji, S. Chen, X. Li, X. Zhang, Y. Yao, and J. Li, “Fano-Enhanced Circular Dichroism in Deformable Stereo Metasurfaces,” Adv. Mater. 32(8), 1907077 (2020). [CrossRef]
38. S. Chen, Z. Liu, H. Du, C. Tang, C. Y. Ji, B. Quan, R. Pan, L. Yang, X. Li, C. Gu, X. Zhang, Y. Yao, J. Li, N. X. Fang, and J. Li, “Electromechanically reconfigurable optical nano-kirigami,” Nat. Commun. 12(1), 1299 (2021). [CrossRef]
39. R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1971).
40. E. D. Palik, Handbook of optical constants of solids (Academic press, 1998), Vol. 3.