## Abstract

Reconfigurable three-dimensional (3D) nanostructures possess additional spatial freedom and rich physical characteristics compared with their two-dimensional (2D) counterparts. Here we demonstrate a facile and automated nano-kirigami method to create the 3D deformed spiral metasurfaces, which can flexibly manipulate optical waves by simply applying external voltages. Through etching Archimedean spirals into Au/SiO_{2}/Si layer, multi-order localized surface plasmon resonances are excited within the spiral nanoslits and are dynamically tuned by floating the nanopatterns and employing the electrostatic forces, which induces a reflection modulation contrast as high as 189%. The 2D-to-3D transformation induces a strong modification of the optical chirality in both aspects of spatial distributions and strength. Importantly, the Pancharatnam-Berry (PB) geometric phase can be carefully designed and dynamically broken in the 2π range by rotating the direction of the spiral units, which results in the dynamic construction and erasing of metasurface holograms. The proposed scheme of tuning plasmonic nanoslits and breaking PB geometric phase by employing the electromechanical deformation provides a new degree of freedom for reconfigurable photonic systems, as well as dynamic applications in quasi-flat optical platforms.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Three-dimensional (3D) nanostructures, compared with their two-dimensional (2D) counterparts, have continuously drawn attention due to the additional spatial freedom and rich physical characteristics, which could provide extra possibilities for the design of compact devices in the fields of mechanics, microelectronics, acoustics, and optics [1–7]. Recently, a novel 3D nanofabrication technology called nano-kirigami [8–12] has been developed for the manufacturing of exceptional micro-/nanophotonic and mechanical devices, owing to the fact that it can implement facile and versatile shape transformations and construct a variety of 3D nanogeometries with unique and flexible functionalities. Unlike the traditional on-chip 3D micro/nanofabrications [13–17], the 2D precursors of nano-kirigami can be directly deformed by mechanical actuation or stress induction to form complex 3D plasmonic nanostructures without the need of spatial translation or multilayer stacking. While the third dimension provides additional opportunities to manipulate the polarization, phase and amplitude of electromagnetic waves, the transformation capability of nano-kirigami could enable a new reconfiguration freedom compared to the static 2D metasurfaces [18–23]. Therefore, the nano-kirigami method may provide promising strategies for reconfigurable nanophotonics such as dynamic metasurfaces with tunable and broadband response, which is still a great challenge at optical wavelengths.

In this article, we propose and demonstrate an effective reconfiguration method to transform the 2D nanopatterns into 3D deformed nanostructures by employing an electromechanical nano-kirigami principle, which can be dynamically adjusted and continuously reconfigured. By etching Archimedean spirals (AS) into Au/SiO_{2}/Si layer, multi-order localized surface plasmon resonances (LSPRs) are excited within the spiral nanoslits, which are dynamically tuned by floating the nanopatterns and employing the electrostatic forces. The associated vertical deformations transform the 2D spiral nanoslits into 3D irregular nanoarchitectures, resulting in a tunable reflection modulation contrast as high as 189%. Meanwhile, such a 2D-to-3D transformation also induces a strong modification of the optical chirality, of which the strength can be tuned via the externally applied voltage. More importantly, by carefully designing Archimedean spirals with different lengths and rotation angles in a metasurface, the Pancharatnam-Berry (PB) geometric phase can be achieved and dynamically tuned in the 2π range, which enables the reconfiguration of a metasurface hologram. The proposed nanostructures, as well as the electromechanical deformation scheme, unfold a new degree of freedom for reconfigurable photonic systems, as well as dynamic applications in quasi-flat optical platforms.

## 2. Results and discussions

#### 2.1 Structural design

The 2D nanopatterns are designed based on the Archimedean spiral, which has rotation periods at equal interval and provides the highest filling rate for the facile construction of nanoslits. In the Cartesian coordinate system, the Archimedean spiral is defined as a function of the initial radius *a*, the spiral growth rate *b* and the angle *θ*:

*W*= 80 nm and

*L*= 7.9 µm, respectively. Considering the experimental realizations, we choose the top gold film with thickness

*d*of 60 nm, the middle SiO

_{2}supporters with thickness of 300 nm, and the thick Si layer as the bottom substrate, as shown in Fig. 1(c). This 2D nanostructure can be readily fabricated by electromechanically reconfigurable nano-kirigami method with thin-film deposition, electron beam lithography, ion beam etching, resist removal and the wet etching process to obtain the hollowed SiO

_{2}supporters [9].

#### 2.2 Optical properties of 2D and 3D Archimedean spiral nanoslits

We first investigate the optical responses of the nanostructures without deformation by using the COMSOL software, the periodic boundary conditions are used in the *x* and *y* directions and the perfectly matched layer boundary condition is applied in the *z* direction to simulation, with material parameters in Ref. [24]. The reflectance spectrum is depicted in Fig. 1(d) under the normal incidence with circularly polarized light (CPL). The results in Fig. 1(e) show that the spiral nanoslits can induce multi-order LSPRs modes in infrared wavelength. The linewidth of co-polarized reflection dip increases gradually with the increase of resonant wavelength. The maximum resonant wavelength is 10.24 µm, which is much larger than the lattice period. This means that the spiral slit nano-kirigami structure can be utilized to gain extraordinary compression of the LSPRs modes in the infrared wavelength range, which can be used to design compact optoelectronic devices. Due to the *C _{2}* rotational symmetry, the reflected light also has cross-polarized component, as shown in Fig. 1(d). In the short wavelength range, the maximum conversion efficiency of the cross polarization is 25% under right-handed circularly polarized (RCP) incidence. There also exists weak chiroptical response in the short wavelength range. It can be seen from the electric field confined in the spiral slits of Fig. 1(e) that the number of the node areas (the areas with enhanced electric field) increases as the wavelength decreases and eventually multi-order resonant electric dipole modes are formed (see below discussions). Thus, it can be expected that both the resonant wavelength and reflection can be adjusted by changing the spiral slits.

By applying the voltage between the metal layer and the Si substrate to generate electrostatic force, the two-dimensional structures are deformed into the three-dimensional structures, as shown in Fig. 2(a). The deformation level can be controlled by the applied voltage, since the initial electrostatic force can be approximately defined as ${{F}_{e}}{ = }\frac{{{k}{{Q}_{1}}{{Q}_{2}}}}{{{{d}^{2}}}}$, where *k* is the proportionality factor, *Q _{1}* and

*Q*are the charges on the arms and the substrates, respectively. The adjustability and reconfigurability of the nano-kirigami structure can be achieved by the local electrostatic force induced torque and the restoring mechanical force within the tolerance of elastic deformation [9]. The right plane in Fig. 2(a) shows the 3D deformed nanoarchitecture with a height of 160 nm under

_{2}*V*= 78 V. Once the nanostructures produce stereo twist under the applied voltages, the morphology of the spiral slits changes dramatically, as illustrated in Fig. 2(a), of which the dynamic modulation frequency can reach 10 MHz in simulations and 200 kHz in experiments [9]. In order to shift the resonance wavelength towards the optical communication band, we choose the period as 1.2 µm,

*b*= 80 nm and

*θ*${\in} $[0.5, 6.5]. The Fig. 2(b) shows the reflection spectrum for the nanostructures with different arc lengths

*L*under the excitation of the RCP polarization with

*V*= 0 V. As the arc length

*L*decreases, the resonant wavelengths of the three LSPRs modes are blue shifted. This is because the resonant wavelength is mainly determined by $\mathrm{\lambda } = 2{\textrm{n}_{\textrm{sp}}}\textrm{L}/\textrm{N}$, where ${\textrm{n}_{\textrm{sp}}}$ is the wavelength-dependent effective refractive index of the LSPRs modes and

*N*is the order of the modes. Such a relationship between the length of spiral nanoslit and the resonant wavelength of the LSPRs can be reflected in Fig. S1 of the Supplementary Information.

The 2D nanostructures produce the downward deformation height of 71 and 103 nm along the negative *z*-axis under the applied voltage of 60 and 70 V, respectively. With the increase of the external bias voltages, the co-polarized component for reflection spectrum can be dynamically regulated and there is also a significant blue shift of *λ* with variable amplitude under the RCP light incident along the negative *z*-axis, shown in Fig. 2(c). Here *ΔR/R* is used evaluate the modulation contrast between the 2D and 3D spiral nanostructures, where *ΔR* is the difference in reflection before and after the deformation and *R* is the reflection under the *V *= 0 V. It can be seen from the Fig. 2(d) that the maximum value of *ΔR/R* is 189% at *λ =* 2.00 µm. The large modulation contrast is attributed to that the optical responses of the LSPRs modes are very sensitive to structural changes, as shown by the *E _{z}* field distributions before and after the structural deformations in Fig. 2(e). The fundamental physics is that the deformed structures break the symmetric distribution of the LSPRs on the upper and lower sides of the film.

#### 2.3 Reconfigurable optical chirality properties

The enhancement of the optical chirality (*C*) reflects the resonance characteristics of the electric and magnetic dipoles [25,26]. It can provide valuable opportunities to realize highly sensitive chirality detection of chiral molecules and offer additional degrees of freedom in chiroptical information processing [27,28]. However, the realization of reconfigurable optical chirality in optical bands still faces great challenges. Here, we realize the reconfiguration of optical chirality by using the electromechanical nano-kirigami. The optical chirality [29,30] can be expressed as

*ω*is the angular frequency,

*E*and

*B*are the electric and magnetic fields, respectively. Here ${\hat{C}^ \pm } = {C^ \pm }/|C_{CPL}^ \pm |$ is used to calculate the enhancement factor of the optical chirality. $C_{CPL}^\textrm{ + }$and $C_{CPL}^ -$ represent the values obtained for RCP and left-handed circularly polarized (LCP) light without the nanostructure [31].

Figure 3 show the distributions of the optical chirality of 2D and 3D kirigami nanostructures at *z* = 0 µm plane, which clearly shows the distinct difference for the RCP and LCP light incident at the resonant wavelength 1.47 µm. When the 2D kirigami nanostructure [see Fig. 3(a)] interacts with the electromagnetic wave, the hot-spots of enhanced optical chirality are concentrated in the slit and the edges of the gold film around the slit [see Fig. 3(b)]. Under different polarization states of light, only the enhancement factor of optical chirality differs and the local positions are similar, as depicted in Fig. 3(b). The Fig. 3(c) is the deformed 3D electromechanical nano-kirigami under *V* = 78 V. It can be seen from the Fig. 3(d) that the optical chirality around the central region has changed dramatically. In addition, the highest absolute values of optical chirality under LCP and RCP are located at different spatial regions [see Fig. 3(d)]. By comparison of the results in Figs. 3(b) and 3(d), it can be seen that the regions and strength of optical chirality can be readily adjusted through the voltage modulation. More importantly, the sign of the optical chirality around the central region can be reversed after the deformation of the nanostructures [see Fig. 3(b) and Fig. 3(d)], which may find important applications in the realm of chiral molecular characterization. The above phenomenon is also applicable in a wide spectral range (see in Figure S2 of the Supporting Information).

The optical chirality can also be controlled by designing different nanostructures. The designed nano-kirigami with centrally disconnected structure is shown in Fig. 3(e). It can be seen that the vertical height of the two arms is obviously difference under the applying voltage. Such an asymmetric deformation is directly observed in mechanical simulations and is caused by the fact that the two arms initially carry the same type of charges, and a mutual repulsive Coulomb force is induced between the tips of the two suspended arms as ${{F}_p}{ = }\frac{{{kQ}_{1}^{2}}}{{{r}_{{tip}}^{2}}}$, where the *r _{tip}* is the distance between the two arm tips. When the tips get closer with the increase of deformations (

*r*becomes very small), the repulsive force increases dramatically and a small perturbation (in modeling or experiments) could cause one arm deformed more intensively than the other. As reflected from the optical chiral fields of the two nanostructures in Figs. 3(d) and 3(f), the nonuniform height distribution of the kirigami structure can lead to the asymmetric optical chirality distribution.

_{tip}#### 2.4 Designs of reconfigurable PB geometric phase metasurfaces

For the CPL incidence along the *z*-axis with ${E_{in}} = {E_0}\left( {\begin{array}{c} \textrm{1}\\ { \pm i} \end{array}} \right)$, the general reflection matrix *R* can be described in the terms of complex linear reflection coefficients

*α*is the orientation angle of the spiral nanoslit. By rotating the angle of the optical elements, the reflection phase of the light will be changed by 2

*α*, which is called PB geometric phase [34–36]. The abrupt phase term will enable the effective birefringence phenomenon generated by the structural anisotropy of the nanostructures to realize the manipulation of polarization and wavefront [32,37].

In order to establish an arbitrary phase distribution of converted cross-polarization in the reflected beam for manipulating wavefront, we introduce optical elements with the PB geometric phase to design the electromechanical metasurface, as illustrated in Fig. 4(a). The six 2D structural units in Fig. 4(b) are used to achieve a linear phase gradient of π*/*3-phase increments between adjacent unit cells. The 3D nano-kirigami units are achieved under the applied voltage 78 V. As the calculated results shown in Fig. 4(c), the 3D nano-kirigami array can achieve the entire phase shift covering from 0 to 2π in the broadband wavelength range from 1.5 to 5 µm.

The period *S* of the nano-kirigami arrays in Fig. 4(b) are 7.2 µm. According to the generalized Snell's law [38,39], we can calculate the reflection angle of the cross-polarized beam in the air as

In order to achieve the reconfigurable PB geometric phase, we design another nano-kirigami structure shown in Fig. 5(a), which possesses centrally disconnected two arms. When the voltage of 59 V is applied to the nano-kirigami nanostructures, all the units reach the maximum deformation height, similar to the 3D structure in Fig. 4(a). The Fig. 5(b) and Fig. 5(c) are the reflection spectra of the 2D and 3D nano-kirigami nanostructures, respectively. Obviously, once the 2D structure is deformed into 3D structure, the cross-polarization efficiency changes significantly. More interestingly, the ideal PB geometric phase gradient distributions are broken, as plotted in Fig. 5(d). In such a case, the amplitude and phase of cross-polarized light can be controlled by structural asymmetric deformations. It should be mentioned that the 3D nano-kirigami structures are sensitive to the light polarization, and for RCP light incidence the breaking of PB geometric phase is not observed. Meanwhile, such a breaking of PB geometric phase is only observed in wavelengths close to the high-order LSPRs modes where the phase is more sensitive to the structural deformations.

As a proof-of-concept demonstration, we use the Gerchberg-Saxton algorithm [40] to build up electromechanically reconfigurable meta-holograms based on such designs of PB geometric phase breaking. As schematically shown in Fig. 5(e), in the Fresnel diffraction range the 2D meta-holograms are designed with proper phase diagram to reconstruct the “smiling face” and “love” images with an image distance of 1 mm under LCP excitation. The 2D metasurface containing the phase profile of the merged hologram is arranged into pixels of 32 × 32, with overall size of 38.4 µm × 38.4 µm. In such a case, two clear images of “smiley face” and “love” are reproduced under *V* = 0 V. The bottom two images in Fig. 5(e) show the results under the same imaging condition but under an applied voltage of 59 V. It can be seen that the “smiley face” and “love” images disappear. At the same time, increasing the number of pixels and finding a unit with greater conversion efficiency in the metasurface are helpful for improving the hologram image quality. In such a way, the reconfigurable metasurface holograms can be achieved at optical wavelengths with the nano-kirigami principle.

## 3. Conclusions

In conclusion, we have introduced a new mechanism to tune the plasmonic nanoslits and break the PB geometric phase of a metasurface. By etching Archimedean spirals into Au/SiO_{2}/Si layer, multi-order LSPRs have been excited within the spiral nanoslits, which were dynamically tuned by employing the electrostatic forces. The 3D deformations of the 2D spiral nanoslits resulted in a tunable reflection modulation contrast as high as 189%. Due to the 3D twist of the deformed structure, the enhanced optical chirality under different CPL incidence varied significantly compared to the 2D spirals. More importantly, by carefully designing Archimedean spirals with different lengths and rotation angles in a metasurface, the PB geometric phase have been carefully designed and dynamically broken in the 2π range. As a proof-of-concept demonstration, two metasurface holograms have been realized in calculations and the generated images can be dynamically “erased” by applying external voltage. Compared with other dynamic metasurface techniques based on smart materials or liquid crystals, here the designs are based on all-solid state electrical configurations, which could be desirable for device integrations [41–43]. The proposed scheme of tuning plasmonic nanoslits and breaking PB geometric phase by employing the electromechanical deformation provides a new degree of freedom for reconfigurable photonic systems, as well as dynamic applications in quasi-flat optical platforms.

## Funding

Science and Technology Planning Project of Guangdong Province (2020B010190001); Beijing Municipal Natural Science Foundation (1212013, Z190006); National Key Research and Development Program of China (2017YFA0303800); National Natural Science Foundation of China (61675227, 61775244, 61975014, 61975016, 62035003).

## Disclosures

The authors declare no conflicts of interest.

## Data availability

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.

## Supplemental document

See Supplement 1 for supporting content.

## References

**1. **J. Park, B. G. Jeong, I. K. Sun, D. Lee, J. Kim, C. Shin, B. L. Chang, T. Otsuka, J. Kyoung, and S. Kim, “All-solid-state spatial light modulator with independent phase and amplitude control for three-dimensional lidar applications,” Nat. Nanotechnol. **16**(1), 69–76 (2021). [CrossRef]

**2. **S. Zhou, Y. M. Xie, S. Lin, X. Q. Feng, and Q. Li, “Buckling-induced assembly of three-dimensional tunable metamaterials,” Phys. Status Solidi–R. **12**(4), 1870314 (2018). [CrossRef]

**3. **L. Wan-Ying, Z. Xiang, S. Xiong-Jun, X. Sheng-Xuan, and M. Qin, “Multi-spectral plasmon induced transparency based on three-dimensional metamaterials,” Opt. Mater. Express **7**(12), 4269–4276 (2017). [CrossRef]

**4. **Z. Wang, L. Jing, K. Yao, Y. Yang, B. Zheng, C. M. Soukoulis, H. Chen, and Y. Liu, “Origami-based reconfigurable metamaterials for tunable chirality,” Adv. Mater. **29**(27), 1700412 (2017). [CrossRef]

**5. **L. Ziwei, Y. Li, T. Han, and X. Wang, “Tailoring MoS_{2} exciton-plasmon interaction by optical spin-orbit coupling,” ACS Nano **11**(2), 1165–1171 (2017). [CrossRef]

**6. **W. Q. Ji, Q. Wei, X. F. Zhu, and D. J. Wu, “3D acoustic metasurface carpet cloak based on groove structure units,” J. Phys. D: Appl. Phys. **52**(32), 325302 (2019). [CrossRef]

**7. **J. F. Liu, S. Cruchon-Dupeyrat, J. C. Garno, J. Frommer, and G. Y. Liu, “Three-dimensional nanostructure construction via nanografting: positive and negative pattern transfer,” Nano Lett. **2**(9), 937–940 (2002). [CrossRef]

**8. **Y. Han, Z. Liu, S. Chen, J. Liu, and J. Li, “Cascaded multilayer nano-kirigami for extensible 3D nanofabrication and visible light manipulation,” Photonics Res. **8**(9), 1506–1511 (2020). [CrossRef]

**9. **S. Chen, Z. Liu, H. Du, C. Tang, and J. Li, “Electromechanically reconfigurable optical nano-kirigami,” Nat. Commun. **12**(1), 1299 (2021). [CrossRef]

**10. **Z. Liu, H. Du, J. Li, L. Lu, and Z. Y. Li, “Nano-kirigami with giant optical chirality,” Sci. Adv. **4**(7), eaat4436 (2018). [CrossRef]

**11. **S. Chen, W. Wei, Z. Liu, X. Liu, S. Feng, H. Guo, and L. I. Jiafang, “Reconfigurable nano-kirigami metasurfaces by pneumatic pressure,” Photonics Res. **8**(7), 1177–1182 (2020). [CrossRef]

**12. **X. Tian, Z. Liu, H. Lin, B. Jia, Z.-Y. Li, and J. Li, “Five-fold plasmonic Fano resonances with giant bisignate circular dichroism,” Nanoscale **10**(35), 16630–16637 (2018). [CrossRef]

**13. **N. Saracogullari, D. Gundogdu, F. N. Ozdemir, Y. Soyer, and E.-G. Irem, “The effect of polyacid on the physical and biological properties of chitosan based layer-by-layer films,” Colloids Surf., A **617**, 126313 (2021). [CrossRef]

**14. **W. E. Lu, Y. L. Zhang, M. L. Zheng, Y. P. Jia, J. Liu, X. Z. Dong, Z. S. Zhao, C. Li, Y. Xia, and T. C. Ye, “Femtosecond direct laser writing of gold nanostructures by ionic liquid assisted multiphoton photoreduction,” Opt. Mater. Express **3**(10), 1660–1673 (2013). [CrossRef]

**15. **J. H. Noh, J. D. Fowlkes, R. Timilsina, M. G. Stanford, B. B. Lewis, and P. D. Rack, “Pulsed laser-assisted focused electron-beam-induced etching of titanium with XeF_{2}: enhanced reaction rate and precursor transport,” ACS Appl. Mater. Interfaces **7**(7), 4179–4184 (2015). [CrossRef]

**16. **J. G. Gibbs, A. G. Mark, T. C. Lee, S. Eslami, D. Schamel, and P. Fischer, “Nanohelices by shadow growth,” Nanoscale **6**(16), 9457–9466 (2014). [CrossRef]

**17. **J. Fischer and M. Wegener, “Three-dimensional direct laser writing inspired by stimulated-emission-depletion microscopy,” Opt. Mater. Express **1**(4), 614–624 (2011). [CrossRef]

**18. **B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. **4**(1), 4971 (2015). [CrossRef]

**19. **Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. **14**(11), 6526–6532 (2014). [CrossRef]

**20. **N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science **334**(6054), 333–337 (2011). [CrossRef]

**21. **W. M. Pan, J. S. Li, and C. Zhou, “Switchable digital metasurface based on phase change material in the terahertz region,” Opt. Mater. Express **11**(4), 1070–1079 (2021). [CrossRef]

**22. **Y. Jia, L. Ying, W. Zhang, J. Wang, and G. Liao, “Ultra-wideband metasurface with linear-to-circular polarization conversion of an electromagnetic wave,” Opt. Mater. Express **8**(3), 597–604 (2018). [CrossRef]

**23. **P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonic metasurface,” Nano Lett. **17**(1), 445–452 (2017). [CrossRef]

**24. **E. D. Palik, *>Handbook of Optical Constants of Solids* (Elsevier, 1998), Vol. 3.

**25. **J. Mun, M. Kim, Y. Yang, T. Badloe, J. Ni, Y. Chen, C. Qiu, and J. Rho, “Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena,” Light: Sci. Appl. **9**(1), 139 (2020). [CrossRef]

**26. **Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. **104**(16), 163901 (2010). [CrossRef]

**27. **J. Garcia-Guirado, M. Svedendahl, J. Puigdollers, and R. Quidant, “Enhanced chiral sensing with dielectric nanoresonators,” Nano Lett. **20**(1), 585–591 (2020). [CrossRef]

**28. **M. L. Solomon, A. Saleh, L. V. Poulikakos, J. M. Abendroth, and J. A. Dionne, “Nanophotonic platforms for chiral sensing and separation,” Acc. Chem. Res. **53**(3), 588–598 (2020). [CrossRef]

**29. **K. Y. Bliokh and F. Nori, “Characterizing optical chirality,” Phys. Rev. A **83**(2), 021803 (2011). [CrossRef]

**30. **H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X **2**(3), 031010 (2012). [CrossRef]

**31. **L. Kang, Q. Ren, and D. H. Werner, “Leveraging superchiral light for manipulation of optical chirality in the near-field of plasmonic metamaterials,” ACS Photonics **4**(6), 1298–1305 (2017). [CrossRef]

**32. **W. Wang, Y. Li, Z. Guo, R. Li, J. Zhang, A. Zhang, and S. Qu, “Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation,” J. Opt. **17**(4), 045102 (2015). [CrossRef]

**33. **M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. **32**(12), 1907308 (2020). [CrossRef]

**34. **J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam-Berry coding metasurfaces,” Nanoscale **11**(12), 5746–5753 (2019). [CrossRef]

**35. **P. Capaldo, A. Mezzadrelli, A. Pozzato, G. Ruffato, and M. Massari, “Nano-fabrication and characterization of silicon meta-surfaces provided with Pancharatnam-Berry effect,” Opt. Mater. Express **9**(3), 1015–1032 (2019). [CrossRef]

**36. **S.-h. Li, J.-s. Li, and J.-z. Sun, “Terahertz wave front manipulation based on Pancharatnam-Berry coding metasurface,” Opt. Mater. Express **9**(3), 1118–1127 (2019). [CrossRef]

**37. **J. Sung, E. M. Hicks, R. Duyne, and K. G. Spears, “Nanoparticle spectroscopy: birefringence in two-dimensional arrays of L-shaped silver nanoparticles,” J. Phys. Chem. C **112**(9), 3252–3260 (2008). [CrossRef]

**38. **Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. **14**(3), 1394–1399 (2014). [CrossRef]

**39. **W. Chao, W. Liu, Z. Li, C. Hua, L. Zhi, S. Chen, and J. Tian, “Dynamically tunable deep subwavelength high-order anomalous reflection using graphene metasurfaces,” Adv. Opt. Mater. **6**(3), 1701047 (2018). [CrossRef]

**40. **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).

**41. **Y. Hu, X. Ou, T. Zeng, J. Lai, J. Zhang, X. Li, X. Luo, L. Li, F. Fan, and H. Duan, “Electrically tunable multifunctional polarization-dependent metasurfaces integrated with liquid crystals in the visible region,” Nano Lett. **21**(11), 4554–4562 (2021). [CrossRef]

**42. **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]

**43. **Y. Chen, X. Duan, M. Matuschek, Y. Zhou, F. Neubrech, H. Duan, and N. Liu, “Dynamic color displays using stepwise cavity resonators,” Nano Lett. **17**(9), 5555–5560 (2017). [CrossRef]