Kirigami Metamaterials for Reconfigurable Toroidal Circular Dichroism

The ancient paper craft of kirigami has recently emerged as a potential tool for the design of functional materials. Inspired by the kirigami concept, we propose a class of kirigami-based metamaterials whose electromagnetic functionalities can be switched between nonchiral and chiral states by stretching the predesigned split-ring resonator array. Single-band, dual-band and broadband circular polarizers with reconfigurable performance are experimentally demonstrated with maximum circular dichroisms of 0.88, 0.94 and 0.92, respectively. The underlying mechanism is explained and calculated via detailed analysis of the excited multipoles, including the electric, magnetic, and toroidal dipoles and quadrupole. Our approach enables tailoring the electromagnetic functionalities in kirigami patterns and provides an alternate avenue for reconfigurable optical metadevices with exceptional mechanical properties.


INTRODUCTION
Metamaterials are artificial materials engineered at the subwavelength scale to achieve electromagnetic functionalities 1 . Several novel optical phenomena have been observed in metamaterial-based devices, such as negative refraction [2][3][4] , superlens 5 , invisibility cloaking [6][7][8] , and strong chiroptical responses 9,10 . Although bulk metamaterials show intriguing optical properties, the complexity of fabrication and large loss in metallic meta-atoms hamper their applications in practice. Recently, new degrees of freedom have been attained by introducing abrupt phase discontinuities on metasurfaces, the two-dimensional counterparts of metamaterials. Metasurfaces show great capabilities in wavefront manipulation and reduce the complexity of fabrication [11][12][13][14][15] . Spin-selective absorption has been demonstrated by designing chiral meta-atoms, with promising potential applications in polarimetry, circular polarization detectors and chiral cavities [16][17][18][19] . However, structural modification is generally challenging once metamaterials or metasurfaces are fabricated, rendering them functionally nonreconfigurable.
Reconfigurable metamaterials are designed to achieve dynamic control over the physical properties to realize multiple functions in one metadevice 20 . Tuning methods include the use of capacitors 21 , semiconductors 22 , phase-change materials 23,24 and ferromagnetic/ferroelectric materials 25 . However, compared with the surrounding media and metamaterial constituents, most of these methods suffer from a limited tuning range because the variation is usually very small. Another strategy is changing the structural shapes for reconfigurable functionality. Recently, origami provided an alternative approach to construct strong, lightweight, and tunable three-dimensional (3D) blocks from flat sheets 26,27 . By applying prescribed sequences of folds to flat surfaces, researchers demonstrated flexible and efficient control over mechanical 26,28 , electronic 29 , acoustic 30 , superconducting [31][32][33] and electromagnetic functionalities 34 .
Although the design capacity of origami is remarkable, achieving complex target shapes with only folds is mathematically challenging. Such complex folding patterns require a convoluted series of deformations from the flat to folded shapes, making fabrication difficult. Different from origami, kirigami is an art form that introduces cuts into folding processes, providing extra degrees of freedom in 3D shape construction 35 . It allows for similarly complicated shapes to be formed with greatly reduced complexity in the design process and less wasted material 36,37 . When applying sufficiently large amounts of stretching, buckling is triggered, resulting in the formation of a 3D structure comprising a well-organized pattern of mountains and valleys. Kirigami is a highly promising technique to design complex 3D metadevices with reconfigurable functionalities but has not been applied in the design of electromagnetic metamaterials with extraordinary chiral properties, especially for reconfigurable toroidal circular dichroism.
A chiral structure can be modeled as electric and magnetic dipoles with parallel or antiparallel orientations of comparable magnitude. Different absorption occurs when circularly polarized waves pass through such a structure. This is the widely discussed phenomenon of conventional circular dichroism. However, for toroidal circular dichroism, the chiroptical effects are mostly attributed to the combination of toroidal dipoles and other higher order electric multipoles.
In this letter, we propose and demonstrate a general class of kirigami-based chiral metamaterials (KCMMs) whose electromagnetic performance can be switched between nonchiral and chiral states at single-band, dual-band and broadband wavelengths. Moreover, for the first time, we propose and investigate the reconfigurable toroidal dipole moments based on the kirigami. Split-ring resonators (SRRs) are periodically arranged on thin, foldable sheets. When transforming the 2D metasurface to 3D kirigami-based metamaterials, the resonant modes exhibit a gradually enhanced chiroptical response. The underlying mechanism is explained via detailed analyses of the excited multipoles, including the electric, magnetic, and toroidal dipoles and electric quadrupole. The nonradiating feature and high flexibility of the toroidal geometry will be useful in many applications, such as lasers 38,39 , ultrasensitive biosensors and nonlinear effects 40,41 . The reconfigurable circular dichroism generated by toroidal dipoles offers an alternative approach to broadband chiroptical responses beyond the widely adopted methods based on parallel electric and magnetic dipoles. Circular dichroisms of 0.88, 0.94 and 0.92 have been experimentally observed for single-band, dual-band and broadband configurations, respectively.

MATERIALS AND METHODS
The schematic of the KCMMs is illustrated in Figure 1. The functionality of the proposed KCMMs is to totally transmit the designated circularly polarized wave and reflect the other spin state with maximum efficiency. Split-ring resonators are adopted as the basic meta-atoms printed on a thin and flexible dielectric substrate. Before cutting and folding, the metasurface is achiral because of its mirror symmetry with respect to the yz plane. Subsequently, the 2D metasurface is transformed into 3D geometries by introducing cuts at the boundary between neighboring meta-atoms in the y direction. The kirigami approach is considerably diverse; we investigate three types of KCMMs that are cut and folded from 2D metasurfaces. Type-I KCMMs represent kirigami structures whose neighboring units are connected by the midpoints of the sides at the cut boundary, whereas type-II KCMMs are based on buckling-induced kirigami in which the meta-atoms are connected by the vertices of the squares. Foldable 3D structures are formed by stretching the cut materials. Both type-I and type-II KCMMs contain four SRRs in a unit cell. To obtain toroidal dipole responses, type-III KCMMs are formed by stacking two type-I layers. The mirror symmetry is broken by introducing cuts and folds along different axes. Notably, all KCMMs can be folded into two kinds of chiral enantiomers, which are mirror images of each other. For simplicity, we label the two enantiomers as R-handed and L-handed.
Additional details on the geometric dimensions of KCMMs and the folding process can be found in the Supporting Information ( Figure S1, S3). Proof-of-concept KCMMs were designed in the microwave region. The unit cell of the 2D metasurface is composed of four SRRs with side length l and width w. The gap size of each SRR is g = 1 mm, and the lattice constant is 20 mm. This unfolded metasurface has mirror symmetry around the yz plane and hence does not exhibit intrinsic chirality. Full-wave numerical simulations were conducted using the commercial software CST Microwave Studio. In simulation, SRRs are assumed to be standing in free space, and the influence of the ultrathin dielectric substrate is neglected. This is reasonable because the dielectric substrate only influences the gap capacity of the SRR and thus produces only a slight shift of the resonant frequency.

RESULTS
The simulation results for the three types of KCMM are illustrated in Figure 2. In the folded state of  = 45°, the type-I KCMMs exhibit chiroptical responses at the resonant frequency of 6.78 GHz, with opposite handedness in the two enantiomers.
For the L-handed enantiomer, as shown in Figure 2 show the left-handed feature and hence could be combined to achieve a broadband feature. In contrast, stacking two R-handed type-I KCMMs can produce an R-handed type-III KCMM that behaves in an opposite manner (Figure 2(j)).
To illustrate the abilities of the KCMMs as circular polarizers, we investigate the circular dichroism (CD) spectra, which are calculated by CD = |tRR| 2 -|tLL| 2 . The dependence of performance on the folding angle is plotted in Figure 2 Figure 3. As expected, when the 2D metasurface is deformed to 3D geometries, the mirror symmetry of the structure is broken, and the chiroptical response emerges. At a resonant frequency of 6.4 GHz, the L-handed enantiomer of the type-I KCMM blocks most of the LCP waves, whereas the R-handed enantiomer is more opaque for the other spin state (Figure 3(a, b)). The measured CD spectra plotted in Figure 3 the type-II KCMM reverses its chirality handedness (Figure 3(d, e, f)). For the type-III KCMMs, broadband chiroptical responses occur between two resonant frequencies of 6.2 GHz and 6.7 GHz. As expected, the L-handed and R-handed enantiomers behave as broadband circular polarizers that transmit only RCP and LCP waves (Figure 3(g, h)), respectively. The measured CD spectra are plotted in Figure   3(i) and are highly consistent with the theoretical prediction. Split-ring resonators produce effective electric, magnetic and toroidal dipoles at the resonance. To determine the origin of the circular dichroism at these resonances in our KCMMs, we conducted a dipolar analysis to determine the underlying mechanism.
The specific combination of the electric and magnetic dipoles, that is, parallel or antiparallel with comparable magnitudes, can induce strong chiral responses similar to those in natural chiral molecules 42,43 . For simplicity, we label the four squares of a superunit with numbers (see Figure S2 in the Supporting Information   To quantitatively analyze the nature of these chiral modes, we performed a multipole analysis by calculating the simulated surface current excited by the plane waves at normal incidence. Then, the multipolar expansions were calculated using the integral of the currents; [44][45][46] additional details can be found in the supplementary materials. We performed a multipole decomposition to quantify their contributions. In our For the L-handed type-II KCMM, Fig 5(c, d) shows that the first resonant mode of type-II KCMM is similar to that of type-I KCMM, and the handedness switching in the second chiral resonant frequency is attributed to the appearance of other components of multipoles (Px, Pz, Mx, Mz, Tz). Notably, the strong electric dipole component Pz, magnetic dipole component Mz and toroidal dipole component Tz do not directly contribute to the far-field radiation at normal incidence but may couple with the surface wave or other dark modes. This is the underlying mechanism of the second chiral resonance mode. For the type-III KCMMs, the microscopic origin of the chiroptical responses is different from those for type-I and type-II. To understand the chiral performance, it is not sufficient to analyze the electric and magnetic dipoles only; toroidal multipolar analysis is needed 40,47 . The presence of the multipole pairs is visually detected in the distributions of the electric and magnetic fields inside the unit cell arising from circularly polarized excitation. At f1 (7.12GHz), the field lines of the electric and magnetic fields are aligned parallel to the y-axis yet with opposite directions, which contributes to the electric and magnetic dipolar excitations with the net dipole moments collinearly oriented along the y-axis (Figure 6(a,b)). This is also the aforementioned microscopic origin of the chiroptical responses in type-I and type-II KCMMs. However, at f2 (6.4GHz), the magnetic field is confined within a well-defined ring-like area where the field lines thread through the individual SRRs and form a closed loop (Figure 6(d)). Such a magnetic-field configuration is formed by poloidal currents flowing in the wire loops of the SRRs and is unique to the toroidal dipolar excitation with a net dipole moment aligned parallel to the x-axis.
Compared with that in Figure 6(a), the distribution of the electric field shows a similar pattern but with field lines on the opposite sides of the SRR aligned antiparallel to each other, indicating an electric quadrupole excitation (Figure 6(c)). Therefore, the additional electric quadrupole and magnetic toroidal dipole excitations contribute to the broadband chiroptical performance of the type-III KCMMs. The analysis was performed using multipole decomposition for x and y polarization waves. Different multipoles contribute to the same resonant features in y polarization and x polarization incidence waves. As shown in Fig 6(e, f) Figure 6, the electric dipole Py and magnetic dipole My can be excited under Ex and Ey incident fields at f1, respectively, indicating strong polarization conversion (tyx and txy). This implies that the circular dichroism that depends on Im(txy-tyx) is highly enhanced at this frequency. However, at f2, the strong chiroptical response is attributed to the simultaneous excitation of Qe-yz (electric quadrupole in the yz plane) and Tx, from which the cross-polarization powers arises. Toroidal moments have been found in nuclear and atomic physics and solid state physics. Recently, toroidal dipole excitations in metamaterials were observed, and the nonradiating feature of the toroidal geometry provides many interesting phenomena, with enhanced light-matter interaction and applications in lasers, ultrasensitive biosensors and nonlinear effects. We investigated the reconfigurable toroidal dipole moments. We also investigated the relationship between Tx and the folding angle  by plotting the resonant strength of toroidal dipole excitation as a function of the folding angle. We also investigate the relationship between the toroidal dipole resonant frequency and the folding angle  . As shown in Figure 7(a), the resonant frequency of the toroidal dipole is sensitive to the folding angle. As the type III KCMM folds from a two-dimensional surface to 3D blocks, the resonant frequency increases to reach its maximum at approximately 45 degrees and then decreases. This feature is consistent with the simulated circular dichroism spectra in Figure 2(k). The radiated power of the toroidal dipole versus the folding angle is depicted in Figure   7(b). The radiated power of the toroidal dipole becomes relatively weak when the folding angle is too large or too small.    Corresponding CD spectra for different folding angles.

DISCUSSION
We proposed and demonstrated a general class of kirigami-based chiral metamaterials whose electromagnetic functionalities can be switched between nonchiral and chiral states. By introducing cuts and selecting the connection points between neighboring meta-atoms, 2D achiral metasurfaces can be deformed to 3D shapes with significantly enhanced chiroptical responses. Highly efficient single-band, dual-band and broadband circular polarizers experimentally demonstrated switchable handedness realized by adjusting the deformation direction. The underlying mechanism was confirmed by detailed analyses of the excited electrical, magnetic and toroidal dipoles.
Compared with the technique of origami, kirigami allows for the practitioner to exploit cuts in addition to folds to achieve large deformations and create complex 3D objects. With the ongoing development of micromanufacturing techniques, we expect our work to lead to alternate approaches to lightweight, reconfigurable, and deployable metadevices.