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. 2022 Dec 16;8(50):eadd6660. doi: 10.1126/sciadv.add6660

Topologically reconfigurable magnetic polaritons

Min Li 1,2,3,4, Guangwei Hu 5,6, Xuan Chen 1,2,3,4, Cheng-Wei Qiu 5,7,*, Hongsheng Chen 1,2,3,4,*, Zuojia Wang 1,2,3,*
PMCID: PMC9757744  PMID: 36525502

Abstract

Hyperbolic polaritons in extremely anisotropic materials have attracted intensive attention due to their exotic optical features. Recent advances in optical materials reveal unprecedented dispersion engineering of polaritons, resulting in twistronics for photons, canalized phonon polaritons, shear polaritons, and tunable topological polaritons. However, the on-demand reconfigurability of polaritons, especially with magnetic anisotropic dispersions, is restricted by weak natural magnetic anisotropy and hence remains largely unexplored. Here, we show how origami fused with artificial magnetism unveils a versatile pathway to topologically reconfigure magnetic polaritons. We experimentally demonstrate that the three-dimensional origami deformation allows to reconfigure hyperbolic or elliptic topology of polariton dispersion and modulate group velocity. With group velocity transitioning from positive to negative directions, we further report reconfigurable origami polariton circuitry in which the polariton propagation and phase distribution can be tailored. Our findings provide alternative perspectives on on-chip polaritonics, with potential applications in energy transfer, sensing, and information transport.

Three-dimensional origami deformation allows to reconfigure the topology of magnetic polariton and modulate the group velocity.

INTRODUCTION

Optical materials with extreme anisotropy have been extensively studied because of their exotic hyperbolic isofrequency contours (IFCs) when they have different signs of some dielectric tensor components. When coupling with light, they would render the half-light, half-matter quasiparticles, known as hyperbolic polaritons. Thus, large momentum of polaritons therein is possible due to the open IFCs, indicating the strong wave confinement and enhanced light-matter interactions (1–5). With optical IFCs playing the role of Fermi surface in electronics, the hyperbolic-to-elliptical topological transition can happen in optical anisotropic media (6) when its IFC changes from open-form hyperbolic to closed-form elliptical function, mimicking the well-known Lifshitz transitions where similar topology deformation happens in Fermi surfaces (7). Various systems including metamaterials, metasurfaces (8), low-dimensional quantum nanomaterials (9–11), and optical crystals (12, 13) have been exploited to actualize such photonic topological transitions, offering unprecedented capability to manipulate photonic band structure for the consequent paradigm shift applications.

Recently, the geometry deformation is demonstrated to play important roles in dispersion engineering of polaritons in anisotropic optical media. For instance, the simple twisted stacking of metasurfaces (14–17) or natural hyperbolic low-dimensional van der Waals (vdW) crystals (18–22) can drive the topological transitions at photonic magic angles, where dispersion lines necessarily become flat. This is in close analogy of flatband at the Fermi surface of twisted bilayer graphene and stimulated the new research frontiers of twistronics for photons (23). In optics, this twist essentially induces the misalignment or rotation of optic axis of each layer in the plane and hence molds the spatially dispersive energy flow in this synthetic system, exhibiting even diffractionless or so-called canalized propagation effects in some critical deformations at magic angles. Such twisted-induced deformation only happens in the plane, as the practical fabrication of vdW crystals with titled optic axis is formidable. More recent works report a new type of surface polaritons, i.e., ghost polaritons (12) in bulky uniaxial calcite crystals with titled optic axis via postprocessed mechanical polishing. The out-of-plane rotation of optic axis modulates the permittivity tensor of calcite and hence regulates surface wave propagations inside the crystals associated with the modulated out-of-plane momentum. It indicates that the anticipation of higher geometry dimensions would offer new freedoms in polaritonics. However, to fully realize practical application potential, facile methods enabling the reconfigurability of polaritons are needed. In particular, it is of a special interest to reconfigure polariton with magnetic anisotropic dispersions for two reasons: (i) The magnetic anisotropy in natural materials is usually weak; and (ii) manipulating magnetic polaritons plays an important role in investigating magnetic light-matter interactions, which would open new opportunities for polariton-controlled magnetic transition enhancement (24) and novel quantum optical apparatuses, for instance, efficiency-tunable magnetic emitters (25). In context of reconfigurable metamaterials, there are two general pathways to realize optical reconfiguration, i.e., modulating optical properties of metamaterials or changing the structure shape. So far, reconfigurable polaritons in hybrid polaritonic metamaterials have been pursed via actively tuning the properties of their constituents. For example, external stimuli allow the modulation of the refractive index of phase change substrate (26, 27) or carrier density of graphene layer (28), enabling electric anisotropic dispersion reconfiguration of polaritons. However, shape deformation–inspired reconfigurable polaritons, especially with magnetic anisotropic dispersions, remain unveiled. The continuous transformation among arbitrary shapes promises an unprecedented opportunity for ultrawide dynamical control over polariton dispersions.

Here, we experimentally report topologically reconfigurable magnetic polaritons in three-dimensional (3D) deformable origami metamaterials. Origami, featuring controllably deformable complex 3D structures via on-demand folding and/or cutting pattern, has widely been explored in electronics (29), biology (30, 31), chemistry (32), engineering (33–35), and especially optics (36–39), due to its flexibility to regulate the wave excitation in the third dimension for enhanced chirality (37), bianisotropy (40), and other applications (36). In this work, we combine the unique mechanical properties of origami, i.e., continuous 3D shape transformations, with artificial magnetic dipolar excitations and unveil a new mechanism to efficiently engineer magnetic polariton dispersions. The 3D rotation of magnetic dipoles inspired by origami allows to reconfigure hyperbolic or elliptic topology of magnetic polariton IFCs and modulate the group velocity of polariton. With group velocity flipped from positive to negative directions, we further report integrated polariton circuitry in which the polariton propagation and phase distribution can be tailored. Our work opens a new avenue for dynamically engineering polariton dispersions and photonic band structures and provides new opportunities on on-chip origami/kirigami-based polaritonics and photonics, with potential applications in controllable energy transfer, sensing, and information transport.

RESULTS

The investigated origami metamaterial is shown in Fig. 1A. As a proof of concept, spiral split ring resonators (SRRs) made of copper are first periodically printed on one of the facets of a flat paper scratched with Miura-ori folding pattern (37). Next, the planar origami is transformed into its 3D geometry following the Miura-ori folding principle (fig. S1). The parameters of the SRRs and the Miura-ori pattern are included in section S1 in the Supplementary Materials. Because each parallelogram is preserved as a rigid facet in the folding process, the origami metamaterial is simple single degree-of-freedom kinematics. For simplification, we refer the facet where the SRR locates as the SRR plane. The folding angle θ, defined as the dihedral angle formed by SRR plane and xy plane of the global Cartesian coordinate, can fully determine the folding state of the origami. The normal vector of the SRR plane is denoted by n, and thus the angle between n and z axis is mathematically equivalent to the folding angle θ (Fig. 1B). The projection of n against xy plane aligns with the local axis x′, which will be used to describe the rotation of polariton IFCs in the following. By using eigenvalue module of a commercial software Computer Simulation Technology Microwave Studio, we get the eigenmodes on the origami metamaterial, where the magnetic polaritons are highly confined both vertically and horizontally (fig. S2A). The magnetic field distribution indicates a strong magnetic dipole, physically arising from the surface currents flowing along the arms of SRR, which is further verified by the multipolar analysis (fig. S2B).

Fig. 1. Origami-inspired topologically reconfigurable magnetic polaritons.

Fig. 1.

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(A) Schematic of the Miura-ori origami metamaterial. Spiral SRRs made of copper are periodically printed on the origami parallelograms. (B) Zoomed-in view of a unit cell of the Miura-ori metamaterial. The arrow indicates the normal vector perpendicular to the plane where the SRR locates. Folding angle θ is defined as the dihedral angle formed by SRR plane and xy plane of the global Cartesian coordinate. The local x′ axis orients along the projection of normal vector n against xy plane. (C) Dispersion diagram of the magnetic polariton in origami metamaterial. The inset shows the dispersions of the magnetic polariton with origami deformed to different states with θ = 0°, 60°, 80°, and 85°. (D) Retrieved constitutive permeability of the origami metamaterials with θ = 0° and 85°. μx and μz are the in-plane and out-of-plane relative permeability, respectively. Calculated dispersions with the retrieval constitutive effective parameters for (E) planar origami metamaterial and (F) deformed origami with a folding angle θ = 85°. The dots represent the simulated eigen frequencies of the magnetic polaritons.

Under mechanical compressing, the geometric rotation of the SRR can be characterized by the components of normal vector n along x, y, and z axes (fig. S3A). The magnetic dipole responses match well with the trajectories of the normal vector, indicating that the SRR can be modeled as ideal magnetic dipole perpendicular to the SRR plane during the deformation. The dispersions of the magnetic polaritons in origami metamaterial with different folding states are summarized in Fig. 1C, where β represents the wave vector of the designer polaritons along the propagating direction, i.e., x direction, and k0 denotes the wave vector in vacuum. The polariton dispersions are extended both in the frequency domain and momentum space, especially in the largely deformed regions. This can be attributed to the spatial density of the SRRs, which is determined by the deformation state of the origami. The sustained compression reduces the distance of the neighboring SRRs and thus enhances the mutual coupling between these meta-atoms. This will increase the bandwidth of the magnetic polaritons. Meanwhile, the lattice constant of the origami along x direction is extremely decreased in largely deformed regions (fig. S3B). The magnetic polaritons in these deeply subwavelength configurations attain high propagation constant. A particular case is that the origami is planar with a large lattice constant that the whole band becomes relatively flat with a narrow bandwidth centered at the magnetic resonance frequency of a single isolated SRR (see the inset in Fig. 1C and the zoomed-in view in fig. S4). The group velocity vg can be calculated as vg = ∂ω/∂k (41), where ω and k are angular frequency and wave vector, respectively. Therefore, the group velocity of the magnetic polaritons undergoes an interesting transition from negative at planar state to positive at folded state.

To understand the underlying mechanism of the topological transition of polariton dispersions, we first construct a layered metamaterial by stacking the metasurface periodically along z direction. By applying a well-established retrieval process (42), we obtain the effective constitutive parameters with optimizing the period along z direction, i.e., the effective thickness of the origami metasurface. On the basis of the retrieved constitutive parameters, we analyze the dispersions of a homogeneous slab with finite thickness in z direction (section S5). Because the magnetic polaritons propagating in the metamaterial slab are the singularity poles in the reflection coefficient, we can visualize the polariton dispersions via a false color plot of calculated |(r)|, where r is the reflection coefficient (43). For simplification, origami metamaterials under two folding states, i.e., planar state and extremely compressed state with θ = 85°, are investigated and approximately treated as uniaxial slabs. The permeability tensor is denoted as diag [μx, μy, μz], with the off-diagonal terms vanished. Planar origami metamaterial behaves strong out-of-plane anisotropy with μx = μy ≠ μz, while strong in-plane anisotropy occurs under extremely compressed state with μx ≠ μy = μz. Therefore, the optic axis of the uniaxial slab points to z and x axes for planar and folded origami metamaterials, respectively. We choose the proper effective thickness to ensure that the calculated dispersions match well with simulated eigen frequencies of magnetic polaritons. The effective thickness of planar and extremely compressed origami metamaterials is identical and chosen to be 5 mm. Considering the distinct wave confinement in two cases, it is reasonable to choose the same effective thickness for different origami configurations (see section S6). The retrieved effective permeability of the origami metamaterial in Fig. 1D indicates that in-plane permeability μx and out-of-plane μz undergo a topological transition from μx > 0, μz < 0 at planar state to μx < 0, μz > 0 at folded state (other retrieved constituent parameters are shown in fig. S6). With retrieved effective constitutive parameters, we can calculate the dispersions of the polaritons as shown in Fig. 1 (E and F). The dots on the false color plot represent the simulated eigen frequencies of the magnetic polaritons. Guided mode exists in planar origami slab due to the strong dispersion of effective permeability around magnetic resonance regimes (see Fig. 1D). Therefore, calculated dispersions in low-k regions reflect this dispersion and slightly deviate from the simulated eigen frequencies of magnetic polaritons in Fig. 1E. The relatively flat band of the magnetic polariton in planar origami and its vanished negative group velocity (Fig. 1E) result from the attenuating coupling between neighbor SRRs. The group velocity vg can be tailored by controlling the effective distance between neighboring meta-atoms, i.e., |vg| ∝ λ/p where p and λ are lattice constant and working wavelength of extended waves in vacuum, respectively (see section S7). The magnetic polaritons supported in planar origami metamaterial mimic the hyperbolic phonon polaritons in hexagonal boron nitride at the lower Reststrahlen band (760 to 820 cm−1). Contrary to the planar case, the folded origami metamaterial with θ = 85° behaves in-plane hyperbolic magnetic responses as demonstrated in Fig. 1D. Because of the extremely in-plane anisotropy and compressed folding geometry, the in-plane hyperbolic polariton in folded origami metamaterial has positive group velocity with a broader bandwidth (Fig. 1F).

Next, we investigate the reconfigurable elliptic and hyperbolic topology of IFCs of magnetic polaritons in origami metamaterials. Figure 2 (A to D) shows the IFCs of the polariton dispersions in the first Brillouin zone with θ = 0°, 40°, 70°, and 85°, respectively. Topological transitions of the polaritons from closed elliptical to open hyperbolic dispersions are expected. Besides, the axis of the dispersion contour rotates according to the local coordinates x′ and y′ defined in Fig. 1B. We further analyze the topological transitions of polariton dispersions with respect to the folding angle around the transition regimes (see section S8). The polariton IFC features elliptic topology below the transition regimes (fig. S8). When the folding angle increases, polariton IFC becomes hybrid topology, and lastly, it changes to hyperbolic topology beyond the transition regimes (fig. S8). It shows that origami shape deformation facilitates fine control of polariton dispersions. Notably, topological transitions from elliptic to hyperbolic dispersions in magnetic optical metamaterials are actualized in a previous work via varying the operating frequencies (44). However, topological transitions in that work originate from the material dispersion, i.e., the effective constitutive parameters of the metamaterials are dependent on the working frequencies (45), which is fundamentally different from the reconfigurable topology triggered by 3D structure shape deformation in our work.

Fig. 2. Numerical simulations for elliptical-to-hyperbolic topological transitions of the magnetic polaritons.

Fig. 2.

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(A to D) Reconfigurable elliptical-to-hyperbolic topology of IFCs of magnetic polaritons. The dashed lines show the IFCs in the first Brillouin zone at different frequencies. (E to H) Numerically simulated field distributions [real part of the z component of the magnetic field, Re (Hz), top] and corresponding dispersions in momentum space [fast Fourier transform (FFT) of Re (Hz), bottom]. The observed frequencies are 3.56, 3,74, 3.8, and 4.3 GHz, respectively. The observation windows consist of 20 by 20, 20 by 20, 20 by 20, and 25 by 8 unit cells, and the areas are 416 mm by 416 mm, 384 mm by 344 mm, 122 mm by 120 mm, and 90 mm by 84.8 mm, respectively. Scale bars, 5 cm. a.u., arbitrary units.

To confirm the elliptical-to-hyperbolic topological transitions of the magnetic polaritons, numerical simulations and microwave experiments were conducted. As illustrated in Fig. 2 (E to H), the magnetic fields of the excited magnetic polaritons, obtained by full-wave simulations (see Methods), change from convex to concave pattern with the increase of the folding angle; this is also reflected in the Fourier spectrum in momentum space, with IFCs changing from closed ellipse to open hyperbola. The principal axis of the dispersion contour also rotates as expected. One interesting point is the titled wavefronts and asymmetric IFCs of hyperbolic magnetic polaritons in extremely compressed origami metamaterial (Fig. 2, D and H), analogous to recently reported hyperbolic shear polaritons in low-symmetry crystals (13). Here, this feature emerges because the in-plane mirror symmetry of the origami metamaterials is broken by the shape deformation (even for origami with θ = 85°, the structure is still symmetry broken), and thus the permeability tensor is technically not diagonalized. It indicates that the origami metamaterials offer new opportunities to control the lattice symmetry and motivate new directions for polariton physics in symmetry-reconfigurable metamaterials.

We have carried out several experiments to characterize the reconfigurable magnetic polaritons in origami metamaterial. The fabricated sample consists of 25 by 21 unit cells (see Fig. 3A and Methods for detail of the sample fabrication). In the experiments, a port of vector network analyzer (VNA) directly connects to a source at the edge of origami metamaterial (see Methods). The detector, a coil antenna, is fixed at an arm of a 3D movement platform to measure the magnetic fields of the excited magnetic polaritons (Fig. 3B). The measured magnetic field distributions are illustrated in Fig. 3 (C to F) (see details of the measurement in Methods). Elliptical-to-hyperbolic topological transition of the magnetic polariton is observed and verified by convex-to-concave wavefront transition (Fig. 3, C to F, top) and its corresponding dispersion curve in the momentum space (Fig. 3, C to F, bottom). The simulated and experimental results show some discrepancies. First, the frequency and wavelength of magnetic polariton in fabricated origami sample undergo a slight red shift. In simulations, the arrays of periodic SRRs are assumed to be in free space, while in practical implementations, the SRRs are printed on polyimide films and sticked into sheet of paper. The permittivity of polyimide film and paper will increase the effective capacitance of meta-atoms, thus reducing the frequency and increasing the wavelength of the designer magnetic polariton. Second, the measured magnetic fields show reflection characteristics compared with simulated results, because we do not use absorbers at the origami edge in experiments. The excited efficiency of magnetic polaritons with high-k vector is relatively low, and consequently, the reflections at the edge in Fig. 3 (E and F), are smaller compared with those in Fig. 3 (C and D). Moreover, the measured magnetic fields indicate trivial propagating waves on origami metamaterial. The source that we use in experiments will radiate electromagnetic fields outwardly, whereas radiation energy of mismatched port in simulations can be neglected (see Methods). The amplitude of the high-k hyperbolic polariton modes in origami with θ = 85° attenuates markedly in z direction due to its strong wave confinement, and the propagating magnetic fields emitted by the source are comparable to the polaritons fields at the measured plane. Hence, we observe propagating waves emitted by the source in Fig. 3F. The central bright spots in momentum space in Fig. 3F represent the magnetic fields radiated from the excited source as well as the background noise. At other cases, source fields and background noise are relatively small compared to the polaritons field intensity. Therefore, there are no bright spots at the center of first Brillouin zone in Figs. 2H and 3 (C to E).

Fig. 3. Experimental demonstrations of topologically reconfigurable magnetic polaritons in origami metamaterials.

Fig. 3.

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(A) Photograph of the origami metamaterial sample. (B) Experimental setup for exciting the designed magnetic polaritons and measuring the z component of the magnetic field Hz via a coil antenna. (C to F) Measured field distributions [real part of the z component of the magnetic field, Re (Hz), top] and corresponding dispersions in momentum space [FFT of Re (Hz), bottom]. The observed frequencies are 3.2, 3, 26, 3.38, and 3.6 GHz, respectively. The green stars in the inset represent the source location. The presented field areas consist of 20 by 20, 20 by 20, 20 by 20, and 25 by 8 unit cells, and the sizes are 416 mm by 416 mm, 384 mm by 344 mm, 122 mm by 120 mm, and 90 mm by 84.8 mm, respectively. Scale bars, 5 cm.

Because the group velocity of the designer magnetic polariton in origami metamaterial is tunable and its sign can be flipped from the negative to positive, it could find plenty of applications for energy transfer (46). For example, here, by tailoring the origami metamaterial to meta-ribbons with a single unit cell width, we demonstrate reconfigurable integrated polariton circuit with tunable group velocity (Fig. 4A). The origami circuit with a single spiral SRR has extremely narrow bandwidth, thus limiting its practical applications (fig. S9A). To obtain a broader bandwidth of the meta-circuit with negative group velocity, both the neighboring facets of Miura-ori unit are printed with spiral SRRs. Other geometry parameters of the meta-circuit and the SRRs are identical with the origami metamaterials. We also investigate the feasibility of adding SRRs in both neighboring facets especially for origami at folded state. We get the eigenmodes on the folded origami circuit, where the magnetic polaritons are highly confined inside the inner space of the SRRs (fig. S9B). The magnetic field flows continuously across the inside of neighboring SRRs. This feature can be understood by assuming the normal vectors of neighboring SRRs point generally in the same direction. The dispersions of the meta-circuits at planar and folded state with θ = 85° are illustrated in Fig. 4 (B and C, respectively). Because of the opposite group velocity of the meta-circuits at the planar and folded states, it is expected that the phase distributions over the meta-circuit can be tailored via controlling the folding geometries of the meta-circuit. To confirm this, we put a source at the left side of the meta-circuit (green stars in Fig. 4, E and G) to excite the designer magnetic polaritons and measure Hz field distributions on the plane 10 mm over the meta-circuit. For planar meta-circuit with negative group velocity, the phase distributions along the propagation direction path (greenline in Fig. 4E) show an anomalous behavior, i.e., the phase after the polariton propagates advances the initial phase at the source with a phase wrap (Fig. 4D and simulated results in fig. S10A). The propagation direction of the excited polaritons is from B to A (see movie S1). Notably, the energy still flows from A to B in this scenario where the group and phase velocity have opposite signs. Besides, we observe that the wavelength of the polariton becomes longer as the frequency increases due to anomalous dispersion of planar meta-circuit (Fig. 4E). On the contrary, for the folded meta-circuit with positive group velocity, the phase after the polariton mode propagates delays that of the source (Fig. 4F and simulated results in fig. S10C), and the propagation direction of the excited polaritons is from A to B (see movie S2), while the wavelength and frequency satisfy the normal dispersion relationship in Fig. 4G. In the simulations, we neglect the influence of the polyimide films and assume that the SRRs are positioned in free space. This, as well as fabrication error, will slightly change the working frequencies of the meta-circuit. Despite the frequency deviation, the measured magnetic fields at all cases match well with the simulated ones (fig. S10, B and D). Moreover, the planar polariton circuit and its folded counterpart can be jointed together as a hetero-circuit (fig. S11A). With the excitation source positioned at the side of the hetero-circuit, the magnetic polaritons with negative and positive group velocity can be excited simultaneously, distributed on the planar and folded geometric regions, respectively. Because of the opposite group velocity, the propagating behaviors of the magnetic polaritons on the planar and folded regions are different (movie S3), and the corresponding phase retardations are opposite (fig. S11B). Previous works on reconfigurable polariton circuits focus on modulating the optical parameters of the constituent elements via various methods, for example, gate voltage applied on graphene (47) and varactor diodes loaded on the structures (48, 49). Our work uses the geometry deformations in origami, which is previously neglected, and hence attains ultrawide dynamical tuning range, i.e., flipping the sign of group velocity from negative to positive directions. The proposed origami circuit with low-profile, lightweight design and geometry-based reconfiguration could serve as an alternative platform in polaritonics and may find other potential applications, such as controllable wireless energy transfer and microwave delay lines. In combination with flexible substrates, we envision further exciting possibilities such as conformal polaritonic sensors with high sensitivity. With the development of advanced nano-kirigami techniques (50), on-chip and integrable nanoscale origami/kirigami circuit with fast and accurate optical switching may be implemented in the future.

Fig. 4. Reconfigurable integrated polariton circuit with tunable group velocity.

Fig. 4.

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(A) Schematic of the origami polariton circuit. The geometry of the origami circuit can be reconfigured between various folding states. (B) Dispersion of the planar meta-circuit with negative group velocity. (C) Dispersion of the folded meta-circuit at θ = 85° with positive group velocity. (D and E) Measured magnetic field distributions on the plane 10 mm over the planar meta-circuit. (D) Amplitude and phase distributions along the dashed line in the scanning area. (E) Magnetic field distributions (real part of the z component of the magnetic field) in scanning area with the size of 180 mm by 80 mm. (F and G) Measured magnetic field distributions on the plane 10 mm over the folded meta-circuit. (F) Amplitude and phase distributions along the dashed line in the scanning area. (G) Magnetic field distributions (real part of the z component of the magnetic field) in scanning area with the size of 100 mm by 80 mm. The green stars in (E) and (G) represent the source location. Point A is on the same side with the excitation source. The arrows in middle in (E) and (G) denote the propagation directions of polaritons.

DISCUSSION

Here, we demonstrate topologically reconfigurable magnetic polaritons in 3D shape deformable origami metamaterials. The 3D deformable origami unveils an unprecedented pathway to reconfigure photonic band structures and polariton dispersions, revealing elliptical-to-hyperbolic IFCs topological transitions and tunable group velocity. Compared with previous reconfigurable polaritons (26–28), our reconfigurable magnetic polaritons benefit from the origami deformation toward the third dimension and feature ultrawide tuning ranges. We report on tunable magnetic polaritons whose group velocity can be switched from the negative to positive direction. Moreover, the origami metamaterials offer new opportunities to control the lattice symmetry, thus motivating new directions for polariton physics in low-symmetry artificial materials. Regarding the switchable group velocity of polaritons, we envision further exciting possibilities such as lightweight and reconfigurable metadevices for wireless signal processing and energy transfer and tunable directional excitation of polaritons without breaking the symmetry of the system (51). Although the demonstrated origami system works at microwave frequencies, the concept of origami-inspired reconfigurable magnetic polaritons is general and is applicable to other 3D deformable systems at higher frequencies with advanced nanofabrication techniques such as focused ion beam irradiation–induced folding technique (39, 52), mechanical stress– and substrate engineering–induced kirigami (53, 54), and origami induced by responsive forces (55, 56). In particular, with electromechanically reconfigurable on-chip kirigami (50) techniques, it may open new avenues on on-chip polaritonics and photonics, with potential applications in controllable energy transfer, sensing, and information transport.

METHODS

Numerical simulations

To efficiently excite the designer magnetic polaritons in origami metamaterials, we put a discrete port between the gaps of the spiral SRR located at the edge of the origami metamaterials. The port is not impedance matching, so its radiation energy can be neglected. We monitor the real part of Hz on the plane 10 mm over the metasurface plane, which is then used as the input of a fast Fourier transform (FFT) to extract the isofrequency dispersion contours. For all simulated magnetic fields presented in this work, we neglect the influence of the substrate (paper and the polyimide films), and the spiral SRRs were placed in free space.

Microwave sample fabrication

The samples were first fabricated by a standard printing circuit board technology. Copper SRRs (thickness, 0.035 mm) are periodically printed on a Halogen-free frame-resistant type polyimide film (thickness, 0.1 mm; tangential loss, 0.003 at 10 GHz) with a permittivity of 3.5. Next, we use adhesive to stick the ultrathin meta-atom units and the Miura-ori origami together. The sample consists of 25 by 21 unit cells, the whole size of the sample is 520 mm by 436 mm at planar state and compressed to 85 mm by 218 mm at folded state with θ = 85°.

Experimental measurements

For the measurement, we connect a spiral SRR end to end via SubMiniature version A (SMA) to drive the electrons flowing in the SRR. A port of VNA directly connects to SMA port as a broadband source (2.5 to 4.5 GHz), which will radiate electromagnetic fields outwardly and excite the magnetic polaritons in origami metamaterials. In addition, a coil antenna to probe the magnetic field along the z direction was fixed on the 3D near-field scanning system. Considering the unique correspondence between the period and the folding angle of the origami metamaterial, the folding angle of the origami can be controlled by compressing the sample to desired sizes. For 2D origami metamaterials, the spatial resolutions in the near-field measurement are px/2 and py/2 for x and y directions, respectively, where px and py are lattice constants of origami metamaterial along x and y directions. Therefore, the spatial resolutions in Fig. 3 (C to F) are 10.4 mm by 10.4 mm, 9.6 mm by 8.6 mm, 6.1 mm by 6 mm, and 1.8 mm by 5.3 mm, respectively. For 1D meta-circuit, the spatial resolution in Fig. 4 (E and G) is 0.4 mm by 2 mm.

Acknowledgments

Funding:The work at Zhejiang University was sponsored by the Key Research and Development Program of the Ministry of Science and Technology under Grants No. 2022YFA1404704, and 2022YFA1405200, the National Natural Science Foundation of China (NNSFC) under Grants No. 62222115, No. 62171407, No. 11961141010 and No. 61975176, and the Fundamental Research Funds for the Central Universities. M. L acknowledges the support by the China Scholarship Council No. 2020063220086. C.-W.Q. acknowledges the support by the grant (A-0005947-16-00) from Advanced Research and Technology Innovation Centre (ARTIC) in National University of Singapore.

Author contributions: All authors contributed extensively to the work presented in this paper. M.L. and Z.W. initiated the idea; M.L. and X.C. performed the simulation and experiment; M.L., G.H., and Z.W. wrote the manuscript; C.-W.Q., Z.W., and H.C. supervised the project.

Competing interests: The authors declare that they have no competing interests.

Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

Supplementary Materials

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Sections S1 to S11

Figs. S1 to S11

References

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Movies S1 to S3

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