Origami Metawall: Mechanically Controlled Absorption and Deflection of Light

Abstract Metamaterials/metasurfaces, which have subwavelength resonating unit cells (i.e., meta‐atoms), can enable unprecedented control over the flow of light. Despite their significant progress, achieving dynamical control of both energy and momentum of light remains a challenge. Here, a mechanically tunable metawall capable of either absorbing light energy or modulating light momentum, by incorporating the magnetic meta‐atoms into a 3D printed origami grating, is theoretically designed and experimentally realized. Through mechanical stretching or compressing of the Miura‐ori pattern, the function of metawall can transit from an absorber, a mirror, to a negative reflector. Particularly, the continuously geometric deformation of the Miura‐ori lattice is a promising approach to compensate the angular dispersion in gradient metasurfaces. Considering the prominent mechanical properties and strong deformation abilities of origami structures, the findings may open an alternative avenue toward lightweight and deployable metadevices with diversified and continuously alterable electromagnetic properties.


Geometry of the metawall with Miura-ori pattern.
The geometry of a unit cell of the designed metawall with Miura-ori pattern is plotted in Figure S1. The parameters of the parallelogram are fixed as a = 10 mm, b = 16 mm and γ = 60°. Two split-ring resonators are located at the centers of the diagonal parallelograms with identical dimensions. The inner and outer radii of each split-ring resonator are r 1 = 2.8 mm and r 2 = 3.3 mm, respectively, while the gap size is g = 0.7 mm and s = 2.7 mm. The solid (dashed) lines correspond to the mountain (valley) creases. Vertices are formed when four creases intersect and each parallelogram is preserved as a rigid facet in the folding process. In this context, we assume the Miura-ori pattern is folded from an ideal material with infinite stretching modulus and therefore it has only one degree of freedom described by the folding angle θ. Figure S1. The geometry of a unit cell of the metawall with Miura-ori pattern. Figure S2 shows the simulation results of the reflectance versus frequency under various folding state. The origami metawall is illuminated with TE plane wave propagating in z-x plane under obliquely incident angle θ in = 40°. The horizontal line in each panel represents the reflectance under various folding state for f 0 = 9.6 GHz.

Reflectance spectrum of all propagating modes
Over the whole deformation, TM 00 and TE (-1)0 is highly suppressed, guaranteeing the efficiency of the metawall. For unfolded 2D metawall, the bandwidth of absorption spectrum (see TE 00 spectrum) is extremely narrow and a slight deformation of the metawall shifts the frequency of absorption, leading to a dramatic decrease of absorption efficiency, which is shown in Figure 2b.  To investigate the optical transition of the fabricated metawall, we measured S 11 parameter under different folding state with oblique incident angle at 40°, as shown in Figure S4a. Compared with simulation results shown in Figure S2, the working frequency undergoes a redshift from 9.6 GHz to 9.24 GHz. Neglect parts of the parallelogram substrate and fabrication errors attribute to this slight redshift. Another fascinating application of metawall is to realized negative reflection at fixed reflection angle. To obtain a high efficiency of negative reflection under different incident angles, the folding angle of metawall is optimized to 50° and the corresponding incident angle is 36°. According to Equation (9) in main text, the reflection angle is calculated as -49.3°. For different incident angles, the metawall can be tuned to a certain folding state to keep the reflection angle unchanged. As illustrated in Figure   S4b, the working frequency of the fabricated metawall undergoes a slight, redshift from 9.36 GHz to 9.07 GHz. For practical operating frequency f 1 = 9.07 GHz, the negative reflection angle θ (-1)0 is corrected to -53°.

Required conditions to suppress higher order modes
Illuminated with TE plane waves propagating in z-x plane, the periodicity along the y direction is smaller than the wavelength to guarantee no radiation in the z-y plane; to ensure sure (-1)0 and 00 are the only possible propagating diffraction orders, the closest higher-order modes [i.e., 10 and (-2)0] are evanescent and the required conditions to suppress higher-order modes are given by 1 : where θ (-1)0 and θ in are the reflection angle for (-1)0 Floquet mode and incident angle respectively. It can be shown that knowing the incidence angle θ in , the metasurface period p and the wavelength λ, the diffraction angle for (-1)0 mode is fixed as: ( 1)0 in () arcsin sin p    

S(2)
Take the circumstance for investigating optical transition of the metawall as an example, i.e., θ in = 40°. The diffraction angle for (-1)0 mode is plotted in Figure S5.
Blue line represents the calculated results of the maximum value of θ (-1)0 = -10.3°.
Orange and yellow lines show simulated and experimental results of θ (-1)0 respectively. The operating frequency of the practical fabricated metawall undergoes a redshift, leading the experimental θ (-1)0 smaller than the simulated one. Both the simulation and experiment results are smaller than the calculated maximum value, guaranteeing (-1)0 and 00 are propagating modes while higher order modes been evanescent. Figure S5. Reflection angle of (-1)0 Floquet mode versus folding angle θ. Over the whole range of deformation, both the simulation and experiment results are smaller than the calculated maximum value, guaranteeing (-1)0 and 00 are propagating modes while higher order modes been evanescent.
6. Figure S6. Measured reflection intensity versus reflection angle with folding angle at: a) 25° and b) 63°. The purple dotted line represents the reflection angle of θ (-1)0 . The brown dotted line represents the specular reflection angle θ 00 = 40°, while the symbols of blue and red balls represent the measured reflection intensity for co and cross-polarized respectively.