Fig. 1. The proposed spin-locked retroreflector based on the Miura origami metagrating design. The origami metagrating is 2D. Therefore, the retroreflection can be achieved in both the x and y directions. When the origami metagratings are in different folding states, P_x ≠ P_y, θ_i,r¹ ≠ θ_i,r² ≠ θ_i,r³ ≠ θ_i,r⁴.

Fig. 2. (a) Schematic representation of a general spin-locked metagrating with three Floquet modes under a TE-polarized incidence. It is worth mentioning that this principle also applies to a TM-polarized incidence. (b) Demonstration of induced electric current on the ground plane. (c) Schematic diagram of the folded Miura origami unit cell. The substrate of the Miura origami is a polyimide material, which is located on a perfect electrical conductor. The thickness of the substrate is only 0.075 mm, and the dielectric constant is ε_r = 3. (d) The distribution of creases. The period of the structure in the x-axis is P_x, and the period in the y-axis is P_y.

Fig. 3. Reflection coefficients and angles versus frequency for different Floquet modes under (a) the TE- and (b) the TM-polarized incidences. When the folding angle β of the retroreflector is tuned to 45°, the corresponding scattered electric field distribution of (c) the TE- and (d) the TM-polarized incidences on the zOx plane is obtained at θ_in = 36° illumination angle. (e) Schematic diagram of spin-locked retroreflection.

Fig. 4. Simulation results of retroreflection amplitude and angle as a function of fold angle β under the TE- and TM-polarized incidences: (a) x-direction and (b) y-direction. The corresponding scattered electric field distribution of the TE- and TM-polarized incidences on the zOx plane: (c)–(d) θ_in = 34°, β = 40° and (e)–(f) θ_in = 42°, β = 50°. The corresponding scattered electric field distribution of the TE- and TM-polarized incidences on the zOy plane: (g)–(h) θ_in = 34°, β = 40° and (i)–(j) θ_in = 38°, β = 50°.

Fig. 5. Relationship between the scattering intensity and θ under TE- and TM-polarization incidences. x-direction: (a) β = 40°, |θ_ref| = 34°, (b) β = 45°, |θ_ref| = 36°, and (c) β = 50°, |θ_ref| = 38°. y-direction: (d) β = 40°, |θ_ref| = 34°, (e) β = 50°, |θ_ref| = 42°, and (f) β = 60°, |θ_ref| = 60°.

Fig. 6. (a) The image shows the arch test platform. (b) Sample picture of the origami retroreflector.

Fig. 7. When the wave vector is along the x-direction, experimental results of the scattered intensity distribution for retroreflection at various incidence angles of (a) 34°, (d) 36°, and (e) 38° under TE- and TM-polarized incidences. When the wave vector direction is along the y-direction, experimental results of the scattered intensity distribution for retroreflection at various incidence angles of (a) 34°, (d) 42°, and (e) 60° under TE- and TM-polarized incidences.