Rotation mechanics of optical scatters in stretchable metasurfaces

Abstract

Stretchable metasurface comprised of an array of optical hard-material scatters on the surface of a soft substrate is emerging as an artificially designed structure to manipulate optical wave propagation through a mechanical means. Upon stretching the soft substrate, along with the increase of the spacing distance between hard scatters, the orientations of the hard scatters will vary due to their strong mechanical mismatch with the soft substrate, but the underlying mechanics mechanism is lacking. In the present study, we establish a theoretical mechanics framework to address the rotation of hard scatters bonded on the surface of a soft substrate subjected to a mechanical stretching load. In this model, we introduce a pseudo-interface between the hard scatters and the soft substrate and decouple the effect of in-plane stretching deformation and out-of-plane deformation in the thickness direction of the soft substrate on the basis of moment equilibrium. Besides, the shear stress field along the thickness direction of three-dimensional soft substrate is formulated from that of a two-dimensional plane model by introducing a thickness factor. The effect of spacing distance, geometric shape, and initial orientation of hard scatters and thickness of the soft substrate on the scatter rotation is elucidated. Extensive finite element analyses (FEA) are performed and the results show good agreement with the theoretical predictions in both scatter rotation and stress distribution. We further construct a stretchable metasurface and demonstrate that the refraction of incident lights can be tuned by controlling the rotation of scatters. The mechanics theory established here provides a foundation to design mechanically controllable metasurfaces by leveraging the rotation of hard-material scatters.