Effects of resonator geometry and substrate stiffness on the tunability of a deformable microwave metasurface

Tunable metasurfaces can shift their resonant frequency through different approaches, one of which is applying mechanical deformations. Here, we show the effects of two key factors on the tunability of deformable metasurfaces; the resonator geometry and substrate stiffness. To show the effects, we compared the tunability of unit cells with three resonator geometries and three common substrates at microwave frequencies from 1 GHz to 10 GHz under a given mechanical deformation. We showed that the resonator geometry affects the deformation field, as a consequence, causes different resonant frequency shifts. Moreover, it affects the stress field in the metasurface which in turn limits the maximum allowable deformation before mechanical failure. In addition, increasing the substrate stiffness has controversial effects on the tunability of the metasurface. It can either increase or decrease the tuning spectrum by transferring more deformation to the resonators and constraining the rigid body motions. On the other hand, increasing the substrate stiffness increases the force required for tuning which is a limiting factor for applications. Accordingly, a trade-off exists between the desired tuning spectrum and the required amount of force for changing the metasurface response. Both of these factors limit the functionality of tunable metasurfaces.