A versatile smart transformation optics device with auxetic elasto-electromagnetic metamaterials

Synergistic integration of electromagnetic (EM) and mechanical properties of metamaterials, a concept known as smart metamaterials, promises new applications across the spectrum, from flexible waveguides to shape-conforming cloaks. These applications became possible thanks to smart transformation optics (STO), a design methodology that utilizes coordinate transformations to control both EM wave propagation and mechanical deformation of the device. Here, we demonstrate several STO devices based on extremely auxetic (Poisson ratio -1) elasto-electromagnetic metamaterials, both of which exhibit enormous flexibility and sustain efficient operation upon a wide range of deformations. Spatial maps of microwave electric fields across these devices confirm our ability to deform carpet cloaks, bent waveguides, and potentially other quasi-conformal TO-based devices operating at 7 ∼ 8 GHz. These devices are each fabricated from a single sheet of initially uniform (double-periodic) square-lattice metamaterial, which acquires the necessary distribution of effective permittivity entirely from the mechanical deformation of its boundary. By integrating transformation optics and continuum mechanics theory, we provide analytical derivations for the design of STO devices. Additionally, we clarify an important point relating to two-dimensional STO devices: the difference between plane stress and plane strain assumptions, which lead to elastic metamaterials with Poisson ratio -1 and -∞, respectively.