The manipulation and control of phonons is important scientifically in understanding nonlinear propagation, caustic formation and shock interactions, as well as from a technological standpoint, in applications ranging from sound insulation to ultrasonic imaging and shock dissipation. Unique to the challenge in phonon manipulation lies in the material‘s inherently nonlinear response, such as phonon-phonon scattering as well as amplitude dependent shock propagation; this stems from the intriguing structure of the different materials across multiple length scales, from the atomic to the meso-scale, which gives rise to this rich behavior. Phononic metamaterials (PMM) enables one to access certain exotic propagation behavior, such as super-tunneling, negative refraction and super-absorption, by controlling the wave propagation behavior through deliberate structuring at a particular length scale. Furthermore, dynamic behavior in PMM are exploited typically through affine deformation or elastic instabilities, leading to symmetry changes in the structure and hence in the dispersion behavior. However, we propose that, by harnessing the intrinsic nonlinear responses in materials, (occurring at a particular length scale) together with the structural symmetry at targeted length scales, we can arrive at novel methods of controlling wave propagation behavior. One explicit example of this is in spider silk fibers, whihc possess macroscopically uniaxial symmetry. We theoretically and experimentally observed an indirect hypersonic polarization band gap (30%) and importantly, negative index behavior; we further demonstrated that these properties can be dynamically and reversibily tuned with large amplitude strains (up to ±40%). This is attributed to the interactions between the elastic nonlinearity arising between the multi-scale structure (sub 50 nm) of the spider silk constituents and its uniaxial structure at a different length scale(sub 1um). The origin of this band gap is distinct from common mechanism attributed to scattering or hybridization while the negative index behavior arises from the elastic nonlinearity, pointing the way forward to new methods of generating negative index behavior through nonlinearities. This unprecedented result reveals the major role of multilevel structural organization on elastic energy flow and the influence of nonlinearity in the mechanical behavior.
We develop this design principle further and show that by designing the multiple length scales, governing both the intrinsic materials response as well as the wave propagation in various PMMs through symmetry principles, we are able to control the nonlinear wave propagation characteristics ranging from efficient dissipation of shock waves, dynamically reconfigurable phonon polarizers, lens as well as ultracompact sound isolation. This provides an avenue for designing novel systems with tailored and importantly, functionally optimized properties.