SUMMARY

The study of wave propagation in linear periodic structures has a long history due to its relevance in a wide range of physical systems, and broad engineering applications including filters, diodes, switches and waveguides. Significant research attention has recently focused on nonlinear periodic structures since nonlinearity introduces amplitude-dependency, PT-symmetry breaking, bifurcation phenomena and other rich dynamical behaviors absent in linear systems. This work explores passive nonlinear non-reciprocity, negative refractive index and dispersion morphing. One-dimensional and two-dimensional discrete lattices, along with isolated unit cells are considered. Non-reciprocity, describing the asymmetric transmission between two points in a system, is informed in an isolated unit cell via nonlinear normal mode analysis, and in a periodic structure via nonlinear dispersion and bifurcation analysis. The negative refractive index and dispersion morphing are explored in an in-plane rotator lattice, where rotational geometry brings forth reconfigurable band structures and nonlinearity. A nonlinear amplitude saturation effect is observed in this lattice and investigated in an evanescent-specific perturbation framework. The theoretical findings are confirmed with numerical simulations. The proposed work will experimentally demonstrate the negative refractive index and the dispersion morphing phenomena in rotator lattices. These findings may inspire and guide future metamaterial and smart materials research aimed at uncovering new approaches for vibration isolation, amplitude saturation, subwavelength imaging and deformation sensing.