Negative Refraction in Mechanical Rotator Lattices

Abstract

This paper presents numerical and experimental investigations of negative refraction at the interface between two mechanical rotator lattices, adding to the recent body of anomalous wave behavior reported for such simple lattices. Each lattice implements easily reconfigured interrotator coupling which determines whether the lattice's passband is acoustic (with positive group velocity) or optic (with negative group velocity). Since the group velocities have opposite signs over the entirety of both lattices' Brillouin zones, the negative refraction at their interface is inherently broadband. The numerical study constructs a large lattice structure for full-wave simulation and quantitatively analyzes the linear and nonlinear negative refraction. The experimental study documents robust negative refraction in a smaller-scale fabricated system and serves as validation for the numerical findings. We observe frequency-dependent transmission in both simulations and experiments. A linear analysis captures the observed phenomenon at low amplitude. At larger amplitudes, numerical simulations are used to document amplitude-dependent transmission. This phenomenon is explained by a nonlinear dispersion shift and transitional evanescent waves analyzed using a perturbation method. A sensitivity test demonstrates the robustness of negative refraction in the proposed rotator lattice structure.