Passive nonreciprocity-induced directional wave scattering

Abstract

Controllable nonreciprocal wave redirection in two dimensions is demonstrated by a monatomic lattice of masses and nonlinear springs. The key is a functional section with a spatially asymmetric arrangement of bilinear stiffness. Regardless of the external force driving frequency or the location of the source relative to the functional section, a stable effect is obtained showing scattered wave motion towards two opposite directions each with oppositely signed displacement offsets. Crucially, the bilinear nature of the springs, with linear response but different stiffness coefficients in compression and tension, makes the passive nonreciprocal redirection effect independent of signal amplitude. Consistent nonreciprocal scattering is demonstrated first for a lattice section with asymmetrically distributed bilinearity. Combinations of these fundamental lattice sections with modified bilinear stiffness and orientation of the asymmetric arrangement demonstrate a wide variety of directional scattering effects, illustrating an ability to control the preferred propagating directions and the signs of the dynamic displacement offsets. These results suggest a novel type of nonreciprocal 2D waveguide whose underlying nonlinear mechanism is fundamentally different from actively-achieved alternative methods such as topologically protected edge states.