Nonreciprocal and directional wave propagation in a two-dimensional lattice with bilinear properties

A passive method of realizing nonreciprocal wave propagation in a two-dimensional (2D) lattice is proposed, using bilinear springs combined with the necessary spatial asymmetry to provide a stable and strong departure from reciprocity. The bilinear property is unique among nonlinear mechanisms in that it is independent of amplitude but sensitive to the sign of the wave motion; the 2D setup allows the flexibility of generating spatial asymmetry at both small and large scales. The starting point is a linear 2D monatomic spring–mass lattice with strong directionally dependent wave propagation. The source and receiver are aligned so that there is virtually no direct wave transmission between them. Adding a region of bilinearity combined with spatial asymmetry that is not in the direct path between the source and receiver causes signal transmission via nonreciprocal scattering. A variety of spatially asymmetric bilinear configurations are considered, ranging from compact modulations confined within the unit cell to extended ones over the whole section, to obtain different dynamic nonreciprocal effects. Simulations illustrate how the combination of bilinearity and spatial asymmetry ensures a passive amplitude-independent nonreciprocal 2D system for a variety of different excitations.