  Recent interest in metamaterials has led to a renewed study of wave mechanics
in different branches of physics. Elastodynamics involves a special intricacy,
owing to a coupling between the volumetric and shear parts of the elastic
waves. Through a study of in-plane waves traversing periodic laminates, we here
show that this coupling can result with unusual energy transport. We find that
the corresponding frequency spectrum contains modes which simultaneously
attenuate and propagate, and demonstrate that these modes coalesce to purely
propagating modes at exceptional points, a property that was recently reported
in parity-time symmetric systems. We show that the laminate exhibits
metamaterial features near these points, such as negative refraction, and beam
steering and splitting. While negative refraction in laminates has been
demonstrated before by considering pure shear waves impinging an interface with
multiple layers, here we realize it for coupled waves impinging a simple
single-layer interface. This feature, together with the appearance of
exceptional points, are absent from the model problem of anti-plane shear waves
which have no volumetric part, and hence from the mathematically identical
electromagnetic waves. Our work further paves the way for applications such as
asymmetric mode switches, by encircling exceptional points in a tangible,
purely elastic apparatus.
