Non-Hermitian elastodynamics

The properties of artificial materials can be tailored to exhibit extraordinary properties by cleverly engineering their composition. The development of such metamaterials is a prominent thrust in engineering today. One of the greatest challenges is to engineer metamaterials that manipulate waves by design.

Of particular interest are elastic waves, since numerous mechanical applications require their control; vibration isolation, ultrasonography, energy harvesting and cloaking, to name a few.

The forefront of research in wave control emerged from a seemingly unrelated theory, quantum mechanics, with the development of its non-Hermitian formalism, describing nonconservative systems that exchange energy with their environment.

By drawing analogies between this formalism and those of classical systems, researchers have discovered phenomena that defy intuition, phenomena such as zero reflection and chiral absorption, and have exploited them to control light, sound, and elastic waves. Can we go beyond these analogies?

I suggest that the answer is hidden in the tensorial nature of elastodynamics, a nature that is unparalleled in other physics.

This conjecture is motivated by my group's recent discovery that even conservative stratified solids can generate non-Hermitian features, such as negative refraction and exceptional points.

The mechanism that obviates external energy is the coupling between shear and pressure waves that is unique to elastodynamics.

What happens when judiciously exploiting this distinctive mechanism together with concepts from non-Hermitian quantum mechanics? In tackling this question I expect to unveil novel phenomena that are inaccessible in other physics.

Understanding the mechanics will lead to exceptional ways of shaping waves, thereby benefiting engineering applications that require robust control of elastic motion.