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A metamaterial cloak, however, causes the light bouncing off it to perfectly cancel the light reflected from the object underneath it, producing undisturbed light waves that conceal the object's presence (right). Several research teams around the world, including mine, have de sign ed and produced metamaterial coatings that can redirect light waves that hit them, effectively preventing light from bouncing off the object and reaching our eyes and even from leaving shadows. The emerging light-matter interactions are controlled by the twisted symmetry of the crystal lattice, en ab ling a large rotation of the incoming light polarization over a broad range of wavelengths. [Extracted from the article]

The cross-coupling between strain and velocity in acoustic materials, known as Willis coupling, has recently been receiving increasing attention within the broad acoustics community. Willis coupling can provide a new degree of freedom to control sound propagation, which has been enabling several novel applications. In this work, based on the general constitutive relations of Willis media and the acoustic Poynting theorem, we study the constraints stemming from fundamental symmetries – parity, time-reversal, reciprocity and energy conservation – in these media. The wave features, such as wave-vectors, wave impedance and orthogonality are also generally investigated. In addition, we put forward a nonlocal model that unveils the relation between Willis media and nonlocal materials, and how Willis phenomena stem from weak forms of nonlocality. • We relate wave properties in Willis media to physical symmeties: parity, time-reversal, reciprocity and energy conservation. • We generally prove orthogonality relations, wave numbers and impedance for eigen-waves in Willis media. • We highlight the exotic responses emerging in purely nonreciprocal Willis media. • We derive an equivalent description of Willis media in terms of weak nonlocality. [ABSTRACT FROM AUTHOR]