Nassar, HusseinYousefzadeh, BehroozFleury, RomainRuzzene, MassimoAlù, AndreaDaraio, ChiaraNorris, Andrew N.Huang, GuoliangHaberman, Michael R.2020-07-072020-07-072020-07-072020-07-0610.1038/s41578-020-0206-0https://infoscience.epfl.ch/handle/20.500.14299/169872The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry between action and reaction in fluids and solids. In its simplest form, it states that the frequency-response functions between any two material points remain the same after swapping source and receiver, regardless of the presence of inhomogeneities and losses. As such, reciprocity has enabled numerous applications that make use of acoustic and elastic wave propagation. A recent change in paradigm has prompted us to see reciprocity under a new light: as an obstruction to the realization of wave-bearing media in which the source and receiver are not interchangeable. Such materials may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. Here, we review how reciprocity breaks down in materials with momentum bias, structured space-dependent and time-dependent constitutive properties, and constitutive nonlinearity, and report on recent advances in the modelling and fabrication of these materials, as well as on experiments demonstrating nonreciprocal acoustic and elastic wave propagation therein. The success of these efforts holds promise to enable robust, unidirectional acoustic and elastic wave-steering capabilities that exceed what is currently possible in conventional materials, metamaterials or phononic crystals.text::journal::journal article::review article