Reciprocity is a fundamental property of the wave equation in a linear medium that originates from time-reversal symmetry, or T symmetry. For electromagnetic waves, reciprocity can be violated by an external magnetic field. It is much harder to realize nonreciprocity for acoustic waves. Here we report the first experimental observation of linear nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric rods. Viscosity of water is the factor that breaks the T symmetry. Asymmetry, or broken P symmetry along the direction of sound propagation, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. Our study demonstrates that a medium with broken PT symmetry is acoustically nonreciprocal. The proposed passive nonreciprocal device is cheap, robust, and does not require an energy source.

A phononic crystal of aluminum rods with an asymmetric cross section in water is used for the study of Anderson localization of sound. Due to asymmetry, these scatterers may be arranged in three different configurations: a periodic 2D structure, a random structure with 2D disorder, and a random structure with 1D disorder. The last configuration where the rods are equally oriented within the columns and disoriented along the rows is fabricated for the experimental study of 1D Anderson localization in the 2D random system. An exponentially weakening transmission of the ultrasound is demonstrated for the waves propagating along the direction of disorder. In the perpendicular direction where the scatterers are ordered, sound propagates as an extended (delocalized) wave. The localization length is controlled by the degree of disorder. For weak disorder, when orientations of the rods weakly fluctuate around a given direction, Thouless’s theoretical prediction for the scaling of the Lyapunov exponent with disorder is experimentally observed for a mode within the transmission band. For the sound mode close to the band edge, anomalous scaling is confirmed.

A fluid channel clad between two solid plates is an acoustic waveguide where excitation of elastic waves at the channel boundaries has been usually neglected. This work develops a rigorous theory of scattering of sound by a finite-length fluid channel which takes into account excitation of elastic eigenmodes of two plates acoustically coupled through a fluid channel. The theory predicts an evidently contradictory result that the transmission and reflection coefficients of a non-dissipative channel do not sum up to one. Moreover, they both exhibit deep minima at the same series of frequencies. It is shown that conservation of acoustic energy occurs due to redirection of sound, since part of the acoustic flux escapes into the solid plates. This scattering becomes possible because the bf uniform flatness of the boundaries of a straight channel is broken by vibrations. Theoretical predictions are supported by the experiments with ultrasound transmission through a narrow slit obtained between two brass or aluminum plates submerged in water. Measured transmission spectra exhibit deep minima exactly at the frequencies where the theory predicts strong redirection of sound.

Scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Due to perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90 • may occur only for a discrete set of frequencies (Wood's anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode since it cannot be excited at normal incidence. However, at slightly oblique incidence both modes can be excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the "wrong" direction, thus allowing splitting of the incoming signal containing two harmonics into two beams propagating along the chain in the opposite directions. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.

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