Localization-antilocalization of soundwaves in a disordered phononic crystal with mirror symmetry

Anderson localization in a disordered potential leads to exponential decay of an incoming wave. However, if a 1D disordered potential possesses mirror symmetry, V(-x) = V(x), then the eigenstates are either even or odd functions of x. As such, a wave localized on one side of such a symmetric disordered potential should elicit a corresponding antilocalized peak at the symmetric position on the other side. The distribution of pressure in a symmetric disordered potential is similar to the wave function profile in a symmetrical double-well potential. This similarity opens a way to demonstrate quantum tunneling using acoustic waves. This effect has an important application to secure communications, as the transmitted signal is reduced by disorder to the level of noise, thus excluding the possibility of signal interception, then enhanced by the symmetric part of the potential at the receiver. This is a secure method of information transmission without the need for encryption and decryption. We developed a methodology for identifying the frequency spectrum consisting of narrow doublets that correspond to eigenstates of different parities. A 2 × 30 phononic crystal with orientational disorder was fabricated for experimental observation of antilocalization. [This work is supported by the NSF under EFRI Grant No. 1741677.]