Characterization of avoided crossings in acoustic superlattices: The Shannon entropy in acoustics

Abstract

We show that Shannon’s information entropy provides a correct physical insight of localization effects taking place in structured fields fashioned by eigenmodes upon substrate. In particular, we find that the localization exchange among levels when an avoided crossing occurs is explainable in terms of an informational trade among those levels. We use it to characterize the resonant Zener-like effect in two types of ultrasonic superlattices, one made of metamaterial slabs and the other made of Plexiglas and water cavities. When the gradient of the layer cavities is varied along the narrow region where the avoided crossing appears, it is found that Shannon’s entropy of both levels maximizes at the critical gradient showing the levels’ anti-crossing.