Abstract
Three-dimensional localization of acoustic waves is investigated for a two-dimensional sonic crystal without defects. By studying the wave packet superposed by Bloch modes at the isofrequency surface, we predict the existence of nonpropagating X-shaped waves at either a local top point or a saddle point of a band, where diffractions in different directions cancel out. Different from traveling X waves in homogeneous media, acoustic energy can be localized stationarily within a small space region. Such a “soliton-like” feature has implication in diverse practical situations of focused ultrasound application where a focal region with high spatial stability is necessary.
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