Based on a phononic crystal (PC) constituted of a square array of cylindrical Polyvinylchloride inclusions in air, a theoretical model is constructed that details three schemes for controlling the relative phase between propagating acoustic waves in this PC. In exploiting the spectral, wave vector and wave-phase properties of this PC, a series of acoustic based Boolean logic gates are constructed. Finite-difference time-domain simulations are employed to validate theoretical models and demonstrate the NAND, XOR and NOT Boolean logic gates.
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