Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study

We report on a phononic crystal (PC) consisting of a square array of cylindrical polyvinylchloride inclusions in air that exhibits positive, negative, or zero refraction depending on the angle of the incident sound beam. For all three cases of refraction, the transmitted beam undergoes splitting upon exiting the crystal. These properties are analyzed theoretically using finite difference time domain method and are demonstrated experimentally. Band structures and equifrequency surfaces (EFSs) calculated with the plane-wave expansion method show that the observed properties result from the unique geometry of the PC's EFS as compared to that of the incident media.