Systematic realization of double-zero-index phononic crystals with hard inclusions

A systematic process is described to realize double-zero-index phononic crystals with Dirac-like points experimentally. This type of crystal normally has softer inclusion material than its surroundings medium, allowing mapping into a zero-index medium under certain conditions but also making experimental implementation difficult. On the other hand, realizing phononic crystals with hard inclusions can be experimentally more feasible, but the mapping conditions cannot be directly applied to hard-inclusion crystals such that mapping is not systematically guaranteed in these cases. Moreover, even if such crystals become realizable, there is a lack of a systematic design process which can be used to optimize or to redesign the crystals, which largely limits their potential applications. In this paper, we discover the essential conditions for realizing phononic crystals with hard inclusions and propose a methodology for the systematic design of these crystals using homogenization based on the effective medium theory. Using the proposed method, a double-zero-index phononic crystal with hard inclusions is optimized and experimentally realized for an underwater ultrasonic wave collimator.