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Abstract
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.
Highlights
Metamaterials have been widely investigated in recent years
As discussed in the previous section, the mapping conditions for a double-zero-index phononic crystals (DZIPnCs) with a Dirac-like point require the Dirac-like point to be at the Brillouin zone (BZ) center and constructed via a linear combination of a monopole mode and dipole modes
These apply to photonic crystals with soft inclusions and not to phononic crystals with hard inclusions and cannot be directly applied to phononic crystals
Summary
Metamaterials have been widely investigated in recent years. These are artificially designed to realize unprecedented physical characteristics such as negative refraction and bandgap[1,2]. Recent studies[6,7,8,12] have shown that crystals with a Dirac-like point can be mapped to a double-zero-index medium (double-ZIM) only if the Dirac-like point firstly originates due to a linear combination of monopole and dipole modes and secondly is formed at or near a Brillouin zone (BZ) center or Γ point These two conditions were found for photonic crystals having soft inclusions surrounded by a hard matrix[6]. It is necessary to define quantitative parameters for an inverse-design method, and the effective medium theory (EMT)[19] has been widely used to provide these parameters[20] According to this theory, the effective density and effective bulk modulus are calculated and represent the local material properties of the DZIPnC. It is important to ensure that the Dirac-like point is located at the BZ center in order to apply the EMT within a unit cell
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