A transfer matrix approach for characterizing spherically symmetric acoustic metamaterials and structures

The plane wave transfer matrix method is a robust process for acquiring the acoustic properties of an arbitrary material. To achieve this, the specimen being tested is inserted in a waveguide and subjected to the four-microphone method to capture the pressure fields. This is a powerful and accurate process for simplifying complex three-dimensional geometries to simpler equivalent acoustic properties suitable for two-dimensional analysis, but it does not work for structures lacking plane wave symmetry. Sometimes, it is favorable to characterize a structure through spherical coordinates. A spherically spiraling acoustic metamaterial horn is an appropriate case of a technology that does not fit this traditional planar model. To acquire the acoustic properties that define structures such as these, the four-microphone method, the transfer matrix, and the scattering matrix, for a spherically symmetric system are derived. Unlike the planar transfer matrix analysis, the resulting acoustic properties in this paper are more complex. Variations of the spiraling acoustic metamaterial horn are evaluated by this method both in experimental measurements and simulated environments. This structure and methodology offer ample opportunities for classifying many spherically symmetric acoustic devices with an application in areas, such as ultrasound and audio technologies.