The sound propagation properties of lossy lamella-crystals are analysed theoretically utilizing a rig- orous wave expansion formalism and an effective medium approach. We investigate both sup- ported and free-standing crystal slab structures and predict high absorption for a broad range of frequencies. A detailed derivation of the formalism is presented, and we show how the results obtained in the subwavelength and superwavelength regimes qualitatively can be reproduced by homogenizing the lamella-crystals. We come to the conclusion that treating this structure within the metamaterial limit only makes sense if the crystal filling fraction is sufficiently large to satisfy an effective medium approach.
Christensen, J., Mortensen, N. A., & Willatzen, M. (2014). Modelling the acoustical response of lossy lamella-crystals. Journal of Applied Physics, 116(16), . https://doi.org/10.1063/1.4898808