The sound propagation properties of lossy lamella-crystals are analysed theoretically utilizing a rigorous wave expansion formalism and an effective medium approach. We investigate both supported 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.
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Christensen et al. (2014) studied this question.
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