The analytical structure of acoustic and elastic material properties

In this paper, we take an in-depth look at the analytical structure of material transfer functions which govern acoustic and elastic response. These include wavenumber (κ) in such media refractive index (n′), density (ρ) its inverse, stiffness (C) compliance (D) tensors as well Bulk modulus (B), finally broader generalization these properties is now known Willis tensor (L). Our goal to clarify appropriate dispersion relations applicable from perspective passivity. Under some mild assumptions, causality ensures that are upper half but deriving for them requires one know how they behave limit |ω|→∞. Unlike electromagnetism, a determination cannot be made on physical grounds since continuum approximation breaks down. Instead, can exploit Herglotz–Nevanlinna (H–N) along with their tensorial counterparts characterize certain passive systems relation known. aim, therefore, relationship have Herglotz functions, turn determines them. analysis shows based upon passivity alone, minimum order 1 apply Fourier transforms D,ρ,n′, inverse B, 3 C,B, ρ, 2 applies κ.