Acoustic omni meta-atom for decoupled access to all octants of a wave parameter space

Abstract

The common behaviour of a wave is determined by wave parameters of its medium, which are generally associated with the characteristic oscillations of its corresponding elementary particles. In the context of metamaterials, the decoupled excitation of these fundamental oscillations would provide an ideal platform for top–down and reconfigurable access to the entire constitutive parameter space; however, this has remained as a conceivable problem that must be accomplished, after being pointed out by Pendry. Here by focusing on acoustic metamaterials, we achieve the decoupling of density ρ, modulus B−1 and bianisotropy ξ, by separating the paths of particle momentum to conform to the characteristic oscillations of each macroscopic wave parameter. Independent access to all octants of wave parameter space (ρ, B−1, ξ)=(+/−,+/−,+/−) is thus realized using a single platform that we call an omni meta-atom; as a building block that achieves top–down access to the target properties of metamaterials.

Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

“…The complex nature of the impedance make Willis materials with even coupling ideal for impedance matching applications, as demonstrated by Koo et al 27 Additionally, Eq. (37) and (38) demonstrate that one cannot determine density and compressibility from only impedance and wavenumber when there exists non-zero coupling, i.e., ρ eff = Z ± k ± /ω and β eff = k ± /ωZ ± , which is counter to general assumptions in reflection/transmission acoustical parameter extraction methods.…”

“…III B, a symmetric inhomogeneity results inα c = 0, and therefore, from Eqs. (27), (29), and (31), χ e eff = 0. However, there will still be odd coupling, χ o eff = 0, due to unit cell interaction and finite phase speed across the unit cell, which in general may not be neglected.…”

“…Independent of the works discussing Willis coupling, Koo et al 27 recently demonstrated numerically and experimentally the use of acoustic bianisotropy to impedance match waveguides with different crosssectional areas and to independently control reflection and transmission angles from a metasurface with a normally incident plane wave. Their demonstrations provide the first experimental evidence of acoustic bianisotropy and were inspired by the analogs to bianisotropy in electromagnetism.…”

“…However from the detailed analysis of the preceding sections, the components ofΛ o c are both mesoscale effects and odd with respect to a reversal of propagation, whereasΛ e c is due asymmetry at the microscale and even with respect to propagation, as presented in Eq. (27).…”

“…This coupling between constitutive relations implies energy conversion in the material response to a particular field, which is distinct from the exchange of energy that occurs in wave propagation. Macroscopic coupled constitutive relations may result from multiple microscale and mesoscale effects including chiral inhomogeneities, 17,20,21 asymmetric inhomogeneities and substrate effects, 5,7,14,[22][23][24][25][26][27][28] nonlocal effects due to a finite unit cell and multiple scattering, 5,9,10,29,30 and in the presence of nonreciprocal biases. [15][16][17]28,[31][32][33] Despite the prevalence of published work in bianisotropy and Willis coupling, the physical analogies between the origins of these effects in electromagnetic and elastic systems have not been fully discussed.…”