Nonlocal metasolid response of homogenized phononic crystals

Abstract

The nonlocal effective dynamic mass-density and stiffness tensors for a solid 3D phononic crystal having Au inclusions embedded in a Si host matrix have been calculated. The applied homogenization theory is based on the Fourier formalism and the form-factor division approach. Using the effective parameters, the phononic band structure of the homogenized elastic crystal can be described even beyond the long wavelength limit. It is found out that the effective dynamic mass-density becomes anisotropic as the frequency of the phononic modes is increased because the nonlocal metasolid response depends on the phononic-mode polarization, the shape of the inclusions, and the type of the periodic array.

Nonlocal electrodynamics of homogenized metal-dielectric photonic crystals

“…This behavior was reported in [24], where the effective parameters of the nonlocal dielectric response for PC lead to wave vectors beyond the first BZ. Interestingly, in the work [25], the same iterative procedure was applied to calculate the phononic dispersion of homogenized 3D solid phononic crystals leading to wave vectors outside the first BZ.…”

Phononic crystal as a homogeneous viscous metamaterial

“…In the longwavelength limit a phononic crystal behaves, in many cases, like a homogeneous medium with effective parameters. The effective parameters for different types of phononic crystals have been calculated in a series of recent publications [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Deformation of photonic and phononic crystal spectra and, in particular, the band-gap width under the influence of weak dissipation was studied in Refs.…”