A layer-multiple-scattering method for phononic crystals and heterostructures of such

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…The calculation for homogeneous spheres can be found in literature [53] as well as the solutions for inhomogeneous core-shell particles. [76] Coming back to our system with N scatterers, the total wave field incident on the n-th scatterer is the sum of the incident plane wave and the wave field scattered from all scatterers n ′ = n.…”

“…[40,76,80] For a slab parallel to a distinct crystallographic plane, the reduced vector parallel to this plane, k , is usually a conserved quantity. Therefore, LMS searches in each individual slab propagating Bloch waves for given ω and k , which are the eigenmodes of the elastic field in that slab.…”

“…le Havre) using a formalism, appropriately developed for this case and presented elsewhere. [76,116] Each resonance mode appearing at frequency f (n, l) in these DOS spectra is characterized by the angular momentum l, imposed by the spherical symmetry of the particle, where n denotes the n-th order solution for a given l. All the shell-localized modes reported in this section have n=1. The materials elastic parameters (c l , c t ) and densities are used as adjustable parameters in order to achieve the least deviation between theoretical and experimental eigenfrequencies.…”

“…section 3.4.1). [76,95] In the computations, a plane sound wave propagating in air and impinging upon a single PS sphere was considered and after subtracting the scattering amplitude for a rigid sphere of equal size, the sphere eigenmodes appear as resonance peaks in the plot of scattering cross-section versus frequency. Thereby the resonance frequencies f (n, l) can be identified as mode with angular momentum quantum number l of n-th order.…”

The transmission properties of elastic waves through multilayers of spheres with planar defects

“…The elastic wave propagation problem through three-dimensional periodic composites formed by arranging spherical scatterers periodically in a homogeneous host matrix with infinite extension has been studied in recent years [1][2][3][4][5]. Compared with the elastic wave propagation through random composites with random distributed spherical scatterers in host material [6][7][8], there are unique band bap effects in the frequency domain for the periodic composites.…”