The Atomistic Green's Function method for acoustic and elastic wave-scattering problems

TL;DR

This paper introduces the Atomistic Green's Function (AGF) method for efficiently analyzing acoustic and elastic wave scattering in infinite systems, avoiding artificial boundaries and applicable to complex structures.

Contribution

The paper presents the AGF formalism for calculating effective Hamiltonians and Green's functions in wave scattering problems, enabling accurate analysis without artificial truncation.

Findings

Successfully applied to 1D and 2D scattering problems

Enables calculation of reflection and transmission ratios

Avoids artificial boundary conditions in scattering analysis

Abstract

In this paper, we present a powerful method (Atomistic Green's Function, AGF) for calculating the effective Hamiltonian of acoustic and elastic wave-scatterers. The ability to calculate the effective Hamiltonian allows for the study of scattering problems in infinite systems without the introduction of any artificial truncating boundaries such as perfectly matched layers or Dirichlet to Neumann (DtN) maps. Furthermore, the AGF formalism also allows for the efficient calculation of the Green's function of the scatterer as well as all relevant scattering metrics including reflection and transmission ratios. The formalism presented here is especially suited to scattering problems involving waveguides, phononic crystals, metamaterials, and metasurfaces. We show the application of the method to three scattering problems: scattering from a slab (1D), scattering from a finite phononic crystal (1D), and scattering from defects in a waveguide (2D).