Extended optical theorem in isotropic solids and its application to the elastic radiation force

TL;DR

This paper extends the optical theorem to elastic wave scattering in solids, deriving new formulas for radiation force calculations on inclusions, with applications in ultrasound elastography and nondestructive testing.

Contribution

We derive an extended optical theorem for elastic waves in solids using vector spherical harmonics, enabling accurate radiation force analysis on inclusions in elastic media.

Findings

Computed scattering and radiation force efficiencies for iron and stainless steel spheres.

Found up to 98% difference compared to previous liquid models.

Demonstrated applications in elastography and nondestructive testing.

Abstract

The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion embedded in a linear elastic solid using a vector spherical harmonics representation of the waves. The sphere can be a rigid, empty cavity, elastic, viscoelastic, or layered material. The theorem expresses the extinction cross-section, i.e. the time-averaged power extracted from the incoming beam per its intensity, regarding the partial-wave expansion coefficients of the incident and scattered waves. We establish the optical theorem for a longitudinal spherically focused beam scattered by a sphere. Moreover, we use the optical theorem formalism to obtain the radiation force exerted on an inclusion by an incident plane wave and focused beam. Considering an iron sphere embedded in an aluminum matrix, we compute the scattering and elastic radiation force efficiencies. In addition, the elastic radiation force is obtained on a stainless steel sphere embedded in a tissue-like medium (soft solid). Remarkably, we find a relative difference of up to $98\%$ between our findings and previous lossless liquid models. Regarding some applications, the obtained results have a direct impact on ultrasound-based elastography techniques, ultrasonic nondestructive testing, as well as implantable devices activated by ultrasound.