Acoustic integrated extinction

TL;DR

This paper derives a comprehensive formula for acoustic integrated extinction applicable to both causal and non-causal scattering, with implications for acoustic cloaking and broadband transparency.

Contribution

It extends the integrated extinction concept to non-causal acoustic scattering and introduces a new metric for broadband acoustic transparency.

Findings

Derived a general IE formula valid for causal and non-causal scattering

Reduced IE to a finite integral for certain scatterers

Discussed implications for acoustic cloaking and transparency

Abstract

The integrated extinction (IE) is defined as the integral of the scattering cross-section as a function of wavelength. Sohl et al. [1] derived an IE expression for acoustic scattering that is causal, i.e. the scattered wavefront in the forward direction arrives later than the incident plane wave in the background medium. The IE formula was based on electromagnetic results, for which scattering is causal by default. Here we derive a formula for the acoustic IE that is valid for causal and non-causal scattering. The general result is expressed as an integral of the time dependent forward scattering function. The IE reduces to a finite integral for scatterers with zero long-wavelength monopole and dipole amplitudes. Implications for acoustic cloaking are discussed and a new metric is proposed for broadband acoustic transparency.