Resonance analysis of one-dimensional acoustic media: a propagation matrix approach

TL;DR

This paper investigates the scattering resonances in one-dimensional acoustic media using a propagation matrix approach, characterizing resonant frequencies, analyzing their distribution, and deriving asymptotics in high-contrast regimes.

Contribution

It introduces a novel analysis of acoustic resonances via the propagation matrix, connecting resonance distribution, asymptotics, and capacitance matrix approximation in a unified framework.

Findings

Resonant frequencies are zeros of an explicit trigonometric polynomial.

Resonance imaginary parts are uniformly bounded, unlike in 3D.

Asymptotics for subwavelength and non-subwavelength resonances are derived in high-contrast regimes.

Abstract

This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric polynomial. Leveraging Nevanlinna's value distribution theory, we establish the distribution properties of the resonances and demonstrate that their imaginary parts are uniformly bounded, which contrasts with the three-dimensional case. In two classes of high-contrast regimes, we derive the asymptotics of both subwavelength and non-subwavelength resonances with respect to the contrast parameter. Furthermore, by applying the Newton polygon method, we recover the discrete capacitance matrix approximation for subwavelength Minnaert resonances in both Hermitian and non-Hermitian cases, thereby establishing its connection to the propagation matrix framework.