Coupled-Mode Theory for Stationary and Nonstationary Resonant Sound Propagation

TL;DR

This paper develops a comprehensive analytical framework for resonant sound wave propagation using Coupled-Mode Theory, deriving parameters from a Hamiltonian formalism, and validating it against numerical simulations for complex resonant systems.

Contribution

It introduces a Hamiltonian-based derivation of Coupled-Mode Theory parameters for both stationary and nonstationary acoustic systems, including moving media, and demonstrates its effectiveness through numerical validation.

Findings

Hamiltonian formalism effectively models resonant sound scattering.

Derived coupling parameters enable analysis of complex resonant systems.

Numerical results confirm the accuracy of the Hamiltonian-based Coupled-Mode Theory.

Abstract

We present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological Coupled-Mode Theory. We calculate the propagating and coupling parameters used in Coupled-Mode Theory directly by utilizing the generalized eigenwave-eigenvalue problem from the Hamiltonian of the sound wave equations. This Hamiltonian formalization can be very useful since it has the ability to describe mathematically a broad range of acoustic wave phenomena. We demonstrate how to use this theory as a basis for perturbative analysis of more complex resonant scattering scenarios. In particular, we also form the effective Hamiltonian and coupled-mode parameters for the study of sound resonators with background moving media. Finally, we provide a comparison between Coupled-Mode theory and full-wave numerical examples, which validate the Hamiltonian approach as a relevant model to compute the scattering characteristics of waves by complex resonant systems.