Coupled mode theory for acoustic resonators

TL;DR

This paper introduces a coupled mode theory framework for acoustic resonators using an effective non-Hermitian Hamiltonian approach, enabling efficient calculation of scattering properties in open resonator-waveguide systems.

Contribution

It develops a novel non-Hermitian Hamiltonian method for acoustic resonators with Neumann boundary conditions, extending coupled mode theory to higher dimensions.

Findings

Effective method for calculating scattering matrices.

Numerical validation in 2D and 3D acoustic systems.

Reduction of transmission problem to linear equations.

Abstract

We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems. In higher than one dimensions the method represents acoustic coupled mode theory in which the scattering solution within an open resonator is found in the form of expansion over the eigenmodes of the closed resonator decoupled from the waveguides. The problem of finding the transmission spectra is reduced to solving a set of linear equations with a non-Hermitian matrix whose anti-Hermitian term accounts for coupling between the resonator eigenmodes and the scattering channels of the waveguides. Numerical applications to acoustic two-, and three-dimensional resonator-waveguide problems are considered.