Quasinormal mode representation of radiating resonators in open phononic systems

TL;DR

This paper introduces a quasinormal mode framework for modeling radiating resonators in open phononic systems, enabling accurate response predictions using a few modes and extending concepts like the Purcell effect to elastodynamics.

Contribution

It develops a complex eigenfunction expansion based on elastic QNMs for open phononic systems, providing a new approach to analyze and approximate their responses.

Findings

QNM-based response approximation matches full elastodynamic solutions

Validated on vibrating nylon rod in water and nanoscale tuning fork

Introduces a complex modal volume concept for elastic QNMs

Abstract

Open phononic systems including resonators radiating inside an unbounded medium support localized phonons characterized by a complex frequency. In this context, the concept of elastic quasinormal mode (QNM) arises naturally, as in the cases of nanophotonic and plasmonic open systems. Based on a complex, unconjugated form of reciprocity theorem for elastodynamics, the eigenfunction expansion theorem expressed on the elastic QNM basis yields an accurate approximation to the response function, for an arbitrary excitation. The description of the elastic Purcell effect then requires defining a complex-valued modal volume for each QNM. For validation, we first consider the case a vibrating nylon rod radiating in water. As a second test example, we consider a slender nickel ridge on the surface of a fused silica substrate, before extending our attention to a nanoscale tuning fork composed of two such ridges. In all cases, the response estimated from only a few elastic QNMs agrees with the solution to the elastodynamic equation.