# Modeling the Geometry–Acoustics Dependence in Photoacoustic Resonators: A Toroidal Case Study

## TL;DR

This paper studies how the shape of a toroidal photoacoustic resonator affects its acoustic performance, offering accurate and interpretable design rules.

## Contribution

The paper introduces corrected analytical models for resonance frequency and quality factor in toroidal resonators, validated experimentally with high accuracy.

## Key findings

- A corrected toroidal-resonance frequency model accounts for effective propagation length and thermo-viscous effects.
- A boundary-layer dissipation model explains the quality factor's dependence on the torus’s minor radius.
- Experimental validation shows average relative error below 1%, outperforming existing models.

## Abstract

In this work we investigate the behavior of a toroidal photoacoustic resonator to provide compact, physics-guided analytical relationships that link its geometry to two key parameters: resonance frequency and quality factor. Finite-element data are combined with reduced-order analytical models to refine a corrected toroidal-resonance frequency model that accounts for effective propagation length and thermo-viscous effects. For the quality factor, a simple law motivated by a boundary-layer dissipation model is proposed. Derived models are validated by experimental tests performed using three 3D printed toroidal resonators in different sizes. Experimental results confirm the prediction both for the first and third resonance frequencies with an average relative error below 1%, outperforming cylindrical and uncorrected baseline models available in the literature. The results also confirm the predicted trend of the quality factor with respect to the torus’s minor radius, highlighting a direct relationship between the cross-sectional area and acoustic losses, which governs the balance between stored acoustic energy and thermo-viscous dissipation. Overall, the framework provides quick, interpretable design rules that reduce dependence on extensive finite-element method simulation campaigns for first-pass estimation of resonant behavior during the early design phase and guiding the optimization of high-performance PAS devices while preserving accuracy.