Acoustic resonators play a critical role in determining the performance of photoacoustic gas sensors. Understanding how geometric parameters influence acoustic modes and noise suppression is essential for developing highly sensitive measurement systems.

This user story describes how researchers used COMSOL Multiphysics® to create a validated virtual prototype of a differential photoacoustic cell and perform simulation-driven design optimization. The study focused on the acoustic buffer geometry, the coupling volume connecting the two resonator branches of the differential photoacoustic cell.

By evaluating the effect of buffer geometry on both useful signal generation and background noise mechanisms, the research team identified a significantly improved resonator configuration.

 

Figure 1. Principle of photoacoustic signal generation.

Challenge

Photoacoustic spectroscopy (PAS) is a highly sensitive gas sensing technique that exploits the conversion of absorbed modulated light into acoustic waves. The generated acoustic signal is directly related to the concentration of the target gas.

The performance of a photoacoustic sensor strongly depends on the acoustic behavior of its resonator. In differential photoacoustic cells (PACs), unwanted background signals can be generated when the laser light interacts with the cell windows instead of the target gas. These non-gas-related signals can interfere with or even mask the desired photoacoustic signal, reducing measurement sensitivity. Minimizing these noise contributions is therefore essential for improving the SBR and achieving lower detection limits.

The challenge was to improve the signal–to–background ratio of an existing differential longitudinal PAC without relying on costly and time-consuming trial-and-error prototyping. The research team needed a reliable method to understand how geometric modifications influence acoustic modes and the background signal.

Figure 2. A differential photoacoustic cell. The red line tracks the laser beam as it heats the gas in the resonator, while the yellow line marks the laser-window interaction, where background noise is generated.

Solution

Researchers at the University of Szeged developed a three–dimensional finite element model of the PAC using COMSOL Multiphysics® and its Acoustics Module. The model incorporated the resonator tubes, buffer volumes, microphone interfaces, and thermoviscous acoustics losses to accurately represent the physical system.

The acoustic field was modeled using Pressure Acoustics, Frequency Domain interface, with humid air as the propagation medium. Photoacoustic signal generation was represented through a distributed heat source (Figure 2.), while viscous and thermal losses at cell walls were accounted for using a thermoviscous boundary layer impedance condition. The microphones were represented by acoustic impedance boundary conditions derived from their measured characteristics. A frequency-domain study was conducted to identify resonant characteristics and evaluate the effects of geometric modifications.

To reproduce the differential sensor’s operation, the microphone signals from the two resonator branches were combined using a nonlocal coupling formulation, thereby enabling direct evaluation of the differential response.

To ensure predictive accuracy, the simulation model was validated against experimental measurements performed on the real photoacoustic sensor. The simulated differential resonance curve showed excellent agreement with experimental measurements across the investigated frequency range from 2 kHz to 20 kHz, confirming the model’s predictive capability.

After validation, the model was used to investigate the influence of buffer geometry on sensor performance regarding SBR. Parametric studies were carried out by varying buffer lengths and diameters, while separately evaluating the useful photoacoustic signal and the background signal originating from laser–window interactions.

Figure 3. Measured and simulated (FEM) differential signal, showing good agreement in the examined frequency range.

Results

The simulation study showed that modifications to the buffer geometry had only a minor effect on the useful photoacoustic signal but could significantly reduce the background signal generated by the laser–window interactions.

Following model validation, a series of parametric studies was conducted to investigate the influence of buffer dimensions on both the useful photoacoustic signal and the background signal. These studies revealed that increasing the buffer length primarily suppresses the background signal by enhancing differential cancellation of acoustic modes generated by laser–window interactions, while leaving the useful photoacoustic signal largely unchanged.

Building on these findings, the researchers employed the COMSOL® Optimization Module to systematically search the parameterized design space for geometries that maximize the signal-to-background ratio. The optimization study identified an improved resonator configuration that combines effective background-noise suppression with strong photoacoustic signal generation.

The optimized design increased the SBR from 1.56 to 57.7, corresponding to an approximately 37-fold improvement in sensor performance. In addition to identifying the optimal geometry, the study also provided a deeper understanding of the acoustic mode structure responsible for signal generation and noise suppression within the resonator system.

Figure 4. The signal-to-background ratio as a function of buffer length, normalized by the resonator length. The figure also contains data series for different buffer lengths, and the lines facilitate tracking of these series.

Summary

Using a validated COMSOL Multiphysics® model of a differential photoacoustic cell, researchers at the University of Szeged identified an optimized buffer geometry that reduced background noise from laser–window interactions and increased the signal-to-background ratio by approximately 37-fold.

Challenge
Designing high-performance PACs often requires multiple design iterations and extensive experimental testing. The challenge was to improve the SBR of a differential PAC by reducing background signals originating from laser–window interactions.
Solution
COMSOL Multiphysics® provided a virtual environment for developing a validated three-dimensional finite element model of the PAC and evaluating the impact of different buffer geometries on acoustic performance.
Results
By simulating both useful signal generation and background noise mechanisms, we identified an optimized buffer geometry that increased the SBR from 1.56 to 57.7, corresponding to an approximately 37-fold improvement in performance.

Related publications

Á. Csókási et al., Validated Numerical Model and Simulation-Based Design Optimization of a Photoacoustic Cell, COMSOL Conference 2025 Amsterdam Proceedings. 

Conference poster presented at the COMSOL Conference 2025 in Amsterdam.

 

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