Photoacoustic ultrasound in metal–polymer layers: A semi-analytical approach to integrated optical, thermal, and acoustic dynamics

Abstract

This study presents a semi-analytical modeling framework for photoacoustic ultrasound generation in multilayered metal–polymer structures, integrating optical, thermal, and acoustic dynamics. The model solves the Maxwell–Helmholtz equation in the frequency domain to determine heat generation distributions, capturing complex optical phenomena, such as multiple reflections, interference, and Fabry–Pérot resonance, surpassing the limitations of the conventional Beer–Lambert law. This optical response is coupled with Fourier transform-based solutions to the heat conduction and elastic–acoustic wave equations, yielding closed-form expressions for the spatiotemporal evolution of temperature and pressure. The unified semi-analytical formulation rigorously incorporates multilayer heterogeneity, interfacial continuity, and realistic boundary conditions. Model predictions are validated against finite-difference (finite-difference frequency-domain and finite-difference time-domain) simulations and experimental measurements, demonstrating excellent agreement and confirming its high accuracy and physical fidelity. The results further reveal how parameters, such as layer thickness, acoustic impedance mismatch, and optical resonance, affect heat localization and acoustic wave generation. This framework offers predictive insight and design guidance for optimizing multilayered photoacoustic structures that generate ultrasound through light absorption in biomedical imaging, non-destructive testing, and optoacoustic devices.