A Fourier transform–based semi-analytical study of photoacoustic ultrasound in multilayered thermal and acoustic structures

This study presents a Fourier transform-based semi-analytical approach for analyzing the generation and propagation of photoacoustic ultrasound in multilayered thermal-acoustic structures. Laser-induced heat generation, described by the Beer-Lambert law, is incorporated into the heat conduction and acoustic wave equations, which are solved semi-analytically in the frequency domain. The general solutions are obtained analytically, while the arbitrary constants are determined numerically using interface and boundary conditions. Inverse Fourier transforms are then applied to reconstruct the time-domain responses. The approach is validated through comparisons with finite-difference time-domain simulations and experimental data. To demonstrate its applicability, it is applied to a water-substrate-polymer-water structural configuration, where the polymer layer serves as the light-absorbing medium, enabling detailed investigation of photoacoustic phenomena in both the time and frequency domains. The results show that laser heating raises the polymer temperature, generating bi-directional pressure waves and inducing acoustic resonances in both the polymer and the substrate. The proposed method accurately captures these coupled thermal and acoustic dynamics, providing new insights into ultrasound propagation in multilayered structures.