Theoretical analysis of pulsed photoacoustic effect in solids

This article presents a one-dimensional theory of a photoacoustic cell, working in the pulse regime. A four-layer system with elements of finite thickness has been assumed to represent consecutive parts of the photoacoustic cell. A parabolic heat equation with an instantaneous, bulk heat source has been solved using the Fourier transform of spatial coordinates. The theory allows one to assume that a heat source is existing in every part of the system and that an arbitrary time profile of the initial pulse is applied. Consequently, the system can be treated as an arbitrary photothermic or photoacoustic one-dimensional system. As a result, one obtains temperature profiles in the entire system at any time instant after its excitation with a light pulse. The gas-pressure evolution is dependent on the thermal and optical properties of the sample, the cell geometry, and duration and shape of the initial pulse.