Theory of the photoacoustic effect with solids

Abstract

Chopped light impinging on a solid sample in an enclosed cell produces an acoustic signal within the cell, A theoretical explanation for this effect is presented, providing a quantitative foundation for photoacoustic spectroscopy. Nonradiative de-excitation of the absorbed light within the solid sample produces a periodically varying heat flow from the sample to the surrounding gas and backing material. The solution to the thermal diffusion equations shows that only a thin boundary layer of gas adjacent to the surface of the sample responds thermally to this periodic heat flow. The boundary layer can then be thought of as acting as an acoustic piston creating the acoustic signal detected in the cell. An explicit formula gives the. magnitude and phase of the acoustic pressure in terms of the optical, thermal, and geometric parameters of the system. Simple approximations for the pressure are given according to the relative magnitudes of the optical absorption length, thermal diffusion length, and thickness of the sample. The results imply, in particular, that absorption data may be obtained by photoacoustic spectroscopy, even from samples that are completely opaque to conventional techniques.