Classical and Quantum Mechanical Aspects of Thermal Wave Physics

The ability of thermal waves to perform non-destructive depth-profiling studies in materials with spatially variable thermal/thermodynamic properties has been exploited mostly qualitatively so far. The lack of appropriate general theoretical models in the literature has been largely responsible for the near absence of quantitative depth-profiling, especially in media with large thermal property variations within depths on the order of the thermal wavelength. As a result of mathematical difficulties, theoretical treatments have been essentially confined to discrete, multilayered solid structures with constant thermal and thermodynamic properties within each thin layer [1,2]. Furthermore, Afromowitz et al. [3] have applied discrete Laplace transformations to the heat conduction equation to treat the production of the photoacoustic signal in a solid with continuously variable optical absorption coefficient as a function of depth, however, the thermal parameters of the solid were assumed constant. Thomas et al. [4] calculated the Green’s function for the three-dimensional heat conduction equation describing thermal wave propagation in a thermally uniform solid with a subsurface discontinuity (“flaw”). More recently, Jaarinen and co-workers [5,6] used Finite Difference and Inverse methods for thermal wave depth-profiling of samples with spatially variant thermal properties from measurements of the surface temperature distribution. Aamodt and Murphy [7] very recently used vector/matrix methods to calculate thermal wave responses from discretely layered samples. These authors further considered the case of continuously varying thermal properties as the limit of infinitely thin layers