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Abstract
An application is presented of the Hamilton‐Jacobi formulation of thermal‐wave physics [A. Mandelis, J. Math. Phys. 26, 2676 (1985)] to the problem of photoacoustic depth profiling in inhomogeneous solids with arbitrary, continuously varying thermal diffusivity profiles. Simple expressions for the modulation frequency dependence of the photoacoustic signal in the case of exponential thermal diffusivity profiles are obtained, and a working general method for solving the inverse problem and obtaining arbitrary diffusivity depth profiles is demonstrated through computer simulations. The method was found to possess excellent profile reconstruction fidelity. As a first experimental application of the theory, an observed change in the photoacoustic signal frequency response upon the application of a transverse magnetic field across octylcyanobiphenyl (8CB) samples in the nematic phase at 37°C is reported. The theory has given quantitative profiles of thermal diffusivity decreases extending to 20–30 μm below the...
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