We present a method for reconstructing the phonon relaxation timedistribution $\tau_{\omega}= \tau (\omega)$ (including polarization) in amaterial from thermal spectroscopy data. The distinguishing feature of thisapproach is that it does not make use of the effective thermal conductivityconcept and associated approximations. The reconstruction is posed as anoptimization problem in which the relaxation times $\tau_{\omega}= \tau(\omega)$ are determined by minimizing the discrepancy between the experimentalrelaxation traces and solutions of the Boltzmann transport equation (BTE) forthe same problem. The latter may be analytical, in which case the procedure isvery efficient, or numerical. The proposed method is illustrated using MonteCarlo solutions of thermal grating relaxation as synthetic experimental data.The reconstruction is shown to agree very well with the relaxation times usedto generate the synthetic Monte Carlo data and remains robust in the presenceof uncertainty (noise).
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