Optically induced temperature variations in a two-layer volume absorber including thermal memory effects

Abstract

In this paper, a theoretical model of temperature variations is derived for a two-layer optically absorbing structure, including thermal memory effects. It is considered that the two-layer structure is surrounded by gas and illuminated on the front side by a harmonically modulated laser beam. This model is based on the hyperbolic theory of heat conduction and Beer–Lambert's law of absorption neglecting multiple optical reflections in each layer. The derived model represents the generalization of the current models in two aspects. First, the influence of thermal memory properties of both layers is accounted for, and second, both layers are regarded as volume absorbers of the incident light. Based on the derived model, the expressions for surface temperature variations are given and discussed for the special type of two-layer structures, irradiated on the coated side, which is a prominent configuration in photoacoustic and photothermal experiments. It is shown that there exists a frequency range in which the influence of the thermal properties of the coating cannot be neglected, especially at the high-frequency range in which thermal memory of coating becomes significant. It is an important result in terms of understanding experimentally measured photothermal and photoacoustic response and, consequently, accurate characterizations of various high optically reflected and/or optically transparent samples by using these experimental techniques.

Thermal Fractional Diffusion: Experimental Evidence from the Discrepancies in the Amplitude and Phase in Photothermal Technique

“…Besides, other parameters are improved with the addition of the fractional factor. The relaxation time obtained is similar for all samples, however, having an order of magnitude much higher than that expected for metals, which should be in the order of τ = 10 −10 s [53,33]. The GCEII model presents a superdiffusive behavior while the GCEIII has a subdiffusive outcome [46,39].…”

“…[17,18,28] In some cases, the classical model of heat propagation does not fit the results obtained for non-homogeneous samples because the values obtained for the thermal diffusivity do not match the expected value. This leads to the application of mathematical models that better explain the propagation of heat in non-homogeneous materials [4,15,19,22,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. The thermal memory theory, which employs the hyperbolic equations of heat propagation (HHE), or Cattaneo equations [44], that account for thermal relaxation time, was used to develop an extended model for the TD and TE phenomena [41,42].…”

Photoacoustic Characterization of TiO2 Thin-Films Deposited on Silicon Substrate Using Neural Networks

“…In order to avoid additional normalizations and the calculation of effective values, we resorted to the use of the two-layer model for determining thin-film parameters where the properties of the silicon substrate are known [ 21 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 ]. Neural networks were formed for the analysis of photoacoustic signals generated from the Si substrate and the TiO 2 thin-film system.…”

Influence of non-irradiated surface optical absorber on temperature gradient induced by photothermal effect in a thin film

“…Photothermal (PT), and consequently photoacoustic (PA) techniques, are based on direct or indirect measurement of phenomena resulting from heat transfer processes in the examined material, whereas the most straightforward approach considers the examination of surface temperature variations of the sample (Popovic et al, 2018(Popovic et al, , 2021. Since these experimental techniques are considered model-dependent, their development largely involves the development and the analysis of theoretical-mathematical models which link physical processes in the examined material and the measured signal (Dramićanin et al, 2000;Galovic et al, , 2014Galović and Dramićanin, 1999;Markushev et al, 2019;Nesic et al, 2016;Nesic, Galovic, et al, 2012;Nesic, Gusavac, et al, 2012;Popovic et al, 2021) (Aleksić et al, 2022;Djordjevic et al, 2022;Markushev et al, 2018Markushev et al, , 2020Popovic et al, 2009;Somer et al, 2013;Soskic et al, 2012Soskic et al, , 2016Todorović, 2003;Todorović and Nikolic, 2000).…”