The Contribution of the Relaxation of the Heat Flow to the Characteristics of the Fundamental Harmonics of a Nonlinear Photoacoustic Signal in Condensed Media

Abstract

Based on the system of nonlinear heat conduction equations, which takes into account the relaxation of the heat flux for the gas layer, the sample, and the substrate, a system of equations is obtained for temperature fluctuations at the fundamental harmonic (FH) of a nonlinear photoacoustic (PA) signal. It is believed that all three layers in the PA-chamber have their own relaxation times, and the irradiated photon flux is modulated according to the harmonic law. The temperature dependence of thermophysical and optical parameters is represented by thermal coefficients. By solving the boundary problem, general expressions were obtained for the oscillatory component of the temperature perturbation in the exhaust gas, and then, according to a well-known scheme, for pressure fluctuations in the gas layer. The obtained expressions are analyzed. The frequency dependence of the amplitude and phase of this signal is numerically calculated for two possible substrates: the substrate is a thermal insulator and the substrate is an ideal conductor. It has been established that the frequency dependence of the PA-signal amplitude for these cases is antiphase. While, this dependence for the phase of the PA-signal is consistent in phases moreover, the values of the maximum and minimum coincide. The only significant difference is that in the region of zero modulation frequencies, the phase of the signal for a substrate made of a thermal insulator is positive, while for a substrate made of an ideal conductor is negative.