Effect of thermal nonlinearity in high-absorption media on the parameters of the photoacoustic signal detected by the gas microphone method: The fundamental and second harmonics

Abstract

A perturbation theory is put forward that describes the effect of thermal nonlinearity due to the temperature dependence of the thermophysical parameters of high-absorption systems with a low thermal conductivity on the parameters of the photoacoustic signal detected by the gas microphone technique. It is found that the dependence of the photoacoustic signal amplitude on incident beam intensity I ₀ stems from the dependence of the illuminated surface temperature on I ₀. This dependence is a complicated function instead of being a simple quadratic function as was expected. In the limiting cases (μ_sβ ≪ 1 and μ_sβ ≫ 1), this contribution to the photoacoustic signal amplitude is described by simple expressions, which are convenient for determining the thermal coefficients of the thermophysical parameters of the medium. It is found that the thermal nonlinearity significantly affects the photoacoustic signal phase in the frequency region meeting the condition μ_sβ ∼ 1. In the above limiting cases, its effect is insignificant. A theory of generation of the photoacoustic signal second harmonic is proposed. The second harmonic is related to the temperature dependence of the thermophysical parameters of the buffer gas and sample. It is shown that the amplitude of the signal is a quadratic function of the incident beam intensity and varies with its frequency as ω^−3/2 for μ_sβ ≫ 1 and ω^−5/2 for μ_sβ ≪ 1.