Thermal lensing approach based on parabolic approximation and Mach-Zehnder interferometer

Abstract

A thermal lensing approach based on parabolic approximation and Mach-Zehnder interferometer for measuring optical absorption and thermal diffusivity coefficients in pure solvents is described in this work. The approach combines the sensitivity of both thermal lensing methods and interferometry techniques. The photothermal effect is induced by a pump laser beam generating localized changes in the refractive index of the sample, which are observed as a shift in phase of the interference pattern. Each interference pattern is recorded by means of a digital camera and stored as digital images as a function of time. The images are then numerically processed to calculate the phase shifting map for a specific time. From each phase shifting map, the experimental phase difference as a function of time is calculated giving a phase-time transient, which is fitted to a mathematical model to estimate the optical absorption and thermal diffusivity of the sample. The experimental results show that the sensitivity is approximately λ/4800 for the minimum phase difference measured.

Keywords: Fourier transform; Interferometry; Photothermal effect; Thermal diffusivity; Thermal lensing.

Fig. 1

Simulations performed with Eq. (6) in order to show the behavior of the phase difference as a function of space and time variables.

Fig. 2

Schematic diagram of the experiment used to validate Eq. (6). The setup is a pump-probe experimental configuration based on the Mach-Zehnder interferometer, where one of their arms is used as a probe beam, while the other is a reference beam. The pump beam is a 405 nm laser diode.

Fig. 3

Digital images showing an experimental interferogram (a) captured with the digital camera and its corresponding numerical photothermal phase shifting map (b). The white circle approximately represents the area delimited by the spot of the pump laser, showing that the photothermal phase shifting extends beyond the area delimited by the laser spot. The experimental space scale is given by white line, ∼1 mm.

Fig. 4

Experimental phase difference surface obtained for ethanol after the numerical processing is performed on the digital interferograms.

Fig. 5

Phase difference as a function of the exposition time for the solvents used in the experiment. Open symbols represent experimental data while continuous lines are the best fittings obtained by means of Eq. (6). The coefficient of determination for the whole set of curves is approximately R² = 0.99883. Dots indicate the root mean square value of noise (fluctuations) phase differences as a function of time.