Time-resolved thermal lens spectroscopy with a single-pulsed laser excitation beam: an analytical model for dual-beam mode-mismatched experiments.

Pulsed laser beam excitations are more commonly used in thermal lens spectroscopy (TLS) than continuous-wave (CW) ones, because CW excitations limit the measurement to linear absorption processes [J. Opt. A5, 256 (2003)]. In this work, we present a new and full analytical model for a single-pulsed laser excitation dual-beam mode-mismatched TLS for low absorption solid-state and liquid samples. Our model has been based on a new solution of time-dependent heat equation for a finite-radius cylindrical sample exposed to a single-pulsed excitation laser beam. For low absorbent samples, unlike previous models, all aberration terms associated in the thermal lens were taken into account in Fresnel integration. Besides, the model provides a full analytical mathematical expression for the temperature rise, normalized signal intensity, and Z-scan photothermal lens signal. The model was confirmed with experimental data of distilled deionized water with excellent agreement. Therefore, the model allows us to extract thermo-optical properties of samples in an analytical and more accurate way.