Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples

TLDR

Conventional thermal‑lens spectrometry assumes an infinite medium and considers only radial temperature rise, which is inadequate for thin‑film samples. The study aims to develop a three‑dimensional model for cw laser‑induced mode‑mismatched thermal‑lens spectrometry that accounts for axial boundary conditions. The model incorporates axial boundary conditions into a three‑dimensional thermal‑lens framework for continuous‑wave laser excitation. Although its mathematical expression is less convenient than conventional theory, the model demonstrates that a small excitation‑spot‑to‑thickness ratio (ωe/l) minimizes axial heat flow, enabling the conventional theory to describe the thermal lens of a thin sample over short times, and experimental data confirm this prediction with good agreement.

Abstract

Conventional thermal lens spectrometry theory assumes that the sample is an infinite medium, and only the radial temperature rise and heat flow in the sample are considered. This approach is not suitable for thin-film samples. Considering the axial boundary conditions of the sample, a three-dimensional model for cw laser-induced mode-mismatched thermal lens spectrometry is presented. However, its mathematical expression is not so convenient as that of the conventional theory to deal with the experimental data. The model shows that, besides axial boundary conditions of the sample, the ratio of excitation laser spot size to the sample thickness ωe/l is a crucial parameter to minimize the axial heat flow. By choosing small ωe/l, it is possible for the conventional theory to describe the development of the thermal lens of a thin sample for a short duration. Experimental proofs for the theoretical prediction are made, and good agreements are achieved.