It has been shown that a top-hat excitation beam gives rise to a more sensitive signal for the thermal lens spectroscopy (TLS). Recently, a numerical model has been presented for a top-hat excitation beam in a dual-beam mod-mismatched TLS [Opt. Lett. 33(13), 1464Lett. 33(13), -1466Lett. 33(13), (2008]. In this work, we present a full analytical version of this model. Our model was based on a new solution of time-dependent heat equation for a finite radius cylindrical sample exposed to a top-hat excitation laser beam. The Fresnel diffraction integration method was then used to calculate on-axis probe-beam intensity variations due to thermal lensing by taking the aberrant nature of the thermal lens into account. The model was confirmed with experimental data of LSCAS-2 with an excellent agreement.
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.
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