An analytical model for finite radius dual-beam mode-mismatched thermal lens spectroscopy

Abstract

In this work, a new model for dual-beam mode-mismatch thermal lens spectroscopy is presented. The model was based on a new analytical solution of time-dependent heat equation for finite radius cylindrical samples exposed to TEM00 excitation laser beams. The Fresnel diffraction integration method was used to calculate time-dependent on-axis probe beam intensity. All aberrations in thermal lens were taken into account. The model yields accurate values for absorption coefficient and thermal diffusivity of methylene blue aqueous solution. Furthermore, the optimized mode-mismatched version of this model when applied to pure water as a very low absorbent yields its absorption coefficient and thermal diffusivity values close to literature data. In contrast to traditional model, this model does not need to omit any term in its theory to fit the experimental data.

An analytical model for top-hat long transient mode-mismatched thermal lens spectroscopy

“…A detailed discussion of above solution have been come in Ref. [34]. As Gordon et al have reported, this solution has the weakness of divergence at large enough time instead of closing to steady-state solution.…”

“…(18), does not exist [34]. However, for a low absorbent case, which is the case in our work, we can used the approximation of exp(−iϕ) ≈ 1 − iϕ [11,14] where ϕ contains aberration terms.…”

“…The steady-state solution can be found in Refs. [9,34]. The parameters used for plotting the curves are as follow: ω e = 275 µm, P e = 66 mW, A e = 1.70 cm −1 , η = 0.84, λ e = 532 nm, < λ em >= 1064 nm, D = K/ρc = 5.7 × 10 −3 cm 2 s −1 ,a = 5 mm, l = 1.5 mm which are taken from Refs.…”

“…In this setup, a sample is exposed to two laser beams having beam waists of ω 1p (for probe beam) and ω e (for excitation beam).The details of this setup has been explained in Ref. [34]. If the sample is located at z, using the Fresnel diffraction theory, the propagation of a TEM 00 Gaussian probe beam through the sample to the detector plane can be obtained as [14]: (18) where…”

“…However, this model led to a numerical model. Sabaeian and Nadgaran [34] more recently have presented a full analytical TLS model based on a thermal model for finite radius cylindrical samples exposed to a Gaussian excitation beam. They showed that at large enough time, the thermal model gets close to steady-state model, and therefore they concluded that this discrepancy on time has been removed.…”