The laser thermal lens spectroscopy is a technique which is based on estimation of the temperature rise that's created in an enlightened sample as a result of nonradiative relaxation of the energy absorbed from a laser as an optical source. Since the procedure is based on optical energy, its sensitivity is higher than customary absorption methods [21]. The first measurements of thermal lensing were made by Gordon et al. in 1965 [22]. He used single beam in this experiment. The first dual-beam thermal lens experiment was performed by Grabiner et al. in 1972. His work was an effort to measure the properties of gases [23]. Snook et al. have used thermal lens technique to chemical measurements in liquid, solid and gaseous phases [24]. Marcano et al. presented a sensitive experiment to determine absorbance as low as 10− 9 in liquid and solid samples by overlapping two beams [25].
The thermal lens spectroscopy method has many advantages in contrast to other techniques due to measuring absolute values of quantum yield [26]. Some of these advantages are the high sensitivity and a nondestructive procedure that used to analysis of biological objects, remote analysis, and on-line determination in the flow and has notable properties [27]. However, there are more advantages of the thermal lens technique namely small volume sample capability and dependency on opto-thermal properties of solvents [21].
The origin of the laser thermal lens spectroscopy is the photothermal phenomenon. In this spectroscopic method a laser beam as an optical source, excites a sample. The radiation has a symmetrical intensity distribution (TEM00 Gaussian mode), this absorbed energy by the sample convert into the form of heat at the center of the laser beam. Thus, the sample treats as an optical lens because there is a temperature gradient between the center of the beam and the bulk material [21] after that, the heat makes molecules excited into vibrational, rotational, or electronic states. The sample particles will have a nonradiative relaxation processes to lose their energy. This process makes a change of the refractive index which can be detected by convergence or divergence of the beam after it gets out of the sample [27]. Because of its high sensitivity and precision, these methods can be used to measure low absorbance with absorption coefficient of less than 10− 7 cm− 1 [28, 29, 30].
In this optical technique, the thermal lens signal is given by Eq. (1) [18, 31].
$$\frac{I\left(t\right)}{I\left(0\right)}={\left(1-\frac{\theta }{2}{tan}^{-1}\left[\frac{2mv}{\frac{{t}_{c}\left[{(1+2m)}^{2}+{v}^{2}\right]}{2t}+1+2m+{v}^{2}}\right]\right)}^{2}$$
1
In this equation I(t) and I(0) are the probe beam intensity at the photo-detector at time t and t = 0, respectively. The time of arrival of the pump laser beam is the t = 0. Also, \(v=\frac{{z}_{1}}{{z}_{c}}\) and \(m={\left(\frac{{\omega }_{p}}{{\omega }_{e}}\right)}^{2}\)are the constant parameters. \({z}_{1}\) is the distance from the sample to the probe beam waist, \({z}_{c}=\frac{{{\omega }_{p}}^{2}}{{\lambda }_{p}}\) is the confocal distance, \({\omega }_{p}\) and \({\omega }_{e}\) are the probe and pump beam waist, respectively. θ is related to the TOC, thermal conductivity (k), probe beam wavelength (λp), thermal lensing thickness (L), laser power (P), and optical absorption coefficient (α) as the Eq. (2) [31].
$$\theta =-\frac{PL\alpha }{k{\lambda }_{p}}\left(\frac{dn}{dT}\right)$$
2
The thermal diffusivity (Dth) is given by Eq. (3) [18].
Where tc is the characteristic time and ω is the beam waist of pump laser. In thermal lens spectroscopy, tc is a constant that relates to beam waist of pump laser and thermal diffusivity. By Eq. (4) the thermal conductivity is related to the heat capacity (Cp) and the density (ρ).
$$k=\rho {D}_{th}{C}_{p}$$
4
Also, (\(\frac{dn}{dQ}\)) is the refractive index dependence with the sample deposited heat per unit volume which given by Eq. (5) [31].
$$\theta =-\frac{PL\alpha }{{D}_{th}{\lambda }_{p}}\left(\frac{dn}{dQ}\right)$$
5
$$\frac{dn}{dQ}=\frac{1}{\rho {C}_{p}}\frac{dn}{dT}$$
6
For more details on the Thermal lens technique, see Ref [18, 22, 24, 31].