We report a theoretical model and experimental results for laser-induced local heating in liquids, and propose a method to detect and quantify the contributions of photochemical and Soret effects in several different situations. The time-dependent thermal and mass diffusion equations in the presence and absence of laser excitation are solved. The two effects can produce similar transients for the laser-on refractive index gradient, but very different laser-off behavior. The Soret effect, also called thermal diffusion, and photochemical reaction contributions in photochemically reacting aqueous Cr(VI)-diphenylcarbazide, Eosin Y, and Eosin Y-doped micellar solutions, are decoupled in this work. The extensive use of lasers in various optical techniques suggests that the results may have significance extending from physical-chemical to biological applications.

A general and complete theoretical model of the time-resolved thermal mirror method for the measurement of thermo-optical-mechanical properties of solid materials is developed. The laser-induced temperature profile in a sample and its thermoelastic surface displacement are derived. The center intensity of a probe beam at the detector plane is calculated using the Fresnel diffraction theory. Additionally, simplified models for high and low optical absorption samples are presented, and the suitability of the simplified models is also analyzed. The influence of experimental parameters on the sensitivity of the thermal mirror method is discussed for the optimization of the experimental apparatus. The presented model and the experimental technique can be used to quantitatively determine the physical properties of transparent and opaque solids.

This work presents a theoretical study of a heat transfer effect, taking into account the heat transfer within the heated sample and out to the surrounding medium. The analytical solution is used to model the thermal lens and thermal mirror effects and the results are compared with the finite element analysis (FEA) software solution. The FEA modeling results were found to be in excellent agreement with the analytical solutions. Our results also show that the heat transfer between the sample surface and the air coupling fluid does not introduce an important effect over the induced phase shift in the sample when compared to the solution obtained without considering axial heat flux. On the other hand, the thermal lens created in the air coupling fluid has a significant effect on the predicted time-dependent photothermal signals. When water is used as fluid, the heat coupling leads to a more significant effect in both sample and fluid phase shift. Our results could be used to obtain physical properties of low optical absorption fluids by using a reference solid sample in both thermal lens and thermal mirror experiments.

An N-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized Gaussian function related to the Tsallis statistics. Furthermore, we show that a rich class of diffusive processes, including normal and anomalous ones, can be obtained by changing the time dependence of the coefficients.

Laser-induced thermal lens in optical components causes wavefront distortion of the laser beam and may affect performance and stability of optical systems such as high-power lasers. The bulging of the heated area, the temperature dependence of the refractive index, and the photoelastic effects are responsible for phase shifts damaging beam quality. The theoretical background for laser-induced beam distortion is well understood and applies only for axially symmetric thermal loadings, with the assumptions that the stresses follow thin-disk or long-rod approximations. This, in fact, limits the overall applications of this model. In this work, we developed an unified theoretical model for the optical path change in optical materials regardless of its thickness. The modeling is based on the solution of the thermoelastic equation and has a real description of the surface deformation caused in the optical element. In the appropriated limits, as expected, the model retrieves the thin-disk and the long-rod type distributions. Furthermore, we provided time-dependent radial expressions for the temperature, surface displacement, and stresses. The theory presented in this paper provides simple analytical tools for designing laser systems, and complements previous work allowing one to access optical distortions of materials ranging from thin-disk to long-rod-like distributions.