The vector Kirchhoff approach to thermal lensing in solids is investigated. The relation of the thermal rise in the sample to the optics of lensing is elucidated. Various analytical results and series representations for the transmitted intensity are derived for the case of Gaussian beams incident on circular samples, in various special limits. An expression for the time-dependent shift in the diffraction focus is obtained. Numerical computations illustrating lensing effects both at small times and in the steady state are presented. Effects of stress-induced birefringence, including the oscillation of the maximum intensity and diffraction focus as a function of time, are illustrated. Similar effects are also shown to occur when the incident power or sample thickness is varied, for solids characterized by large stress-induced contributions.
Bernard Bendow and Peter D. Gianino, "Optics of Thermal Lensing in Solids," Appl. Opt. 12, 710-718 (1973)