A model describing the thermal effects in type II second harmonic generation (SHG) of Gaussian continuous-wave (CW) in a double-pass cavity is presented. The thermally induced phase mismatching (TIPM) along with thermal lensing was included in the classical SHG formalism through the interposing the heat and TIPM equations. To this end, eight equations were coupled together and solved simultaneously to reveal how the SHG is affected in time when heat is generated in the crystal. The model showed an excellent agreement with experimental data [Opt. Laser Tech.34, 333-336 (2002)]. Furthermore, a numerical procedure, which was developed in this work, is introduced for simultaneously solving the SHG, heat, and TIPM equations with home-used computing machines.

In this work, a thorough and detailed solution for the time-dependent heat equation for a cylindrical nonlinear potassium titanyl phosphate (KTP) crystal under a repetitively pulsed pumping source is developed. The convection and radiation boundary conditions, which are usually ignored in the literature, have been taken into account, and their importance on the temperature distribution has been discussed in detail. Moreover, the temperature dependence of thermal conductivity of KTP was considered in the calculations, and its impact is discussed. It is shown that the radiation term has a negligible effect and can be dropped safely, while the temperature dependence of thermal conductivity is more influential, such that ignorance of it brings some errors into the modeling. The time evolution of the temperature while the crystal is pumping with a train of successive Gaussian pulses until reaching equilibrium is shown. To accomplish numerical calculations, we developed a homemade code written with the finite difference time domain method in Intel Fortran (ifort) and ran it with the Linux operating system.

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In this work, the effect of temperature increase on the efficiency of a double-pass cavity type II second-harmonic generation (SHG) is investigated. To this end, a depleted wave model describing the continuous-wave SHG process with fundamental Gaussian waves was developed. First, six coupled equations were proposed to model a double-pass cavity to generate the second harmonic of a Gaussian fundamental wave in type II configuration. Then, the effect of temperature increase in the nonlinear crystal due to the optical absorption was modeled. To do this, a mismatched phase arising from changes in refractive indices was added to the coupled equations. Although the nondepleted assumption is usually used in such problems, a simultaneous solving of coupled equations with assumption of fundamental beam depletion was performed. The results were obtained by a homemade code written in Intel Fortran, and show how the efficiency of the SHG process decreases when the crystal is warmed up by 5, 10, and 15 K. Dramatic reductions in SHG efficiency were observed due to small changes in temperature. The results show excellent agreement with the experimental data [Opt. Commun.173, 311-314 (2000)].

Thermally induced phase mismatching (TIPM) has been proven to be an influential issue in nonlinear phenomena. It occurs when refractive indices of crystal are changed due to temperature rise. In this work, the authors report on a modeling of spatiotemporal dependence of TIPM in a repetitively pulsed pumping KTP crystal. Gaussian profiles for both spatial and temporal dependences of pump beam were used to generate second-harmonic waves in a type II configuration. This modeling is of importance in predicting the nonlinear conversion efficiency of crystals when heat is loaded in the system. To this end, at first, an approach to solve the heat equation in a repetitively pulsed pumping system with consideration of the temperature dependence of thermal conductivity and realistic cooling mechanisms such as conduction, convection, and radiation, is presented. The TIPM is then calculated through the use of experimental thermal dispersion relations of KTP crystal. The results show how accumulative behaviors of temperature and TIPM (with its reverse sign) happen when the number of pulses is increased. Fluctuations accompanying temperature and TIPM were observed which were attributed to the off-time between successive pulses. Moreover, in this work, a numerical procedure for solving a repetitively pulsed pumped crystal is introduced. This procedure enables us to solve the problem with home-used computing machines.