Rezaee Mostafa Mohammad, Sabaeian Mohammad, Motazedian Alireza, Jalil-Abadi Fatemeh Sedaghat, Askari Hadi, Khazrk Iman
Appl Opt. 2015 May 20;54(15):4781-8. doi: 10.1364/AO.54.004781.
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.
热致相位失配（TIPM）已被证明是影响非线性现象的一个重要问题。当晶体的折射率因温度升高而改变时，就会发生热致相位失配。在这项工作中，作者报告了在重复脉冲泵浦的磷酸钛氧钾（KTP）晶体中热致相位失配时空依赖性的建模。泵浦光束的空间和时间依赖性均采用高斯分布，以II型配置产生二次谐波。当系统中存在热负载时，这种建模对于预测晶体的非线性转换效率具有重要意义。为此，首先提出了一种在重复脉冲泵浦系统中求解热方程的方法，该方法考虑了热导率的温度依赖性以及传导、对流和辐射等实际冷却机制。然后通过使用KTP晶体的实验热色散关系来计算热致相位失配。结果表明，当脉冲数增加时，温度和热致相位失配（及其相反符号）的累积行为是如何发生的。观察到了伴随温度和热致相位失配的波动，这归因于连续脉冲之间的关断时间。此外，在这项工作中，还介绍了一种求解重复脉冲泵浦晶体的数值方法。该方法使我们能够用家用计算机解决该问题。
