Rezaee Mostafa Mohammad, Sabaeian Mohammad, Motazedian Alireza, Jalil-Abadi Fatemeh Sedaghat, Khaldi-Nasab Ali
Appl Opt. 2015 Feb 20;54(6):1241-9. doi: 10.1364/AO.54.001241.
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.
在这项工作中，针对圆柱形非线性磷酸钛氧钾（KTP）晶体在重复脉冲泵浦源作用下的含时热方程，开发了一种全面且详细的求解方法。考虑了文献中通常忽略的对流和辐射边界条件，并详细讨论了它们对温度分布的重要性。此外，在计算中考虑了KTP热导率的温度依赖性，并讨论了其影响。结果表明，辐射项的影响可忽略不计，可以安全地舍弃，而热导率的温度依赖性影响更大，忽略它会给建模带来一些误差。展示了晶体在一系列连续高斯脉冲泵浦直至达到平衡时温度的时间演化。为了完成数值计算，我们用英特尔Fortran（ifort）中的时域有限差分法编写了一个自制代码，并在Linux操作系统上运行。
