Abstract

A technique is suggested for an approximate solution of the set of equations responsible for second harmonic generation in nonlinear uniaxial crystals. The algorithm of this technique is reduced to numerical calculation of a triple integral. The study consists of two parts. In the first part, two approximations are considered, which allow a reduction of nearly two orders of magnitude in the computation time of double integrals over the transverse coordinates. In the second part, we discuss an approximate technique for estimating the power of interacting waves, which also allows a further reduction in the computation time by an order of magnitude by reducing minimum number of required steps in the recurrence process. The test results show that the use of these approximations can decrease the accuracy of the solution of the nonlinear problem but can keep the errors acceptably low.

中文翻译：

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解决非线性晶体二次谐波产生问题的近似技术：第1部分

摘要

建议使用一种技术来近似求解非线性单轴晶体中产生二次谐波的方程组。该技术的算法简化为三重积分的数值计算。该研究包括两个部分。在第一部分中，考虑了两个近似值，这使得在横向坐标上的双积分的计算时间减少了近两个数量级。在第二部分中，我们讨论了一种估计相互作用波功率的近似技术，该技术还可以通过减少递归过程中所需步骤的最小数量，将计算时间进一步减少一个数量级。