激光技术, 2016, 40 (5): 619, 网络出版: 2016-08-29  

谐振腔模式的特征向量法快速计算分析

Analysis of fast calculation about eigenvector method of laser resonator modes
作者单位
华中科技大学 光学与电子信息学院, 武汉 430074
摘要
用特征向量法模拟较大菲涅耳数激光谐振腔时, 采用梯形积分法计算效率较低。为了解决这一问题, 通过理论分析谐振腔输出模式的空间带宽积, 确定计算传输矩阵时最少的取样点数。采用高斯积分法计算传输矩阵, 该方法在保证啁啾函数计算精度的同时使传输矩阵尺寸满足最少取样要求。通过对菲涅耳数为10的方形镜平凹谐振腔进行数值模拟可知, 传统方法的传输矩阵尺寸为10000×10000, 谐振腔特征模式的计算时间为412.47s, 本文中的计算方法需要的传输矩阵尺寸为3600×3600, 计算时间为51.34s。结果表明, 本文中的计算方法能大幅度提高特征向量法的计算效率, 同时减少计算机内存的消耗。
Abstract
When eigenvector method was used to perform numerical simulation on laser resonator with big Fresnel number, the calculation efficiency was low by using trapezoidal integral method. In order to solve the problem, the minimum sampling numbers for numerical simulation were determined by analyzing the space-bandwidth product of resonator’s output mode and Gaussian quadrature was used to calculate the transmission matrix. This method not only ensured the calculation accuracy of chirp function but also reduced the transmission matrix size.Through numerical simulation of plane-concave resonator with square mirrors which Fresnel number is 10, the results show that, transmission matrix size of trapezoidal integration is 10000×10000 and computation time of laser resonator modes is 412.47s. Transmission matrix size of Gaussian quadrature is 3600×3600 and computation time is 51.34s. These results indicate that the new method greatly improves computational efficiency of eigenvector method and reduces the consumption of computer memory at the same time.

王炜, 肖瑜, 唐霞辉, 秦应雄, 吴超, 王振. 谐振腔模式的特征向量法快速计算分析[J]. 激光技术, 2016, 40(5): 619. WANG Wei, XIAO Yu, TANG Xiahui, QIN Yingxiong, WU Chao, WANG Zhen. Analysis of fast calculation about eigenvector method of laser resonator modes[J]. Laser Technology, 2016, 40(5): 619.

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