基于时域有限差分算法改进卷积完全匹配层的稳定性

谢国大; 黄志祥; 王丽华; 吴先良

doi:doi:10.3788/gzxb20174608.0826001

光子学报, 2017, 46 (8): 0826001, 网络出版: 2017-10-30

基于时域有限差分算法改进卷积完全匹配层的稳定性

Improvement of the Stability of Convolutional Perfect Matched Layer Based on Finite Difference Time-domain Algorithm

论文大纲

谢国大 ^*黄志祥王丽华吴先良

作者单位

安徽大学电子信息工程学院计算智能与信号处理教育部重点实验室，合肥 230039

摘要

为了克服时域有限差分算法中卷积完全匹配层对消逝波吸收效果差的缺点，提出一种在卷积完全匹配层后添加特殊吸收层的方法.在不增加物体与吸收层内层距离的情况下,通过调节特殊吸收层中两个衰减因子,使其为常数,并令吸收因子逐层从1增加到10，来增强吸收层对消逝波的吸收性能.平面波垂直入射到单层光子晶体的算例表明，添加了特殊吸收层的吸收边界在与散射体相距5个网格的情况下仍能够保持计算结果收敛, 而传统的吸收边界则需要相距80个网格才能保证结果收敛，说明该方法提高了对消逝波的吸收性能.进一步在结构中采用此吸收边界来计算多层光子晶体的传输特性曲线,并将其与常规方法计算所得结果做比较，两种结果吻合较好.数值算例验证了该方法的有效性和正确性.

Abstract

In order to overcome the convolutional perfectly matched layer′s shortcoming of the poor absorption effect on evanescent wave in the finite difference time domain algorithm, a method of adding special absorption layer after convolutional perfectly matched layer was proposed. Without increasing the distance between the object and the inner layer of the absorbent layer, the decay factors in the special absorption layer were adjusted to make them constants and the absorption factor was increased from 1 to 10 to enhance the absorption layer′s absorption performance to the evanescent wave. An example in which the plane wave is incident vertically to the single-layer photonic crystal shows that the absorption boundary with the addition of the special absorption layer can keep the convergence of the calculation result when the distance from the scatterer is 5 mesh, while the traditional absorption boundary is required to be separated by 80 grids to ensure the results converge. By using this absorption boundary in the structure, the transmission characteristic curve of the multilayer photonic crystal was calculated and compared with the result obtained by the conventional method, the results were in good agreement with each other. The numerical results show that the method is effective and correct.

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谢国大, 黄志祥, 王丽华, 吴先良. 基于时域有限差分算法改进卷积完全匹配层的稳定性[J]. 光子学报, 2017, 46(8): 0826001. XIE Guo-da, HUANG Zhi-xiang, WANG Li-hua, WU Xian-liang. Improvement of the Stability of Convolutional Perfect Matched Layer Based on Finite Difference Time-domain Algorithm[J]. ACTA PHOTONICA SINICA, 2017, 46(8): 0826001.

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