折射率补偿法修正边界元电磁场模拟误差  

Refractive Index Compensation to Fix the Error of Electromagnetic Field Simulation by Boundary Element Method

作　　者：舒方杰[1] 胡平林[2] 李健聪[3] 

机构地区：[1]商丘师范学院物理与电气信息学院 [2]中国人民解放军,96325部队 [3]中国人民解放军,海军航空仪器计量站

出　　处：《光学学报》2013年第8期229-234,共6页Acta Optica Sinica

基　　金：国家自然科学基金青年科学基金(11204169);理论物理专项基金(11247289)

摘　　要：边界元方法是一种数值求解偏微分方程的高效算法,在微纳光学求解电磁场问题中有广泛的应用。在实际计算中,边界元数目的选择直接关系着数值模拟的精度。研究不同边界元数目下微腔谐振频率的计算误差,发现主要误差可视作微腔对电磁波的吸收或放大,因此提出折射率补偿法对离散求解边界积分方程引入的误差加以修正。加入折射率补偿之后,边界元方法计算谐振频率的精度能提高至少一个数量级,并且该修正可以有效用于较大频率范围内的所有模式。因此折射率补偿使边界元方法的计算精度和运算速度得到大幅提升,时间和内存消耗锐减。同时,从物理角度分析、修正数值计算误差的思想也可以推广到其他数值计算方法中。The boundary element method is a highly efficient algorithm for numerical solution of partial differential equations, which is widely used in solving electromagnetic field problems in micro-and nano-optics. The complex resonance frequency of circular cavity with different numbers of boundary elements is obtained, and its error is discussed. Major error can be regarded as absorption or amplification of electromagnetic waves by microcavity, which is concluded from the analysis of the quality factor. Then refractive index compensation method for fixing the error introduced by discrete process of boundary integral equation is proposed. The accuracy of the boundary element method is improved at least an order of magnitude after the amendment. Moreover, the correction amount obtained by a center frequency is valid, when it is used in a wide range of frequency around the central frequency. Therefore, the refractive index compensation method makes the calculation accurate and the computing speed significantly improved, the time and memory consumption sharply dropped. At the same time, correcting the simulation error from the physical point of view can be extended to other numerical methods.

关 键 词：微纳光学 误差修正 边界元方法 回音壁模式微腔 

分 类 号：O436[机械工程—光学工程]