光波导计算中全矢量-罚项有限元方法新解  

Physical background of penalty method in full vector finite element method for modeling of optical waveguide

作　　者：曹共柏[1] 林志浪[1] 肖海波[1] 张峰[1] 

机构地区：[1]上海微系统与信息技术研究所离子束开放实验室,上海200050

出　　处：《量子电子学报》2004年第5期658-664,共7页Chinese Journal of Quantum Electronics

摘　　要：数值求解光波导模式的方法,矢量元方法应用比较普遍,能够消除伪模,但由于矢量元的构造和求解过程比较烦琐,而用传统的节点有限元方法求解全矢量波动方程时,在得到物理模式的同时,也出现了伪模。本文在传统的罚项节点有限元方法的启发下,从麦克斯韦方程组本身的物理意义出发,导出了伪模的产生源,并对传统的罚项做了改正,大大提高了数值解的质量;尽管没有彻底消除伪模,它相对于矢量元方法优越的地方,体现在解(本征值)的精度,模场的特性,和高的数值稳定性等方面。The methods to solve Maxwell Equations have been researched and developed for almost 50 years. The finite element method now plays a dominant role in this field. But the spurious solutions always come up with the physical modes, though we developed many methods trying to eliminate them and find the edge element method. In this paper, the author analyzed the physical background and the numerical behavior of the spurious modes in conventional nodal finite element formulations, and give the direction of the numerical method to eliminate them. The first time, the author derive out the spurious source term which influence the quality of the physical modes, and counteracting this source using the new penalty term can improve the field profile of physical modes. We also give the numerical results of a rib waveguide and a directional coupler.

关 键 词：纤维与波导光学 有限元方法 罚项 伪模 

分 类 号：TN252[电子电信—物理电子学]