光纤模式分析的伽辽金有限元模型  

Fiber Mode Analysis Using Galerkin Finite Element Method

作　　者：卫延[1] 常德远[1] 郑凯[1] 简水生[1] 

机构地区：[1]北京交通大学光波技术研究所,北京100044

出　　处：《光子学报》2008年第5期924-930,共7页Acta Photonica Sinica

基　　金：国家863计划(2002AA312190)资助

摘　　要：提出了采用二阶吸收边界条件的全矢量平面伽辽金有限元模型,用于分析任意横截面形状和各向异性折射率分布的光纤的传导模式和泄漏模式,能精确求出各模式传输常量的实部和虚部以及模场分布,既不出现伪解,又不漏解.推导了各向异性介质全矢量耦合波动方程及其变分形式,给出了基于结点的二阶三角形单元的离散公式和单元矩阵,成功的将二阶吸收边界条件加入外边界二次线性单元的离散公式.计算表明采用该模型分析光子晶体光纤模式有效折射率与采用多极方法和基于离散函数展开的有限差分法所得结果吻合很好,采用二阶吸收边界条件计算限制损耗比一阶吸收边界条件结果精确.The 2-D Galerkin Vectorial finite-element method with the 2^nd transparent boundary conditions is reported in modeling fibers with arbitrary cross-section shape and arbitrary refractive indices distribution. By it the real part and imaginary part of propagation constant and field distribution of one certain mode are exactly solved without lost of any actual mode, and spurious modes have been picked out effectively. The vectorial wave equation in anisotropic material and its variational form are deduced, the discretized formulation of finite element method based on node shape function and stiff matrices of the 2^nd triangle elements,interface line elements and boundary line elements are derived in detail, the 2^nd transparent boundary conditions are applied successfully. The computed results by this algorithm agreed well with that in multipole method and finite difference equations with the discrete function expansion when modeling photonic crystal fibers. It＇s also shown that the 2^nd transparent boundary conditions are more accurate than the 1^st transparent boundary conditions.

关 键 词：光纤光学 模式分析 有限元法 二阶吸收边界条件 

分 类 号：TN25[电子电信—物理电子学]