Variational Formulation for Guided and Leaky Modes in Multilayer Dielectric Waveguides

作     者：David Stowell Johannes Tausch 

作者机构：Department of MathematicsSouthern Methodist UniversityDallasTX 75275USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2010年第7卷第3期

页      面：564-579页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

主　　题：Dielectric waveguide polynomial eigenvalue problem variational formulation finite elements singular Sturm-Liouville problem continuation method 

摘      要：The guided and leaky modes of a planar dielectric waveguide are eigensolutions of a singular Sturm-Liouville problem. The modes are the roots of a characteristicfunction which can be found with several methods that have been introduced in thepast. However, the evaluation of the characteristic function suffers from numericalinstabilities, and hence it is often difficult to find all modes in a given range. Here anew variational formulation is introduced, which, after discretization, leads either to aquadratic or a quartic eigenvalue problem. The modes can be computed with standardsoftware for polynomial eigenproblems. Numerical examples show that the method isnumerically stable and guarantees a complete set of solutions.