Variational Formulation for Guided and Leaky Modes in Multilayer Dielectric Waveguides (Communications in Computational Physics, 2010)
The guided and leaky modes of a planar dielectric waveguide are eigensolutionsof 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.