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 ha...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.展开更多
文摘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.
