@Article{CiCP-7-3,
author = {},
title = {Variational Formulation for Guided and Leaky Modes in Multilayer Dielectric Waveguides},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {3},
pages = {564--579},
abstract = {<p style="text-align: justify;">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 characteristic
function which can be found with several methods that have been introduced in the
past. However, the evaluation of the characteristic function suffers from numerical
instabilities, and hence it is often difficult to find all modes in a given range. Here a
new variational formulation is introduced, which, after discretization, leads either to a
quadratic or a quartic eigenvalue problem. The modes can be computed with standard
software for polynomial eigenproblems. Numerical examples show that the method is
numerically stable and guarantees a complete set of solutions.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.043},
url = {https://global-sci.com/article/80994/variational-formulation-for-guided-and-leaky-modes-in-multilayer-dielectric-waveguides}
}