@Article{CiCP-16-1355,
author = {Dirk Klindworth and Kersten Schmidt},
title = {An Efficient Calculation of Photonic Crystal Band Structures Using Taylor Expansions},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {5},
pages = {1355--1388},
abstract = {<p style="text-align: justify;">In this paper we present an efficient algorithm for the calculation of photonic crystal band structures and band structures of photonic crystal waveguides. Our
method relies on the fact that the dispersion curves of the band structure are smooth
functions of the quasi-momentum in the one-dimensional Brillouin zone. We show the
derivation and computation of the group velocity, the group velocity dispersion, and
any higher derivative of the dispersion curves. These derivatives are then employed
in a Taylor expansion of the dispersion curves. We control the error of the Taylor expansion with the help of a residual estimate and introduce an adaptive scheme for the
selection of nodes in the one-dimensional Brillouin zone at which we solve the underlying eigenvalue problem and compute the derivatives of the dispersion curves. The
proposed algorithm is advantageous <span style="text-align: justify;">not only&nbsp;</span>as it decreases the computational effort
to compute the band structure but also because it allows for the identification of crossings and anti-crossings of dispersion curves, respectively. This identification is not
possible with the standard approach of solving the underlying eigenvalue problem at
a discrete set of values of the quasi-momentum without taking the mode parity into
account.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.240513.260614a},
url = {http://global-sci.org/intro/article_detail/cicp/7083.html}
}