TY - JOUR
T1 - Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions
AU - Xiao , Wenqiang
AU - Gong , Bo
AU - Lin , Junshan
AU - Sun , Jiguang
JO - Communications in Computational Physics
VL - 2
SP - 628
EP - 646
PY - 2023
DA - 2023/03
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0233
UR - https://global-sci.org/intro/article_detail/cicp/21502.html
KW - Band structure, dispersive photonic crystal, Maxwell’s equations, nonlinear eigenvalue problem, edge element, holomorphic operator function.
AB - <p style="text-align: justify;">We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D. The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function. The Néd<span style="text-align: justify;">é</span>lec edge elements are employed to discretize the operators, where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier. The
convergence of the eigenvalues is proved using the abstract approximation theory for
holomorphic operator functions with the regular approximation of the edge elements.
The spectral indicator method is then applied to compute the discrete eigenvalues.
Numerical examples are presented demonstrating the effectiveness of the proposed
method.</p>