Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities
Optimization and Control
2019-06-03 v2 Numerical Analysis
Optics
Abstract
We derive Euler-Lagrange equations for the topology optimization of decay rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear Maxwell systems with switching functions of special types. Our approach is based on the notion of Pareto optimal frontier and on the multi-parameter perturbation theory for eigenfrequencies. Parallels with optimal control theory are discussed.
Keywords
Cite
@article{arxiv.1904.09840,
title = {Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities},
author = {Matthias Eller and Illya M. Karabash},
journal= {arXiv preprint arXiv:1904.09840},
year = {2019}
}
Comments
16 pages, the introduction section is extended, the conclusions and discussion section is added, typos are corrected, references are added. OCIS codes: (120.4570) Optical design of instruments; (140.3945) Microcavities; (230.5750) Resonators