Generalized Finite Differences Method Applied to Finite Photonic Crystal
Computational Physics
2026-02-06 v1 Optics
Abstract
We propose a Generalized Finite-Differences in the Frequency Domain method for the computation of photonic band structures of finite photonic crystals. Our approach is to discretize some fundamental domain instead of a single unit cell, such that boundary conditions of interest can be introduced into the eigenvalue problem. The validity and effectiveness of the proposed method are shown for the case of a one-dimensional photonic crystal embedded in an optical cavity. The limit from finite to infinite photonic crystals is reviewed in view of the proposed method.
Keywords
Cite
@article{arxiv.2312.06671,
title = {Generalized Finite Differences Method Applied to Finite Photonic Crystal},
author = {Santiago Bustamante and Esteban Marulanda and Jorge Mahecha and Herbert Vinck},
journal= {arXiv preprint arXiv:2312.06671},
year = {2026}
}