A finite element based fast eigensolver for three dimensional anisotropic photonic crystals

So Hsiang Chou, Tsung Ming Huang, Tiexiang Li, Jia Wei Lin, Wen Wei Lin

Research output: Contribution to journalArticle

Abstract

The standard Yee's scheme for the Maxwell eigenvalue problem places the discrete electric field variable at the midpoints of the edges of the grid cells. It performs well when the permittivity is a scalar field. However, when the permittivity is a Hermitian full tensor field it would generate un-physical complex eigenvalues or frequencies. In this paper, we propose a finite element method which can be interpreted as a modified Yee's scheme to overcome this difficulty. This interpretation enables us to create a fast FFT eigensolver that can compute very effectively the band structure of the anisotropic photonic crystal with SC and FCC lattices. Furthermore, we overcome the usual large null space associated with the Maxwell eigenvalue problem by deriving a null-space free discrete eigenvalue problem which involves a crucial Hermitian positive definite linear system to be solved in each of the iteration steps. It is demonstrated that the CG method without preconditioning converges in 37 iterations even when the dimension of a matrix is as large as 5,184,000.

Original languageEnglish
Pages (from-to)611-631
Number of pages21
JournalJournal of Computational Physics
Volume386
DOIs
Publication statusPublished - 2019 Jun 1
Externally publishedYes

    Fingerprint

Keywords

  • Face-centered cubic lattice
  • Finite element method
  • Maxwell's equations
  • Null-space free eigenvalue problem and fast Fourier transforms
  • Three-dimensional anisotropic photonic crystals

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this