Electromagnetic field behavior of 3D Maxwell's equations for chiral media

Tsung Ming Huang, Tiexiang Li*, Ruey Lin Chern, Wen Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This article focuses on numerically studying the eigenstructure behavior of generalized eigenvalue problems (GEPs) arising in three dimensional (3D) source-free Maxwell's equations with magnetoelectric coupling effects which model 3D reciprocal chiral media. It is challenging to solve such a large-scale GEP efficiently. We combine the null-space free method with the inexact shift-invert residual Arnoldi method and MINRES linear solver to solve the GEP with a matrix dimension as large as 5,308,416. The eigenstructure is heavily determined by the chirality parameter γ. We show that all the eigenvalues are real and finite for a small chirality γ. For a critical value γ=γ, the GEP has 2×2 Jordan blocks at infinity eigenvalues. Numerical results demonstrate that when γ increases from γ, the 2×2 Jordan block will first split into a complex conjugate eigenpair, then rapidly collide with the real axis and bifurcate into positive (resonance) and negative eigenvalues with modulus smaller than the other existing positive eigenvalues. The resonance band also exhibits an anticrossing interaction. Moreover, the electric and magnetic fields of the resonance modes are localized inside the structure, with only a slight amount of field leaking into the background (dielectric) material.

Original languageEnglish
Pages (from-to)118-131
Number of pages14
JournalJournal of Computational Physics
Publication statusPublished - 2019 Feb 15


  • Anticrossing eigencurves
  • Maxwell's equations
  • Null-space free eigenvalue problem
  • Resonance mode
  • Shift-invert residual Arnoldi method
  • Three-dimensional chiral medium

ASJC Scopus subject areas

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


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