Matrix representation of the double-curl operator for simulating three dimensional photonic crystals

Tsung Ming Huang*, Han En Hsieh, Wen Wei Lin, Weichung Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Three dimensional photonic crystals can be modeled by the Maxwell equations as a generalized eigenvalue problem (GEVP). Simulations based on the numerical solutions of the GEVP are used to reveal physical properties and boost innovative applications of photonic crystals. However, to solve these GEVP remains a computational challenge in both timing and accuracy. The GEVP corresponding to the photonic crystals with face centered cubic (FCC) lattice is one of the challenging eigenvalue problems. From a viewpoint of matrix computation, we demonstrate how such obstacles can be overcome. Our main contribution is an explicit matrix representation of the double-curl operator associated with the photonic crystal with FCC lattice. This particular matrix represents the degenerate coefficient matrix of the discrete GEVP obtained by Yee's scheme. The explicit matrix leads to an eigendecomposition of the degenerate coefficient matrix and then a fast eigenvalue solver. Promising numerical results in terms of timing and accuracy are reported for solving the discrete GEVP arising in three dimensional photonic crystals with various geometric parameters.

Original languageEnglish
Pages (from-to)379-392
Number of pages14
JournalMathematical and Computer Modelling
Issue number1-2
Publication statusPublished - 2013 Jul


  • Double-curl operator
  • Face centered cubic lattice
  • Matrix representation
  • Photonic crystals
  • The Maxwell equations
  • Yee's scheme

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications


Dive into the research topics of 'Matrix representation of the double-curl operator for simulating three dimensional photonic crystals'. Together they form a unique fingerprint.

Cite this