Analysis of photonic crystals using the hybrid finite-element/finite-difference time domain technique based on the discontinuous Galerkin method

• Published in: International journal for numerical methods in engineering Vol. 92; no. 5; pp. 495 - 506
• Main Authors: Zhu, Bao, Chen, Jiefu, Zhong, Wanxie, Liu, Qing Huo
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 02.11.2012; Wiley; Wiley Subscription Services, Inc
• Subjects: discontinuous Galerkin method; domain decomposition; Exact sciences and technology; finite-difference time-domain method; finite-element time-domain method; Fundamental areas of phenomenology (including applications); Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); non-conformal mesh; Numerical analysis; Numerical analysis. Scientific computation; Optical materials; Optics; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Photonic bandgap materials; photonic bandgap structures; Physics; Sciences and techniques of general use; discontinuous Galerkin method; Photonic crystals; photonic bandgap structures; finite-difference time-domain method; finite-element time-domain method; Surface structure; Galerkin-Petrov method; Finite element method; non-conformal mesh; Time domain method; Hybrid finite element; Modelling; Curved surface; Domain decomposition; Finite difference method; Crystal structure; Periodic structures
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4348

SUMMARY Two‐dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite‐element time‐domain (FETD) method and the finite‐difference time‐domain (FDTD) method. This hybrid FETD/FDTD method uses the discontinuous Galerkin method as framework for domain decomposition. To the best of our knowledge, this is the first hybrid FETD/FDTD method that allows non‐conformal meshes between different FETD and FDTD subdomains. It is also highly parallelizable. These properties are very suitable for the computation of periodic structures with curved surfaces. Numerical examples for the computation of the scattering parameters of two‐dimensional photonic bandgap structures are presented as applications of the hybrid FETD/FDTD method. Numerical results demonstrate the efficiency and accuracy of the proposed hybrid method. Copyright © 2012 John Wiley & Sons, Ltd.