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Keywords:

  • Ewald transformation;
  • Green's functions;
  • integral equations;
  • periodic structures;
  • electromagnetic/photonic band-gap materials;
  • metamaterials

Abstract

We apply the Ewald acceleration technique to the efficient evaluation of periodic Green's functions (GFs) for 3-D skewed lattices like those arising in electromagnetic/photonic band-gap (EBG/PBG) structures and metamaterials (MTMs). We develop the expression for the optimal value of an associated splitting parameter, derive the gradient of the scalar potential GFs and address the extraction of singularity for both vector/scalar potential GF and their curl/gradient. Several numerical implementation issues are also discussed leading to further enhancement in computational speed, accuracy, and numerical stability. Finally, the accuracy of the developed GFs is verified against well established algorithms. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1353–1357, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22429