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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 2 — Jan. 27, 2003
  • pp: 167–175

Simple plane wave implementation for photonic crystal calculations

Shangping Guo and Sacharia Albin  »View Author Affiliations

Optics Express, Vol. 11, Issue 2, pp. 167-175 (2003)

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A simple implementation of plane wave method is presented for modeling photonic crystals with arbitrary shaped ‘atoms’. The Fourier transform for a single ‘atom’ is first calculated either by analytical Fourier transform or numerical FFT, then the shift property is used to obtain the Fourier transform for any arbitrary supercell consisting of a finite number of ‘atoms’. To ensure accurate results, generally, two iterating processes including the plane wave iteration and grid resolution iteration must converge. Analysis shows that using analytical Fourier transform when available can improve accuracy and avoid the grid resolution iteration. It converges to the accurate results quickly using a small number of plane waves. Coordinate conversion is used to treat non-orthogonal unit cell with non-regular ‘atom’ and then is treated by standard numerical FFT. MATLAB source code for the implementation requires about less than 150 statements, and is freely available at http://www.lions.odu.edu/~sguox002.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(350.3950) Other areas of optics : Micro-optics

ToC Category:
Research Papers

Original Manuscript: December 19, 2002
Revised Manuscript: January 21, 2003
Published: January 27, 2003

Shangping Guo and Sacharia Albin, "Simple plane wave implementation for photonic crystal calculations," Opt. Express 11, 167-175 (2003)

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