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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 7 — Jul. 1, 2010
  • pp: 1364–1380

Analysis of photonic crystal defect modes by maximal symmetrization and reduction

B. Gallinet, J. Kupec, B. Witzigmann, and M.-A. Dupertuis  »View Author Affiliations

JOSA B, Vol. 27, Issue 7, pp. 1364-1380 (2010)

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We analyze in depth the eigenmodes symmetry of the vectorial electromagnetic wave equation with discrete symmetry, using a recently developed maximal symmetrization and reduction scheme leading to an automatic technique which decomposes every mode into its most fundamental internal geometrical components carrying independent symmetries, the ultimately reduced component functions (URCFs). Using URCFs, geometrical properties of photonic crystal defect modes can be analyzed in great details. In particular we analytically identify the kind of modes that display non-vanishing transverse electric or transverse magnetic amplitude at the cavity center in C 2 v , C 3 v , C 4 v , and C 6 v symmetries, and their degeneracies. We also build a postprocessing tool able to extract and identify URCFs out of the modes whether from experimental or numerical origin. In the latter case it is independent of the eigenmode computation method. In another variant the whole eigenmode computation can be systematically reduced to a minimal domain, without any need for applying specific non-trivial boundary conditions. The approach leads to strong analytical predictions which are illustrated for specific H 1 and L 3 cavities using the postprocessing tool on full three-dimensional computed modes. It not only constitutes an unprecedented check of the symmetry of the computational results, but it is shown to also deliver a deep geometrical and physical insight into the structure of the modes of photonic bandgap microcavities, which is of direct use for most modern applications in quantum photonics.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(140.3945) Lasers and laser optics : Microcavities
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: December 18, 2009
Revised Manuscript: April 7, 2010
Manuscript Accepted: April 26, 2010
Published: June 17, 2010

B. Gallinet, J. Kupec, B. Witzigmann, and M.-A. Dupertuis, "Analysis of photonic crystal defect modes by maximal symmetrization and reduction," J. Opt. Soc. Am. B 27, 1364-1380 (2010)

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