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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 22 — Oct. 22, 2012
  • pp: 25181–25194

Proof of the universality of mode symmetries in creating photonic Dirac cones

Kazuaki Sakoda  »View Author Affiliations

Optics Express, Vol. 20, Issue 22, pp. 25181-25194 (2012)

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We formulate a degenerate perturbation theory for the vector electromagnetic field of periodic structures and apply it to the problem of the creation of Dirac cones in the Brillouin-zone center by accidental degeneracy of two modes. We derive a necessary condition by which we can easily select candidates of mode combinations that enable the creation of the Dirac cone. We analyze the structure of a matrix that determines the first-order correction to eigen frequencies by examining its transformation by symmetry operations. Thus, we can obtain the analytical solution of dispersion curves in the vicinity of the zone center and can judge the presence of the Dirac cone. All these findings clearly show that the presence or absence of the Dirac cone in the zone center is solely determined by the spatial symmetry of the two modes.

© 2012 OSA

OCIS Codes
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: September 11, 2012
Revised Manuscript: October 13, 2012
Manuscript Accepted: October 13, 2012
Published: October 19, 2012

Kazuaki Sakoda, "Proof of the universality of mode symmetries in creating photonic Dirac cones," Opt. Express 20, 25181-25194 (2012)

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