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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 22 — Oct. 26, 2009
  • pp: 19629–19643

Modes of Shallow Photonic Crystal Waveguides: Semi-Analytic Treatment

S. Mahmoodian, C.G. Poulton, K.B. Dossou, R.C. McPhedran, L.C. Botten, and C.M. de Sterke  »View Author Affiliations

Optics Express, Vol. 17, Issue 22, pp. 19629-19643 (2009)

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We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off.

© 2009 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(260.2110) Physical optics : Electromagnetic optics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(130.5296) Integrated optics : Photonic crystal waveguides
(050.5298) Diffraction and gratings : Photonic crystals
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: July 9, 2009
Revised Manuscript: September 7, 2009
Manuscript Accepted: September 7, 2009
Published: October 15, 2009

S. Mahmoodian, C. G. Poulton, K. B. Dossou, R. C. McPhedran, L. C. Botten, and C. M. de Sterke, "Modes of shallow photonic crystal waveguides: semi-analytic treatment," Opt. Express 17, 19629-19643 (2009)

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