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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 680–694

Band gaps and leaky-wave effects in resonant photonic-crystal waveguides

Y. Ding and R. Magnusson  »View Author Affiliations

Optics Express, Vol. 15, Issue 2, pp. 680-694 (2007)

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The paper addresses the leaky stop bands associated with resonant photonic crystal slabs and periodic waveguides. We apply a semianalytical model pertinent to the second band to compute the dispersion curves describing the leaky stop band and verify its correctness by rigorous band computations. This approximate model provides clear insights into the physical properties of the leaky stop band in terms of explicit analytical expressions found. In particular, it enables comparison of the structure of the bands computed in complex propagation constant, implying spatially decaying leaky modes, with the bands computed in complex frequency, implying temporally decaying modes. It is shown that coexisting Bragg-coupling and energy-leakage mechanisms perturb the bands in complex propagation constant whereas these mechanisms are decoupled in complex frequency. As a result, the bands in complex frequency are well defined exhibiting a clear gap. These conclusions are verified by numerical diffraction computations for both weak and strong grating modulations where the resonance peaks induced by external illumination are shown to closely track the band profile computed in complex frequency. Thus, in general, phase matching to a resonant leaky mode occurs via real propagation constant that is found by dispersion computations employing complex frequency.

© 2007 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1970) Diffraction and gratings : Diffractive optics
(310.0310) Thin films : Thin films
(310.2790) Thin films : Guided waves

ToC Category:
Photonic Crystals

Original Manuscript: December 1, 2006
Revised Manuscript: January 11, 2007
Manuscript Accepted: January 12, 2007
Published: January 22, 2007

Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007)

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