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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9261–9275

Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides

Karen K. Y. Lee, Yehuda Avniel, and Steven G. Johnson  »View Author Affiliations

Optics Express, Vol. 16, Issue 13, pp. 9261-9275 (2008)

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We derive a sufficient condition for the existence of indexguided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as “holey fibers”), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of cutoff-free index-guided modes in any such structure where the core is formed by increasing the index of refraction (e.g. removing a hole). It also provides a weaker guarantee of guidance in cases where the refractive index is increased “on average” (precisely defined). The proof is based on a simple variational method, inspired by analogous proofs of localization for two-dimensional attractive potentials in quantum mechanics.

© 2008 Optical Society of America

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(130.2790) Integrated optics : Guided waves
(060.4005) Fiber optics and optical communications : Microstructured fibers
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: March 20, 2008
Revised Manuscript: April 17, 2008
Manuscript Accepted: April 18, 2008
Published: June 9, 2008

Karen K. Lee, Yehuda Avniel, and Steven G. Johnson, "Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides," Opt. Express 16, 9261-9275 (2008)

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Fig. 1. Fig. 2. Fig. 3.

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