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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 21 — Oct. 21, 2002
  • pp: 1227–1243

Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates

M. Skorobogatiy, Steven A. Jacobs, Steven G. Johnson, and Yoel Fink  »View Author Affiliations

Optics Express, Vol. 10, Issue 21, pp. 1227-1243 (2002)

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Perturbation theory formulation of Maxwell’s equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electro-magnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fail when applied to the problem of shifted material boundaries. In this paper we developed a novel coupled mode and perturbation theory formulations for treating generic non-uniform (varying along the direction of propagation) perturbations of a waveguide cross-section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate and rapidly converges to an exact result when used in a coupled mode theory framework even for the high index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of induced PMD due to a generic distortion of a waveguide profile, analysis of mode filters, mode converters and other optical elements such as strong Bragg gratings, tapers, bends etc., and arbitrary combinations of thereof. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary non-uniform profile variations in high index-contrast waveguides.

© 2002 Optical Society of America

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Research Papers

Original Manuscript: August 30, 2002
Revised Manuscript: October 16, 2002
Published: October 21, 2002

Maksim Skorobogatiy, Steven Jacobs, Steven Johnson, and Yoel Fink, "Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates," Opt. Express 10, 1227-1243 (2002)

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  1. Steven G. Johnson, Mihai Ibanescu, M. Skorobogatiy, Ori Weisberg, Torkel D. Engeness, Marin Soljacic, Steven A. Jacobs, J. D. Joannopoulos, and Yoel Fink, �??Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,�?? Opt. Express 9, 748 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748</a>. [CrossRef] [PubMed]
  2. Steven G. Johnson, Mihai Ibanescu, M. Skorobogatiy, Ori Weisberg, J. D. Joannopoulos, and Yoel Fink, �??Perturbation theory for Maxwell�??s equations with shifting material boundaries,�?? Phys. Rev. E 65, 66611 (2002). [CrossRef]
  3. M. Skorobogatiy, Mihai Ibanescu, Steven G. Johnson, Ori Weisberg, Torkel D. Engeness, Marin Soljacic, Steven A. Jacobs, and Yoel Fink, �??Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarization-mode dispersion and group-velocity dispersion,�?? J. Opt. Soc. Am. B 19, (2002). [CrossRef]
  4. M. Skorobogatiy, Steven A. Jacobs, Steven G. Johnson, and Yoel Fink, �??Dielectric prole variations in high index-contrast waveguides, coupled mode theory and perturbation expansions,�?? to be published in J. Opt. Soc. Am. B, 2003.
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