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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

Maksim Skorobogatiy, Steven Jacobs, Steven Johnson, and Yoel Fink  »View Author Affiliations


Optics Express, Vol. 10, Issue 21, pp. 1227-1243 (2002)
http://dx.doi.org/10.1364/OE.10.001227


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-21-1227


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References

  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>.
  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).
  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.
  5. M. Lohmeyer, N. Bahlmann, and P. Hertel, �??Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,�?? Opt. Commun. 163, 86­94 (1999).
  6. N. R. Hill,�??Integral-equation perturbative approach to optical scattering from rough surfaces,�?? Phys. Rev. B 24, 7112 (1981). [CrossRef]
  7. D. Marcuse, Theory of dielectric optical waveguides (Academic Press, 2nd ed., 1991).
  8. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).
  9. B. Z. Katsenelenbaum, L. Mercader del Rıo, M. Pereyaslavets, M. Sorolla Ayza, and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Inst. of Electrical Engineers, London, 1998).
  10. L. Lewin , D. C. Chan g, and E. F. Kuester, Electromagnetic waves and curved structures (IEE Press, Peter Peregrinus Ltd., Stevenage 1977).
  11. F. Sporleder and H. G. Unger, Waveguide tapers transitions and couplers (IEE Press, Peter Peregrinus Ltd., Stevenage 1979).
  12. H. Hung-Chia, Coupled mode theory as applied to microwave and optical transmission (VNU Science Press, Utrecht 1984).
  13. Steven G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos �??The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,�?? to be published in Phys. Rev. E, 2002.
  14. L. D. Landau and E. M. Lifshitz, Quantum mechanics (non-relativistic theory) (Butterworth Heinemann, 2000).
  15. C. Vassallo, Optical waveguide concepts (Elsevier, Amsterdam, 1991).
  16. R. Holland, �??Finite-dierence solution of Maxell�??s equation in generalized nonorhogonal coordinates,�?? IEEE Trans. Nucl. Sci. 30, 4589 (1983).
  17. J.P. Plumey, G. Granet, and J. Chandezon, �??Dierential covariant formalism for solving Maxwell�??s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,�?? IEEE Trans. on Antennas Propag. 43, 835 (1995).
  18. E.J. Post, Formal Structure of Electromagnetics (Amsterdam: North-Holland, 1962).
  19. F.L. Teixeira and W.C. Chew, �??Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves,�?? Microwave Opt. Technol. Lett. 17, 231 (1998). [CrossRef]
  20. P. Bienstman, software at <a href="http://camfr.sf.net">http://camfr.sf.net</a>.

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