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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 10 — Oct. 1, 2002
  • pp: 2322–2330

Multipole method for microstructured optical fibers. I. Formulation

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten  »View Author Affiliations

JOSA B, Vol. 19, Issue 10, pp. 2322-2330 (2002)

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We describe a multipole method for calculating the modes of microstructured optical fibers. The method uses a multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the method and give representative results.

© 2002 Optical Society of America

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2400) Fiber optics and optical communications : Fiber properties
(060.4510) Fiber optics and optical communications : Optical communications

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002)

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  1. H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO 2001), Vol. 56 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001), paper CPD3.
  2. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998). [CrossRef]
  3. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (2000). [CrossRef]
  4. J. C. Knight, J. Broeng, T. A. Birks, and P. St. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]
  5. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]
  6. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).
  7. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991), Chap. 2.
  8. M. Midrio, M. P. Singh, and C. G. Someda, “The space filling mode of holey fibres: an analytic vectorial solution,” J. Lightwave Technol. 18, 1031–1048 (2000). [CrossRef]
  9. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. Mater., Devices Syst. 6, 181–191 (2000). [CrossRef]
  10. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000). [CrossRef]
  11. A. A. Maradudin and A. R. McGurn, “Out of plane propagation of electromagnetic waves in two-dimensional periodic dielectric medium,” J. Mod. Opt. 41, 275–284 (1994). [CrossRef]
  12. J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguide guidance by the photonic bandgap effect in optical fibre,” J. Opt. Pure Appl Opt. 1, 477–482 (1999). [CrossRef]
  13. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystals,” J. Lightwave Technol. 17, 2078–2081 (2000). [CrossRef]
  14. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, “Cladding-mode-resonances in air–silica microstructure optical fibers,” J. Lightwave Technol. 18, 1084–1100 (2000). [CrossRef]
  15. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Optical properties of high-delta air–silica microstructure optical fibers,” Opt. Lett. 25, 796–797 (2000). [CrossRef]
  16. K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, “An electromagnetic theory of dielectric waveguides with multiple embedded cylinders,” J. Lightwave Technol. 12, 396–410 (1994). [CrossRef]
  17. E. Centeno and D. Felbacq, “Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals,” J. Opt. Soc. Am. A 17, 320–327 (2000). [CrossRef]
  18. P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. MTT-23, 421–429 (1975). [CrossRef]
  19. M. J. Steel, T. P. White, C. M. De Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001). [CrossRef]
  20. D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994). [CrossRef]
  21. E. Yamashita, S. Ozeki, and K. Atsuki, “Modal analysis method for optical fibers with symmetrically distributed multiple cores,” J. Lightwave Technol. 3, 341–346 (1985). [CrossRef]
  22. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002). [CrossRef]
  23. W. Wijngaard, “Guided normal modes of two parallel circular dielectric rods,” J. Opt. Soc. Am. 63, 944–949 (1973). [CrossRef]
  24. C.-S. Chang and H.-C. Chang, “Theory of the circular harmonics expansion method for multiple-optical-fiber system,” J. Lightwave Technol. 12, 415–417 (1994). [CrossRef]
  25. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  26. D. Maystre and P. Vincent, “Diffraction d’une onde electromagnetique plane par an object cylindrique non infinitement conducteur,” Opt. Commun. 5, 327–330 (1972). [CrossRef]
  27. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Sec. 2.9.
  28. L. Schwartz, Mathematics for the Physical Sciences (Addison-Wesley, Reading, Mass., 1966).

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