Abstract

It is shown from basic principles that the core modes of an air-core photonic-bandgap fiber (PBF) exhibit similar qualitative and quantitative behavior as the linearly polarized (LP) modes of an equivalent conventional fiber whose step-index profile is entirely determined by the band edges of the PBF. This analogy leads to the concept of effective numerical aperture (NA), which is used to provide an intuitive interpretation of the qualitative behavior of PBF modes. By using this equivalence, several key properties, including the number of modes, their cutoff, effective index, size, and divergence, and the dependence of these quantities on the PBF core and cladding parameters, can be predicted approximately by simulating the LP modes of the equivalent step-index fiber using standard LP-mode simulators or well-known formula. Besides providing a convenient tool to model the modes of a PBF, this analogy gives new physical insight into the fundamental characteristics of these complex waveguides.

© 2005 IEEE

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  1. T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith and C. Martijn de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method", Opt. Express, vol. 9, no. 13, pp. 721-732, Nov. 2001.
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  7. N. A. Mortensen, J. R. Folken, P. M. W. Skovgaard and J. Broeng, "Numerical aperture of single-mode photonic crystal fibers", IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1094-1096, Aug. 2002.
  8. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in planewave basis", Opt. Express, vol. 8, no. 3, pp. 173-190, Jan. 2001.
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  10. H. K. Kim, M. J. F. Digonnet, J. Shin, S. Fan and G. S. Kino, "Nomenclature and properties of the modes of air-core photonic-bandgap fibers", Nomenclature and properties of the modes of air-core photonic-bandgap fibers,,
  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983, p. 320.
  12. D. Gloge, "Weakly guiding fibers", Appl. Opt., vol. 10, no. 10, pp. 2252-2258, Oct. 1971.
  13. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts and D. A. Allan, "Single-mode photonic band gap guidance of light in air", Science, vol. 285, no. 5433, pp. 1537-1539, Sep. 1999.
  14. T. P. Hansen, et al. "Air-guiding photonic bandgap fibers: Spectral properties, macrobending loss and practical handling", J. Lightw. Technol., vol. 22, no. 1, pp. 11-15, Jan. 2004.

Other (14)

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith and C. Martijn de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method", Opt. Express, vol. 9, no. 13, pp. 721-732, Nov. 2001.

J. Broeng, S. Barkou, T. Sondergaard and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers", Opt. Lett., vol. 25, no. 2, pp. 96-98, Jan. 2000.

K. Saito, N. A. Mortensen and M. Koshiba, "Air-core photonic band-gap fibers: The impact of surface modes", Opt. Express, vol. 12, no. 3, pp. 394-400, Feb. 2004.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang and K. W. Koch, "Surface modes and loss in air-core photonic band-gap fibers", in Proc. SPIE, vol. 5000, 2003, pp. 161-174.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes", IEEE J. Quantum Electron., vol. 40, no. 5, pp. 551-556, May 2004.

V. Dangui, M. J. F. Digonnet and G. S. Kino, "A fast and accurate numerical tool to model the modal properties of photonic-bandgap fibers", Opt. Express,

N. A. Mortensen, J. R. Folken, P. M. W. Skovgaard and J. Broeng, "Numerical aperture of single-mode photonic crystal fibers", IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1094-1096, Aug. 2002.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in planewave basis", Opt. Express, vol. 8, no. 3, pp. 173-190, Jan. 2001.

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystal: Molding the Flow of Light, Princeton, NJ: Princeton Univ. Press, 1995, p. 96.

H. K. Kim, M. J. F. Digonnet, J. Shin, S. Fan and G. S. Kino, "Nomenclature and properties of the modes of air-core photonic-bandgap fibers", Nomenclature and properties of the modes of air-core photonic-bandgap fibers,,

A. W. Snyder and J. D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983, p. 320.

D. Gloge, "Weakly guiding fibers", Appl. Opt., vol. 10, no. 10, pp. 2252-2258, Oct. 1971.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts and D. A. Allan, "Single-mode photonic band gap guidance of light in air", Science, vol. 285, no. 5433, pp. 1537-1539, Sep. 1999.

T. P. Hansen, et al. "Air-guiding photonic bandgap fibers: Spectral properties, macrobending loss and practical handling", J. Lightw. Technol., vol. 22, no. 1, pp. 11-15, Jan. 2004.

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