Abstract

We describe a multipole formulation that can be used for high-accuracy calculations of the full complex propagation constant of a microstructured optical fiber with a finite number of holes. We show how the imaginary part of the microstructure, which describes confinement losses not associated with absorption, varies with hole size, the number of rings of holes, and wavelength, and give the minimum number of rings of holes required for a specific loss for given parameters.

© 2001 Optical Society of America

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References

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  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
    [Crossref] [PubMed]
  2. J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 796 (2000).
    [Crossref]
  3. J. Broeng, S. E. Barkou, T. Søndergaard, and A. Bjarklev, Opt. Lett. 25, 96 (2000).
    [Crossref]
  4. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, J. Lightwave Technol. 17, 2078 (2000).
    [Crossref]
  5. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, J. Lightwave Technol. 17, 1093 (2000).
    [Crossref]
  6. M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, Opt. Lett. 26, 488 (2001).
    [Crossref]
  7. K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
    [Crossref]
  8. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.
  9. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
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    [Crossref]
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    [Crossref]
  13. R. S. Windeler, J. L. Wagener, and D. J. DiGiovanni, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG1.
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2001 (1)

2000 (4)

1999 (1)

1998 (1)

1996 (1)

1994 (1)

K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
[Crossref]

1982 (1)

L. G. Cohen, D. Marcuse, and W. L. Mammel, IEEE J. Quantum Electron. QE-18, 1467 (1982).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

Atkin, D. M.

Barkou, S. E.

Bassett, I. M.

K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
[Crossref]

Bennett, P. J.

Birks, T. A.

Bjarklev, A.

Botten, L. C.

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, Opt. Lett. 26, 488 (2001).
[Crossref]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Broderick, N. G. R.

Broeng, J.

Cohen, L. G.

L. G. Cohen, D. Marcuse, and W. L. Mammel, IEEE J. Quantum Electron. QE-18, 1467 (1982).
[Crossref]

de Sterke, C. M.

DiGiovanni, D. J.

R. S. Windeler, J. L. Wagener, and D. J. DiGiovanni, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG1.

Knight, J. C.

Kuhlmey, B. T.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Lo, K. M.

K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
[Crossref]

Mammel, W. L.

L. G. Cohen, D. Marcuse, and W. L. Mammel, IEEE J. Quantum Electron. QE-18, 1467 (1982).
[Crossref]

Marcuse, D.

L. G. Cohen, D. Marcuse, and W. L. Mammel, IEEE J. Quantum Electron. QE-18, 1467 (1982).
[Crossref]

Martijn de Sterke, C.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Maystre, D.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

McPhedran, R. C.

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, Opt. Lett. 26, 488 (2001).
[Crossref]

K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
[Crossref]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Milton, G. W.

K. M. Lo, R. C. McPhedran, I. M. Bassett, and G. W. Milton, J. Lightwave Technol. 12, 396 (1994).
[Crossref]

Mogilevtsev, D.

Monro, T. M.

Ranka, J. K.

Renversez, G.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Richardson, D. J.

Russell, P. St. J.

Søndergaard, T.

Steel, M. J.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Stentz, A. J.

Wagener, J. L.

R. S. Windeler, J. L. Wagener, and D. J. DiGiovanni, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG1.

White, T. P.

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, Opt. Lett. 26, 488 (2001).
[Crossref]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

Windeler, R. S.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 796 (2000).
[Crossref]

R. S. Windeler, J. L. Wagener, and D. J. DiGiovanni, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG1.

IEEE J. Quantum Electron. (1)

L. G. Cohen, D. Marcuse, and W. L. Mammel, IEEE J. Quantum Electron. QE-18, 1467 (1982).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

Opt. Lett. (5)

Other (4)

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole formulation for propagation and loss in microstructured optical fibers,” to be submitted to J. Lightwave Technol.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

R. S. Windeler, J. L. Wagener, and D. J. DiGiovanni, in Optical Fiber Communication Conference (OFC), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG1.

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Figures (4)

Fig. 1
Fig. 1

Longitudinal component of the Poynting vector of the leaky fundamental mode of the MOF consisting of 18 holes of diameter d=0.92 μm with spacing Λ=2.3 μm. At λ=1.55 μm the structural loss of this mode is 1600  dB/m. Contour lines are at 0.5-dB intervals.

Fig. 2
Fig. 2

Comparison of real and imaginary parts of the effective index from the multipole method (crosses) and the vector beam propagation method (circles). The curves were added to aid the eye.

Fig. 3
Fig. 3

Confinement loss (in decibels per meter) for MOF’s in silica as a function of the number of hexagonally packed rings and their diameter to spacing ratio d/Λ, with Λ=2.3 μm, for a wavelength λ=1.55 μm. Inset, five-ring, d/Λ=0.3 structure.

Fig. 4
Fig. 4

Confinement loss (in decibels per meter) as a function of wavelength for a MOF with three rings of holes (thirty-six holes) for various hole sizes. The hole spacing is fixed at 2.3 μm.

Equations (2)

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Ez=m=-amlJmkerl+bmlHm1kerl×expimϕlexpiβz,
Ez=m=-cmlJmkirlexpimϕtexpiβz,

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