Abstract

We analyze the nature of modal cutoff in microstructured optical fibers of finite cross section. In doing so, we reconcile the striking endlessly single-mode behavior with the fact that in such fibers all propagation constants are complex. We show that the second mode undergoes a strong change of behavior that is reflected in the losses, effective area, and multipolar structure. We establish the parameter subspace in which the fibers are single mode and an accurate value for the limit of the endlessly single-mode regime.

© 2002 Optical Society of America

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References

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  1. T. A. Birks, J. C. Knight, and P. J. St. Russell, Opt. Lett. 22, 961 (1997).
    [CrossRef] [PubMed]
  2. N. A. Mortensen, Opt. Express 10, 341 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  3. A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).
  4. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).
  5. B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).
  6. T. P. White, R. C. McPhedran, C. M. de Sterke, and M. J. Steel, Opt. Lett. 26, 488 (2001).
    [CrossRef]
  7. For enhanced color versions of Figs. 1–4, see http://www.physics.usyd.edu.au/~borisk/physics/cutoff.html .
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  9. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, J. Lightwave Technol. 18, 1084 (2000).
    [CrossRef]
  10. M. Midrio, M. P. Singh, and C. G. Someda, J. Lightwave Technol. 18, 1031 (2000).
    [CrossRef]
  11. J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
    [CrossRef]

2002 (1)

2001 (1)

2000 (2)

1999 (1)

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

1997 (1)

Agrawal, G. P.

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

Barkou, S. E.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Birks, T. A.

Bjarklev, A.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Botten, L. C.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

Broeng, J.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Burdge, G. L.

de Sterke, C. M.

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

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

Eggleton, B. J.

Kerbage, C.

Knight, J. C.

Kuhlmey, B. T.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

Love, J. D.

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Maystre, D.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

McPhedran, R. C.

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

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

Midrio, M.

Mogilevstev, D.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Mortensen, N. A.

Renversez, G.

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

Russell, P. J. St.

Singh, M. P.

Someda, C. G.

Steel, M. J.

Synder, A. W.

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Westbrook, P. S.

White, C. A.

White, T. P.

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

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

Windeler, R. S.

J. Lightwave Technol. (2)

Opt. Express (1)

Opt. Fiber Technol. (1)

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Opt. Lett. (2)

Other (5)

For enhanced color versions of Figs. 1–4, see http://www.physics.usyd.edu.au/~borisk/physics/cutoff.html .

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

A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B (to be published).

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B (to be published).

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Figures (4)

Fig. 1
Fig. 1

Imneff as a function of wavelength/pitch, for a structure of eight rings of holes in silica at a wavelength of λ=1.55 µm for several diameter-to-pitch ratios. Ineff decreases monotonically with increasing d/Λ, as this parameter takes the values 0.40 [curve (1)], 0.41, 0.42, 0.43, 0.45, 0.46, 0.48, 0.49, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75 [curve (14)].

Fig. 2
Fig. 2

Variation of physical quantities during the transition for a MOF with d/Λ=0.55 used at λ=1.55 µm. Curves (1), (2), and (3) are Imneff for 4, 8, and 10 rings, and curves (4), (5), (6), and (7) are Q, Reff/Λ, Aeff/Λ2, and M, respectively, as defined in the text, for eight rings. Points (a)–(d) indicate the positions of the field plots in Fig. 3.

Fig. 3
Fig. 3

Density plots of the real part of the z component of the Poynting vector of the second mode for four values of the pitch about the localization transition, for a structure of eight rings of holes with a diameter-to-pitch ratio d/Λ=0.55. (a) Cladding filling state λ/Λ=0.81; (b), (c) transition states λ/Λ=0.599 and λ/Λ=0.537, respectively; (d) localized state λ/Λ=0.445. The corresponding points are marked in Fig. 2.

Fig. 4
Fig. 4

Phase diagram of the second mode. The curves correspond to different definitions of the transition point: solid, Aeff; long-dashed, M minimum; short-dashed, Q minimum; dotted, fit from Eq. (6); squares, as in Ref. 2. In the lower region the second mode is confined and the fiber is therefore dual moded. The dashed vertical line shows the approximation to the limit of the endlessly single-mode regime.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Imneff=Imβ/k0,
L=2πλ20ln10109 Imneff,
Q=d2 logImneffd2 logΛ.
Reff=r2Szr,θdrdθrSzr,θdrdθ,
Aeff=E22E4.
Hzr,θ=nBnHHnkrexpinθ,
λ/Λαd/Λ-0.406γ,

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