Abstract

The dispersion properties of photonic crystal fibers are calculated by expression of the modal field as a sum of localized orthogonal functions. Even simple designs of these fibers can yield zero dispersion at wavelengths shorter than 1.27 µm when the fibers are single mode, or a large normal dispersion that is suitable for dispersion compensation at 1.55 µm.

© 1998 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); erratum,  22, 484 (1997).
    [CrossRef] [PubMed]
  2. T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
    [CrossRef] [PubMed]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. DeSandro, J. Opt. Soc. Am. A 15, 748 (1998).
    [CrossRef]
  4. T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.
  5. J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.
  6. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  7. B. J. Ainslie and C. R. Day, J. Lightwave Technol. 4, 967 (1986).
    [CrossRef]
  8. J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps (Kluwer Academic, Dordrecht, The Netherlands, 1996).
    [CrossRef]
  9. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

1998 (1)

1997 (1)

1996 (1)

1986 (1)

B. J. Ainslie and C. R. Day, J. Lightwave Technol. 4, 967 (1986).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Ainslie, B. J.

B. J. Ainslie and C. R. Day, J. Lightwave Technol. 4, 967 (1986).
[CrossRef]

Atkin, D. M.

Birks, T. A.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. DeSandro, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996); erratum,  22, 484 (1997).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

Cregan, R. F.

T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.

Day, C. R.

B. J. Ainslie and C. R. Day, J. Lightwave Technol. 4, 967 (1986).
[CrossRef]

DeSandro, J. P.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. DeSandro, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

Knight, J. C.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. DeSandro, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996); erratum,  22, 484 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Mangan, B. J.

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

Russell, P. St. J.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. DeSandro, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996); erratum,  22, 484 (1997).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Vienne, G. G.

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

J. Lightwave Technol. (1)

B. J. Ainslie and C. R. Day, J. Lightwave Technol. 4, 967 (1986).
[CrossRef]

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

Opt. Lett. (2)

Other (5)

J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps (Kluwer Academic, Dordrecht, The Netherlands, 1996).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

T. A. Birks, J. C. Knight, R. F. Cregan, and P. St. J. Russell, in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 226.

J. C. Knight, T. A. Birks, B. J. Mangan, P. St. J. Russell, G. G. Vienne, and J. P. DeSandro, in Optical Fiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), postdeadline paper PD5.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

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Figures (3)

Fig. 1
Fig. 1

(a) Calculated and (b) experimentally measured contour plots of the guided mode field at λ=458 nm for a PCF with Λ=2.3 µm and d/Λ=0.23.

Fig. 2
Fig. 2

Normalized waveguide dispersion g against Λ/λ for (a) PCF’s with different hole sizes d/Λ and (b) the corresponding SIF’s. The values of d/Λ are 0.15, 0.25, 0.35, and 0.45 in order of increasing peak g. The curves are plotted only where the accuracy is high; the dotted curves indicate regions in which the fibers are multimode. For λ=1.55 µm, one can convert g to units of ps nm-1 km-1 by multiplying by -13,500×Λ/λ.

Fig. 3
Fig. 3

Calculated net GVD of a real PCF with Λ=2.3 µm and d/Λ=0.15. Inset, scanning electron microscope image of the fiber’s cross section.

Equations (6)

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

2+k02n2+ ln n2××h=β2h,
H=h expiβz-ck0t.
ϕmnx,y=exp-x2+y2/2Λ2Hmx/ΛHny/Λ,
k,lLk,lm,nhk,l=β2hm,n
g=2βΛkΛ2,
D=-2πΛcλ2g.

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