Abstract

We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCF’s). This analysis includes a thorough description of the dependence of the fiber geometrical dispersion on the structural parameters of a PCF. The interplay between material dispersion and geometrical dispersion allows us to established a well-defined procedure to design specific predetermined dispersion profiles. We focus on flattened, or even ultraflattened, dispersion behaviors both in the telecommunication window (around 1.55 µm) and in the Ti-Za laser wavelength range (around 0.8 µm). We show the different possibilities of obtaining normal, anomalous, and zero dispersion curves in the above frequency domains and discuss the limits for the existence of the above dispersion profiles.

©2001 Optical Society of America

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References

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  1. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Donor and acceptor guided modes in photonic crystal fibers,” Opt. Lett. 25, 1238–1330 (2000).
    [Crossref]
  2. D. Mogilevtsev, T. A. Birks, and P. S. J. Russell, “Dispersion of photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
    [Crossref]
  3. M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
    [Crossref]
  4. P. J. Bennet, T. M. Monro, and D. J. Richardson, “Toward practical holey fiber technology: fabrication, splicing, modeling, and fabrication,” Opt. Lett. 24, 1203–1205 (1999).
    [Crossref]
  5. A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
    [Crossref]
  6. J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
    [Crossref]
  7. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
    [Crossref]
  8. E. Silvestre, M. V. Andrés, and P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber modes,” J. Lightwave Technol. 16, 923–928 (1998).
    [Crossref]
  9. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
    [Crossref]
  10. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
    [Crossref]
  11. D. Davidson, Optical-Fiber Transmission (E. E. Bert Basch, ed., Howard W. Sams & Co, 1987).

2000 (3)

1999 (5)

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
[Crossref]

P. J. Bennet, T. M. Monro, and D. J. Richardson, “Toward practical holey fiber technology: fabrication, splicing, modeling, and fabrication,” Opt. Lett. 24, 1203–1205 (1999).
[Crossref]

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

1998 (2)

Andrés, M. V.

Andrés, P.

Barkou, S. E.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

Bennet, P. J.

Birks, T. A.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

D. Mogilevtsev, T. A. Birks, and P. S. J. Russell, “Dispersion of photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[Crossref]

Bjarklev, A.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

Broeng, J.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

Davidson, D.

D. Davidson, Optical-Fiber Transmission (E. E. Bert Basch, ed., Howard W. Sams & Co, 1987).

Ferrando, A.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Donor and acceptor guided modes in photonic crystal fibers,” Opt. Lett. 25, 1238–1330 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
[Crossref]

Gander, M. J.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

Jones, J. D. C.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

Knight, J. C.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

McBride, R.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

Miret, J. J.

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Donor and acceptor guided modes in photonic crystal fibers,” Opt. Lett. 25, 1238–1330 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
[Crossref]

Mogilevtsev, D.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

D. Mogilevtsev, T. A. Birks, and P. S. J. Russell, “Dispersion of photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[Crossref]

Monro, T. M.

Monsoriu, J. A.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

Richardson, D. J.

Russell, P. S. J.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

D. Mogilevtsev, T. A. Birks, and P. S. J. Russell, “Dispersion of photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[Crossref]

Silvestre, E.

Electron. Lett. (2)

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibers,” Electron. Lett. 35, 63–64 (1999).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, and P. S. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 24, 325–327 (1999).
[Crossref]

J. Lightwave Technol. (1)

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

Opt. Fib. Tech. (1)

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crys tal fibers : a new clas s of optical waveguides,” Opt. Fib. Tech. 5, 305–330 (1999).
[Crossref]

Opt. Lett. (5)

Other (1)

D. Davidson, Optical-Fiber Transmission (E. E. Bert Basch, ed., Howard W. Sams & Co, 1987).

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Figures (7)

Fig. 1.
Fig. 1. Transformations of the lattice structure with the dimensionless parameters f and M: (a) two structures with different filling fraction f and same magnification M (a/Λ≠a′/Λ); (b) two structures with different magnification M and same filling fraction f (a/Λ=a′/Λ).

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Fig. 2.
Fig. 2. Dependence of the geometrical dispersion curves on: (a) the magnification M; and (b) the filling fraction f.

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Fig. 3.
Fig. 3. The total dispersion D (red curve) is, in a first-order approximation, the result of substracting the sign-changed material dispersion -D m (black curve) from the geometrical dispersion D g (blue curve). A typical case exhibiting positive ultraflattened dispersion in the 1.55 µm window is obtained.

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Fig. 4.
Fig. 4. Ultraflattened dispersion behavior for three different PCF configurations near the communication window with: (a) positive dispersion (a=0.4 µm and Λ=3.12 µm); (b) nearly-zero dispersion (a=0.316 µm and Λ=2.62 µm); and (c) negative dispersion (a=0.27 µm and Λ=2.19 µm). The ultraflattened behavior bandwidth, that corresponds to an allowed dispersion variation of 2 psnm-1 km-1, is668 nm, 523nm, and 411nm, respectively.

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Fig. 5.
Fig. 5. As in Fig. 3 but for a typical case exhibiting positive flattened dispersion in the 0.8 µm window.

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Fig. 6.
Fig. 6. Flattened dispersion behavior for three different PCF configurations centered near the Ti-Za window at 0.8 µm: (a) with positive dispersion (a=0.28µm and Λ=0.88µm); (b) with nearly-zero dispersion (a=0.27µm and Λ=0.90µm); and (c) with negative dispersion (a=0.255µm and Λ=0.91µm). The allowed variation of the flattened dispersion profiles is 2 ps nm-1 km-1 and their corresponding flattened dispersion bandwidths are 58 nm, 57nm, and 59nm, respectively.

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Fig. 7.
Fig. 7. Four flattened dispersion curves corresponding to different values of the dispersion centered near 1.55 µm. With positive dispersion: (a) D≈+45 psnm -1 km-1 with a=0.49 µm and Λ=2.32 µm, and (b) D ≈ +22 psnm -1 km-1 with a=0.40 µm and Λ=2.71 µm. With negative dispersion: (c) D≈-23 psnm -1 km-1 with a=0.28 µm and Λ=2.16 µm, and (d) D≈-43 psnm -1 km-1 with a=0.27 µm and Λ=1.93 µm. The allowed variation of the flattened dispersion profiles is 2 ps nm-1 km-1 and their corresponding flattened dispersion bandwidths are 270nm, 294 nm, 259 nm, and 195nm, respectively.

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Equations (4)

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D ≡ − λ c d 2 n eff d λ 2 ,
D ( λ ) ≈ D g ( λ ) + D m ( λ ) .
D g ( λ ; M , f ) = 1 M D g ( λ M ; f ) .
D ( λ ) ≈ D g ( λ ) − ( − D m ( λ ) ) .

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