Abstract

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabrication tolerances.

© 2006 Optical Society of America

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References

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  1. A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
    [CrossRef]
  2. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 25, 790 (2000).
    [CrossRef]
  3. A. Ferrando, E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andrés, Opt. Express 9, 687 (2001).
    [CrossRef] [PubMed]
  4. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, Opt. Express 10, 609 (2002).
    [PubMed]
  5. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, Opt. Express 11, 843 (2003).
    [CrossRef] [PubMed]
  6. F. Poletti, V. Finazzi, T. M. Monro, N. G. T. Broderick, V. Tse, and D. J. Richardson, Opt. Express 13, 3728 (2005).
    [CrossRef] [PubMed]
  7. F. Poli, A. Cucinotta, M. Fouchi, S. Selleri, and L. Vincetti, J. Opt. Soc. Am. A 20, 1958 (2003).
    [CrossRef]
  8. L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
    [CrossRef]
  9. K. Saitoh and M. Koshiba, Opt. Express 13, 267 (2005).
    [CrossRef] [PubMed]
  10. J. M. Fini, Opt. Express 12, 4535 (2004).
    [CrossRef] [PubMed]
  11. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
  12. E. Silvestre, T. Pinheiro-Ortega, P. Andrés, J. J. Miret, and A. Ortigosa-Blanch, Opt. Lett. 30, 453 (2005).
    [CrossRef] [PubMed]
  13. E. Silvestre, M. V. Andrés, and P. Andrés, J. Lightwave Technol. 16, 923 (1998).
    [CrossRef]
  14. ''Corning(R) SMF-28 CPC6 Single-Mode Optical Fiber,'' Product Information (Corning, Ithaca, N.Y., 1998).

2005 (3)

2004 (1)

2003 (4)

A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, Opt. Express 11, 843 (2003).
[CrossRef] [PubMed]

F. Poli, A. Cucinotta, M. Fouchi, S. Selleri, and L. Vincetti, J. Opt. Soc. Am. A 20, 1958 (2003).
[CrossRef]

2002 (1)

2001 (2)

2000 (1)

1998 (2)

E. Silvestre, M. V. Andrés, and P. Andrés, J. Lightwave Technol. 16, 923 (1998).
[CrossRef]

''Corning(R) SMF-28 CPC6 Single-Mode Optical Fiber,'' Product Information (Corning, Ithaca, N.Y., 1998).

Andrés, M. V.

Andrés, P.

Bjarklev, A.

A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

Broderick, N. G. T.

Broeng, J.

A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

Chen, G. X.

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

Cucinotta, A.

Ferrando, A.

Finazzi, V.

Fini, J. M.

Fouchi, M.

Hasegawa, T.

Huang, W. P.

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

Jian, S. S.

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Knight, J. C.

Koshiba, M.

Miret, J. J.

Monro, T. M.

Ortigosa-Blanch, A.

Pinheiro-Ortega, T.

Poletti, F.

Poli, F.

Reeves, W. H.

Richardson, D. J.

Roberts, P. J.

Russell, P. St. J.

Saitoh, K.

Sánchez Bjarklev, A.

A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

Sasaoka, E.

Selleri, S.

Shen, L. P.

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

Silvestre, E.

Tse, V.

Vincetti, L.

IEEE Photon. Technol. Lett. (1)

L. P. Shen, W. P. Huang, G. X. Chen, and S. S. Jian, IEEE Photon. Technol. Lett. 15, 540 (2003).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (7)

Opt. Lett. (2)

Other (2)

A. Bjarklev, J. Broeng, and A. Sánchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

''Corning(R) SMF-28 CPC6 Single-Mode Optical Fiber,'' Product Information (Corning, Ithaca, N.Y., 1998).

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Figures (3)

Fig. 1
Fig. 1

Dispersion versus wavelength for the fundamental mode of the UFDF shown in the inset. The pitch is Λ = 2.103 μ m , and the radii of the inner and outer air holes are r 1 = 0.305 μ m and r 2 = 0.845 μ m , respectively.

Fig. 2
Fig. 2

Dispersion versus wavelength, corresponding to the BDCF (solid curve) shown in the inset. The values of the BDCF parameters that match the target dispersion (dashed curve) are Λ = 0.968 μ m , r 1 = 0.385 μ m , r 2 = 0.333 μ m , and r 3 = 0.410 μ m .

Fig. 3
Fig. 3

Sensitivity analysis corresponding to the BDCF design shown in Fig. 2.

Equations (8)

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L h t = β 2 h t ,
L = t t T + η ϵ ̂ tt η T { ω 2 c 2 η t [ ( ϵ ̂ 1 ) z z t T η ] } ,
( L β 2 ) h t + ( L β 2 ) h t = 0 ,
β = L ( 2 β ) ,
χ 2 [ P ] = λ { D [ P ] ( λ ) D target ( λ ) } 2 .
D [ P ] ( λ ) D [ P 0 ] ( λ ) + i = 1 N D [ P 0 ] p i ( λ ) ( p i p i , 0 ) ,
D M [ P ] ( λ ) 1 M { D [ P ] ( λ M ) D m ( λ M ) } + D m ( λ ) ,
σ D 2 ( D M [ P ] M ) 2 σ M 2 + i = 1 N ( D M [ P ] p i ) 2 σ p i 2 ,

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