Abstract

We present a two-dimensional modal approach for the evaluation, in an analytical manner, of chromatic dispersion in any kind of optical fiber. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical procedure to calculate its derivatives. The proposed formulation takes into account the effective anisotropy of the interfaces and allows us to deal with microstructured fibers, in general, and specifically with realistic photonic crystal fibers (PCFs), including arbitrary spatial refractive-index distributions of dispersive and absorbing materials. This fast and accurate numerical technique is extremely useful for both analysis and design. We show some results of analysis of PCFs with high anisotropy, and we also describe PCFs with new dispersive properties.

© 2005 Optical Society of America

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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. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
    [CrossRef]
  3. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 24, 276 (1999).
    [CrossRef]
  4. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
    [CrossRef] [PubMed]
  5. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, Opt. Lett. 25, 1328 (2000).
    [CrossRef]
  6. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 25, 790 (2000).
    [CrossRef]
  7. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, Opt. Express 10, 609 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  8. A. Ferrando, E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andrés, Opt. Express 9, 687 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  9. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, Opt. Express 11, 843 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  10. J. Lægsgaard, A. Bjarklev, and S. E. Barkou Libori, J. Opt. Soc. Am. B 20, 443 (2003).
    [CrossRef]
  11. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  12. E. Silvestre, M. V. Andrés, and P. Andrés, J. Lightwave Technol. 16, 923 (1998).
    [CrossRef]
  13. A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
    [CrossRef]

2004 (1)

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

2003 (2)

2002 (1)

2001 (2)

2000 (2)

1999 (2)

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 24, 276 (1999).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

1998 (2)

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

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

1996 (1)

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Andrés, M. V.

Andrés, P.

Atkin, D. M.

Barkou, S. E.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

Barkou Libori, S. E.

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

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

Bjarklev, A.

J. Lægsgaard, A. Bjarklev, and S. E. Barkou Libori, J. Opt. Soc. Am. B 20, 443 (2003).
[CrossRef]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

Broeng, J.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Cruz, J. L.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

Delgado-Pinar, M.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

Díez, A.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

Ferrando, A.

Hasegawa, T.

Joannopoulos, J. D.

Johnson, S. G.

Knight, J. C.

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, Opt. Express 10, 609 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

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

Koshiba, M.

Lægsgaard, J.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Miret, J. J.

Ortigosa-Blanch, A.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

Reeves, W. H.

Roberts, P. J.

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, Opt. Express 10, 609 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Russell, P. St. J.

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, Opt. Express 10, 609 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

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

Saitoh, K.

Sasaoka, E.

Silvestre, E.

IEEE Photon. Technol. Lett. (1)

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, IEEE Photon. Technol. Lett. 16, 1667 (2004).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, Opt. Commun. 156, 240 (1998).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Science (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Variation of group index with wavelength for the two components of the polarization doublet that form the fundamental mode of the birefringent PCF shown in the inset. Circles correspond to the analytical evaluation with Eq. (2) of ng at eight wavelengths. We obtained both curves by interpolating the values of β calculated at the same wavelengths and by subsequent derivation.

Fig. 2
Fig. 2

Dispersion D and relative dispersion slope (RDS), dD/dλ/D, that correspond to a triangular PCF with lattice period Λ=2.700 µm and airhole radius a=0.281 µm. Solid curves are the results of the conventional approach (interpolation of β calculated at seven wavelengths and subsequent double derivation); dashed curves, a semianalytical procedure [interpolation of β1 evaluated analytically with Eq. (2) and subsequent derivation]; circles, analytical evaluation of β2 with Eq. (3) at the same wavelengths. RDS curves that correspond to the analytical and to the semianalytical procedures cannot be differentiated in this figure.

Fig. 3
Fig. 3

Flattened, anomalous dispersion centered near 1.55 µm for triangular PCFs with the following values for lattice period Λ and airhole radius a: (a) Λ=1.050 µm and a=0.230 µm; (b) Λ=0.778 µm and a=0.236 µm; (c) Λ=0.653 µm and a=0.257 µm. Solid curves are the results of the semianalytical approach (see the caption to Fig. 2). Circles correspond to the pure analytical method.

Equations (5)

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

Lht=β2ht,
L=ttT+ηˆttηTω2c2-ηtˆ-1zztTη,
β1β·=L·/2β,
β2β̈=1βL̈2-β·2-L·βLβ-1L·β,
L·βLβ-1L·β=-h˜tL·βh·th˜tht.

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