Abstract

A photonic crystal fiber is optimized for chromatic dispersion compensation by using inner cladding modes. To this end, a photonic-oriented version of the downhill-simplex algorithm is employed. The numerical results show a dispersion profile that accurately compensates the targeted dispersion curve, as well as its dispersion slope. The presented fiber has a simple structure, while radiation losses can be reduced simply by adding a few more air-hole rings. Fabrication tolerances are also considered showing how fabrication inaccuracies effects can be overridden by just adjusting the compensation length.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
    [CrossRef] [PubMed]
  2. 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(18), 1328–1330 (2000).
    [CrossRef]
  3. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. S. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25(18), 1325–1327 (2000).
    [CrossRef]
  4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [CrossRef]
  5. E. Silvestre, T. Pinheiro-Ortega, P. Andrés, J. J. Miret, and A. Coves, “Differential toolbox to shape dispersion behavior in photonic crystal fibers,” Opt. Lett. 31(9), 1190–1192 (2006).
    [CrossRef] [PubMed]
  6. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25(11), 790–792 (2000).
    [CrossRef]
  7. A. Ferrando, E. Silvestre, P. Andrés, J. Miret, and M. Andrés, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 (2001).
    [CrossRef] [PubMed]
  8. W. Reeves, J. Knight, P. Russell, and P. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10(14), 609–613 (2002).
    [PubMed]
  9. B. Eggleton, P. Westbrook, C. White, C. Kerbage, R. Windeler, and G. Burdge, “Cladding-mode-resonances in air-silica microstructure optical fibers,” J. Lightwave Technol. 18(8), 1084–1100 (2000).
    [CrossRef]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.
  11. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005).
    [CrossRef] [PubMed]
  12. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
    [CrossRef]
  13. S. Cui, D. Liu, S. Yu, B. Huang, C. Ke, M. Zhang, and C. Liu, “Downhill simplex algorithm based approach to holey fiber design for tunable fiber parametric wavelength converters,” Opt. Express 18(10), 9831–9839 (2010).
    [CrossRef] [PubMed]
  14. Corning© LEAF© optical fiber. Product Information (Corning Inc., N.Y. 2009).
  15. K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
    [CrossRef]
  16. T. Fujisawa, K. Saitoh, K. Wada, and M. Koshiba, “Chromatic dispersion profile optimization of dual-concentric-core photonic crystal fibers for broadband dispersion compensation,” Opt. Express 14(2), 893–900 (2006).
    [CrossRef] [PubMed]
  17. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
    [CrossRef]
  18. A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230(7), 2369–2377 (2011).
    [CrossRef]

2011 (1)

A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230(7), 2369–2377 (2011).
[CrossRef]

2010 (1)

2006 (3)

2005 (1)

2002 (1)

2001 (1)

2000 (4)

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

1996 (3)

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

Andrés, M.

Andrés, M. V.

Andrés, P.

Arriaga, J.

Atkin, D. M.

Birks, T. A.

Broderick, N. G. R.

Burdge, G.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Coves, A.

Cui, S.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Eggleton, B.

Ferrando, A.

Finazzi, V.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.

Fujisawa, T.

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Ghatak, A.

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

Goyal, I.

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

Huang, B.

Johnson, S. G.

A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230(7), 2369–2377 (2011).
[CrossRef]

Ke, C.

Kerbage, C.

Knight, J.

Knight, J. C.

Koshiba, M.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

Liu, C.

Liu, D.

Mangan, B. J.

Miret, J.

Miret, J. J.

Monro, T. M.

Ortigosa-Blanch, A.

Oskooi, A.

A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230(7), 2369–2377 (2011).
[CrossRef]

Palai, P.

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

Pinheiro-Ortega, T.

Poletti, F.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

Reeves, W.

Richardson, D. J.

Roberts, P.

Russell, P.

Russell, P. S. J.

Saitoh, K.

Silvestre, E.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.

Thyagarajan, K.

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

Tse, V.

Varshney, R.

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.

Wada, K.

Wadsworth, W. J.

Westbrook, P.

White, C.

Windeler, R.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

Yu, S.

Zhang, M.

IEEE Photon. Technol. Lett. (1)

K. Thyagarajan, R. Varshney, P. Palai, A. Ghatak, and I. Goyal, “A novel design of a dispersion compensating fiber,” IEEE Photon. Technol. Lett. 8(11), 1510–1512 (1996).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

J. Comput. Phys. (1)

A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230(7), 2369–2377 (2011).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (5)

Opt. Lett. (5)

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

SIAM J. Optimiz. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder–mead simplex method in low dimensions,” SIAM J. Optimiz. 9(1), 112–147 (1998).
[CrossRef]

Other (2)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), chap. 10, pp. 408–412.

Corning© LEAF© optical fiber. Product Information (Corning Inc., N.Y. 2009).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Left, initial fiber structure used during the optimization process. Right, one of the LP11 modes used here for dispersion compensation and a fundamental mode, LP01, for illustration purposes.

Fig. 2
Fig. 2

Fitness function vs. number of iterations for the in-house (solid red) and the conventional (dashed blue) simplex algorithm.

Fig. 3
Fig. 3

(a) Residual dispersion for the optimized fiber with four (dashed red) and seven (solid blue) air-hole rings. (b) Radiation losses as a function of the additional rings included at the periphery of the cladding.

Fig. 4
Fig. 4

Residual chromatic dispersion for the optimized fiber (dashed red curve) delimited by the maximum deviations calculated for tolerances of (a) ±1% and (b) ±5% (dotted red curves). The residual dispersion was severely reduced by adjusting the free parameter X in Eq. (1) (solid blue bundled curves); differences between all the considered configurations can not be appreciated within these scales.

Equations (2)

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

χ 2 [ P ] = λ { D [ P ] ( λ ) + X D SMF ( λ ) } 2 ,
D [ M P ] ( λ ) 1 M { D [ P ] ( λ M ) D m ( λ M ) } + D m ( λ ) ,

Metrics