Abstract

We establish that Microstructured Optical Fibers (MOFs) have a fundamental mode cutoff, marking the transition between modal confinement and non-confinement, and give insight into the nature of this transition through two asymptotic models that provide a mapping to conventional fibers. A small parameter space region where neither of these asymptotic models holds exists for the fundamental mode but not for the second mode; we show that designs exploiting unique MOF characteristics tend to concentrate in this preferred region.

© 2002 Optical Society of America

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References

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  1. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
    [Crossref] [PubMed]
  2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999).
    [Crossref]
  3. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [Crossref]
  4. 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]
  5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
    [Crossref]
  6. W. H. Reeves, J. C. Knight, and P. St. J. Russell,“Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609.
    [Crossref] [PubMed]
  7. B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.
  8. T. A. Birks, J. C. Knight, and P. St. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [Crossref] [PubMed]
  9. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
    [Crossref]
  10. R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbìldt, K. G¤bel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001)
    [Crossref]
  11. A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [Crossref] [PubMed]
  12. J. P. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002).
    [Crossref]
  13. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
    [Crossref]
  14. B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
    [Crossref]
  15. T. P. White, R. C. McPhedran, C. M. de Sterke, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
    [Crossref]
  16. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-341.
    [Crossref] [PubMed]
  17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002).
    [Crossref]
  18. G. W. Milton, The Theory of Composites (Cambridge University Press, 2002).
    [Crossref]
  19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).
  20. J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
    [Crossref]
  21. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
    [Crossref]
  22. T. Monro, P. J. Bennett, N. G. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000).
    [Crossref]

2002 (6)

2001 (3)

2000 (5)

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (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]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

T. Monro, P. J. Bennett, N. G. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000).
[Crossref]

1999 (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

1998 (2)

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
[Crossref]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

1997 (1)

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

Andrés, P.

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

Bennett, P. J.

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
[Crossref]

T. A. Birks, J. C. Knight, and P. St. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

Botten, L. C.

Brechet, F.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Broderick, N. G.

Broderick, N. G. R.

Coen, S.

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

de Sandro, J. P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
[Crossref]

de Sterke, C. M.

Dudley, J. P.

Eggleton, B. J.

Ferrando, A.

G¤bel, K.

Grossard, N.

Hänsch, T. W.

Herrmann, J.

A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Holzwarth, R.

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Knight, J. C.

W. H. Reeves, J. C. Knight, and P. St. J. Russell,“Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609.
[Crossref] [PubMed]

R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbìldt, K. G¤bel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001)
[Crossref]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
[Crossref]

T. A. Birks, J. C. Knight, and P. St. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

Kuhlmey, B.

B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.

Kuhlmey, B. T.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Maillotte, H.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

Marcou, J.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Maystre, D.

McPhedran, R. C.

Milton, G. W.

G. W. Milton, The Theory of Composites (Cambridge University Press, 2002).
[Crossref]

Miret, J. J.

Monro, T.

Monro, T. M.

Mortensen, N. A.

Ortigosa-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

Pagnoux, D.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Poprawe, R.

Provino, L.

Ranka, J. K.

Reeves, W. H.

Renversez, G.

Richardson, D. J.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

Roy, P.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Russbìldt, P.

Russel, P.S.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

Russell, P. S.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

Russell, P. St.

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998).
[Crossref]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

T. A. Birks, J. C. Knight, and P. St. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

Russell, P. St. J.

Silvestre, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Steel, M. J.

Stentz, A. J.

Udem, Th.

Wadsworth, W. J.

R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbìldt, K. G¤bel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001)
[Crossref]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

White, T. P.

Windeler, R. S.

Zimmermann, M.

Electron. Lett. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

IEEE Photonic Tech. Lett. (1)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (4)

Opt. Express (2)

Opt. Fiber Technol. (1)

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Opt. Lett. (7)

Phys. Rev. Lett. (1)

A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Science (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[Crossref] [PubMed]

Other (3)

B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.

G. W. Milton, The Theory of Composites (Cambridge University Press, 2002).
[Crossref]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

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Figures (3)

Fig. 1.
Fig. 1.

Operation regimes of MOFs. Lower right inset: cross section of a MOF with 3 rings of holes. Other insets: asymptotic models for large (CF1) and small (CF2) wavelengths. The shaded transition region represents the parameter subspace where MOFs cannot be described by either asymptotic model and therefore behave most unlike conventional optical fibers. Data sets are described in the text.

Fig. 2.
Fig. 2.

A: Imaginary part of n eff as a function of wavelength on pitch, rescaled by (λ/Λ)2, for a silica structure with 3 layers of holes, with d/Λ taking the values 0.075 (top curve), 0.15, 0.3, 0.45, 0.6, 0.75, 0.8 and 0.85. B: Imaginary (thin curves) and real (thick curves) part of n eff as a function of fiber radius N r Λ divided by λ for MOFs with d/Λ=0.3, for 4 (red), 6 (blue) and 8 (green) rings of holes, and for the corresponding homogenized fiber (black). All calculations in this report were done for varying pitch at fixed λ=1.55μm, where the losses in dB/m are given by 3.52×107Im(n eff).

Figure 3:
Figure 3:

Width of the transition between the large wavelength asymptotic regime (CF1) and the intermediate regime as a function of Nrb, for the fundamental mode (A, b f≈ 2.97) and the second mode (B, b 2≈ 1.55). For the second mode the width of the intermediate regime tends to zero with increasing number of rings, whereas a finite transition region remains for the fundamental mode, even for N r→∞.

Equations (4)

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

n ¯ z = [ f n air 2 + ( 1 f ) n m 2 ] 1 2 , ( Extraordinary index )
n ¯ n m [ ( T f ) ( T + f ) ] 1 2 , ( Ordinary index )
where T = ( n m 2 + n air 2 ) ( n m 2 n air 2 ) .
n FSM = n m n 2 ( λ Λ ) 2

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