Abstract

In this paper we evaluate the cut-off properties of holey fibers (HFs) with a triangular lattice of air holes and the core formed by the removal of a single (HF1) or more air holes (HF3 and HF7). With the aid of finite-element simulations we determine the single-mode and multi-mode phases and also find the air hole diameters limiting the endlessly single-mode regime. From calculations of V and W parameters we find that in general HF1 is less susceptible to longitudinal non-uniformities compared to the other designs for equivalent effective areas. As an example we illustrate this general property for the particular case of a macro-bending induced loss.

© 2005 Optical Society of America

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References

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  1. J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
    [CrossRef] [PubMed]
  2. T. A. Birks, J. C. Knight, and P. S. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  3. M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, "Singlemode photonic crystal fibre with effective area of 600 µm2 and low bending loss," Electron. Lett. 39, 1802-1803 (2003).
    [CrossRef]
  4. M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibers," Opt. Express 12, 1775-1779 (2004).
    [CrossRef] [PubMed]
  5. M. D. Nielsen, J. R. Folkenberg, N. A. Mortensen, and A. Bjarklev, "Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers," Opt. Express 12, 430-435 (2004).
    [CrossRef] [PubMed]
  6. J. R. Folkenberg, M. D. Nielsen, N. A. Mortensen, C. Jakobsen, and H. R. Simonsen, "Polarization maintaining large mode area photonic crystal fiber," Opt. Express 12, 956-960 (2004).
    [CrossRef] [PubMed]
  7. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, "Broadband single-polarization photonic crystal fiber," Opt. Lett. 30, 1446-1448 (2005).
    [CrossRef] [PubMed]
  8. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, "Improved large-mode-area endlessly single-mode photonic crystal fibers," Opt. Lett. 28, 393-395 (2003).
    [CrossRef] [PubMed]
  9. J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, "Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier," Opt. Express 12, 1313-1319 (2004).
    [CrossRef] [PubMed]
  10. N. A. Mortensen, "Effective area of photonic crystal fibers," Opt. Express 10, 341-348 (2002).
    [PubMed]
  11. B. T. Kuhlmey, R. C. Mcphedran, and C. M. de sterke, "Modal cutoff in microstructured optical," Opt. Lett. 27, 1684-1686 (2002).
    [CrossRef]
  12. K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
    [CrossRef]
  13. 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]
  14. M. Koshiba, "Full-vector analysis of photonic crystal fibers using the finite element method," IEICE Trans. Electron. 85-C, 881-888 (2002).
  15. G. Renversez, F. Bordas, and B.T. Kuhlmey, "Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size," Opt. Lett. 30, 1264-1266 (2005).
    [CrossRef] [PubMed]
  16. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
    [CrossRef] [PubMed]
  17. M. D. Nielsen and N. A. Mortensen, "Photonic crystal fiber design based on the V-parameter," Opt. Express 11, 2762-2768 (2003).
    [CrossRef] [PubMed]
  18. M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 1739-1741 (2004).
    [CrossRef] [PubMed]
  19. K. Saitoh and M. Koshiba, "Empirical relations for simple design of photonic crystal fibers," Opt. Express 13, 267-274 (2005).
    [CrossRef] [PubMed]
  20. M. Koshiba and K. Saitoh, "Simple evaluation of confinement losses in holey fibers," Opt. Commun. 253, 95-98 (2005).
    [CrossRef]
  21. N. A. Mortensen and J. R. Folkenberg, "Low-loss criterion and effective area considerations for photonic crystal fibres," J. Opt. A-Pure Appl. Opt. 5, 163-167 (2003).
    [CrossRef]
  22. Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express 13, 4770-4779 (2005).
    [CrossRef] [PubMed]
  23. J. Riishede, N. A. Mortensen, and J. Lægsgaard, "A ‘poor man’s approach’ to modelling micro-structured optical fibres," J. Opt. A-Pure Appl. Opt. 5, 534-538 (2003).
    [CrossRef]
  24. N. A. Mortensen, "Semianalytical approach to short-wavelength dispersion and modal properties of photonic crystal fibers," Opt. Lett. 30, 1455-1457 (2005).
    [CrossRef] [PubMed]
  25. J. Olszewski, M. Szpulak, and W. Urbañczyk, "Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers," Opt. Express 13, 6015-6022 (2005).
    [CrossRef] [PubMed]

Electron. Lett.

M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, "Singlemode photonic crystal fibre with effective area of 600 µm2 and low bending loss," Electron. Lett. 39, 1802-1803 (2003).
[CrossRef]

IEEE J. Quantum Electron.

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

IEICE Trans. Electron.

M. Koshiba, "Full-vector analysis of photonic crystal fibers using the finite element method," IEICE Trans. Electron. 85-C, 881-888 (2002).

J. Opt. A-Pure Appl. Opt.

N. A. Mortensen and J. R. Folkenberg, "Low-loss criterion and effective area considerations for photonic crystal fibres," J. Opt. A-Pure Appl. Opt. 5, 163-167 (2003).
[CrossRef]

J. Riishede, N. A. Mortensen, and J. Lægsgaard, "A ‘poor man’s approach’ to modelling micro-structured optical fibres," J. Opt. A-Pure Appl. Opt. 5, 534-538 (2003).
[CrossRef]

Opt. Commun.

M. Koshiba and K. Saitoh, "Simple evaluation of confinement losses in holey fibers," Opt. Commun. 253, 95-98 (2005).
[CrossRef]

Opt. Express

N. A. Mortensen, "Effective area of photonic crystal fibers," Opt. Express 10, 341-348 (2002).
[PubMed]

M. D. Nielsen and N. A. Mortensen, "Photonic crystal fiber design based on the V-parameter," Opt. Express 11, 2762-2768 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, J. R. Folkenberg, N. A. Mortensen, and A. Bjarklev, "Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers," Opt. Express 12, 430-435 (2004).
[CrossRef] [PubMed]

J. R. Folkenberg, M. D. Nielsen, N. A. Mortensen, C. Jakobsen, and H. R. Simonsen, "Polarization maintaining large mode area photonic crystal fiber," Opt. Express 12, 956-960 (2004).
[CrossRef] [PubMed]

J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, "Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier," Opt. Express 12, 1313-1319 (2004).
[CrossRef] [PubMed]

M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibers," Opt. Express 12, 1775-1779 (2004).
[CrossRef] [PubMed]

K. Saitoh and M. Koshiba, "Empirical relations for simple design of photonic crystal fibers," Opt. Express 13, 267-274 (2005).
[CrossRef] [PubMed]

Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express 13, 4770-4779 (2005).
[CrossRef] [PubMed]

J. Olszewski, M. Szpulak, and W. Urbañczyk, "Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers," Opt. Express 13, 6015-6022 (2005).
[CrossRef] [PubMed]

Opt. Fiber Technol.

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.

B. T. Kuhlmey, R. C. Mcphedran, and C. M. de sterke, "Modal cutoff in microstructured optical," Opt. Lett. 27, 1684-1686 (2002).
[CrossRef]

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, "Improved large-mode-area endlessly single-mode photonic crystal fibers," Opt. Lett. 28, 393-395 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

G. Renversez, F. Bordas, and B.T. Kuhlmey, "Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size," Opt. Lett. 30, 1264-1266 (2005).
[CrossRef] [PubMed]

J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, "Broadband single-polarization photonic crystal fiber," Opt. Lett. 30, 1446-1448 (2005).
[CrossRef] [PubMed]

N. A. Mortensen, "Semianalytical approach to short-wavelength dispersion and modal properties of photonic crystal fibers," Opt. Lett. 30, 1455-1457 (2005).
[CrossRef] [PubMed]

M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 1739-1741 (2004).
[CrossRef] [PubMed]

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

T. A. Birks, J. C. Knight, and P. S. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Cut-off properties in a λ c /Λ versus d/Λ phase-diagram for HF1, HF3, and HF7. The open data points are the FEM results while the solid curves show the predictions from Eq. (1) with V c )=2.405.

Fig. 2.
Fig. 2.

Impact of the number of air-hole rings on the value of Δn=neff (2nd mode)-nFSM , where neff (2nd mode) is the effective index of the second order mode.

Fig. 3.
Fig. 3.

Plot of the V and W parameters versus Aeff 2 for air-hole diameters corresponding to the endlessly single-mode limit.

Fig. 4.
Fig. 4.

Macro-bending loss for HF1 and HF3 with equivalent effective area of Aeff = 200 μm2 at λ = 1.55 μm. The structural parameters are Λ = 12.4 μm and d/Λ = 0.424 for HF1 and Λ = 7.0 μm and d/Λ = 0.165 for HF3, respectively. Macro-bending loss for HF3 with Λ = 7.25 μm and d/Λ = 0.25 is also plotted.

Tables (1)

Tables Icon

Table 1. Table of central fiber parameters.

Equations (2)

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V = k a eff n co 2 n FSM 2 ,
W = k a eff n eff 2 n FSM 2 .

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