Abstract

Using a novel computational method, the fundamental mode in index-guided microstructured optical fibers with genuinely infinite cladding is studied. It is shown that this mode has no cut-off, although its area grows rapidly when the wavelength crosses a transition region. The results are compared with those for w-fibers, for which qualitatively similar results are obtained.

©2005 Optical Society of America

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References

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  1. A.W. Snyder and J.D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).
  2. A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic crystal fibers (Kluwer, Boston, 2003).
    [Crossref]
  3. B.T. Kuhlmey, R.C. McPhedran, and C.M. de Sterke, “Modal ‘cutoff’ in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
    [Crossref]
  4. B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
    [PubMed]
  5. S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.
  6. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
    [Crossref]
  7. S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” J. Quantum Electron. 10, 879–887 (1974).
    [Crossref]
  8. M. Koshiba and K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29, 1739–1741 (2004).
    [Crossref] [PubMed]
  9. T.A. Birks, J.C. Knight, and P.St .J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [Crossref] [PubMed]
  10. 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]
  11. R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).
  12. M. Yan and P. Shum, “Antiguiding in microstructured optical fibers,” Opt. Express12, 104–116 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-104.
    [Crossref] [PubMed]

2004 (1)

2003 (1)

2002 (1)

2001 (1)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

1999 (1)

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

1997 (1)

1974 (1)

S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” J. Quantum Electron. 10, 879–887 (1974).
[Crossref]

Asatryan, A. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

Asatryan, A.A.

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

Birks, T.A.

Bjarklev, A.

A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic crystal fibers (Kluwer, Boston, 2003).
[Crossref]

Bjarklev, A.S.

A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic crystal fibers (Kluwer, Boston, 2003).
[Crossref]

Botten, L. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

Botten, L.C.

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

Broeng, J.

A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic crystal fibers (Kluwer, Boston, 2003).
[Crossref]

de Sterke, C.M.

B.T. Kuhlmey, R.C. McPhedran, and C.M. de Sterke, “Modal ‘cutoff’ in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
[Crossref]

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

Folkenberg, J.R.

Hansen, K.P.

Kawakami, S.

S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” J. Quantum Electron. 10, 879–887 (1974).
[Crossref]

Knight, J.C.

Koshiba, M.

Kuhlmey, B.T.

B.T. Kuhlmey, R.C. McPhedran, and C.M. de Sterke, “Modal ‘cutoff’ in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
[Crossref]

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

Love, J.D.

A.W. Snyder and J.D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).

Martijn de Sterke, C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

Maystre, D.

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

McPhedran, R. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

McPhedran, R.C.

B.T. Kuhlmey, R.C. McPhedran, and C.M. de Sterke, “Modal ‘cutoff’ in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
[Crossref]

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

Mortensen, N.A.

Nicorovici, N. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

Nicorovici, N.A.

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

Nielsen, M.D.

Nishida, S.

S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” J. Quantum Electron. 10, 879–887 (1974).
[Crossref]

Poulton, C.G.

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

Renversez, G.

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

Robinson, P.A.

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

Russell, P.St .J.

Saitoh, K.

Shum, P.

M. Yan and P. Shum, “Antiguiding in microstructured optical fibers,” Opt. Express12, 104–116 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-104.
[Crossref] [PubMed]

Snyder, A.W.

A.W. Snyder and J.D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).

Wilcox, S.

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

Yan, M.

M. Yan and P. Shum, “Antiguiding in microstructured optical fibers,” Opt. Express12, 104–116 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-104.
[Crossref] [PubMed]

Aust. J. Phys. (1)

R.C. McPhedran, L.C. Botten, A.A. Asatryan, N.A. Nicorovici, C.M. de Sterke, and P.A. Robinson, “Ordered and disordered photonic bandgap materials,” Aust. J. Phys. 52, 791–809 (1999).

J. Quantum Electron. (1)

S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” J. Quantum Electron. 10, 879–887 (1974).
[Crossref]

Opt. Lett. (4)

Phys. Rev. E (1)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603:1-20 (2001).
[Crossref]

Other (5)

M. Yan and P. Shum, “Antiguiding in microstructured optical fibers,” Opt. Express12, 104–116 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-104.
[Crossref] [PubMed]

A.W. Snyder and J.D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).

A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic crystal fibers (Kluwer, Boston, 2003).
[Crossref]

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where is the edge?,” Opt. Express10, 1285–1291 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

S. Wilcox, L.C. Botten, R.C. McPhedran, C.G. Poulton, and C.M. de Sterke, “Exact modelling of defect modes in photonic crystals,” in press, Phys. Rev. E.

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Figures (3)

Fig. 1.
Fig. 1. Parameter U versus V for (a) MOF with parameters given in the text. Solid curve refers to a structure with infinite cladding. The three closed circles correspond to wavelengths λ=0.25Λ, 0.15Λ and 0.05Λ from left to right. The open circles correspond to the wavelengths indicated. The long (short)-dashed curve is the equivalent result for a MOF with a finite cross section with five (three) rings of holes. Dotted curve, included for convenience, gives U=V. (b) Same as (a) but for a conventional geometry with parameters given in the text. The points indicated by the circles in (a) have no equivalent here.

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Fig. 2.
Fig. 2. Axial Poynting vector for a MOF with finite cross section with three rings of holes (top row), and an infinite cross section (bottom row), for V=1.55 (λ/Λ=0.133), V=1.23 (λ/Λ=0.50), V=0.79 (λ/Λ=1.1), and V=0.58 (λ/Λ=1.6) for the first, second, third and fourth columns, respectively. The small circles indicate the air holes.

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Fig. 3.
Fig. 3. Axial Poynting vector for a w-fiber (top row), and a step-index fiber with infinite cladding (bottom row), for V=1.55,1.23,0.79,0.58 for the first, second, third and fourth column, respectively. The cladding’s inner and outer edges are indicated by white circles.

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Equations (3)

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V ≡ 2 π λ ρ n co 2 − n cl 2 = 2 π λ Λ 3 n b 2 − n fsm 2 ,
U ≡ 2 π λ ρ n co 2 − n eff 2 = 2 π λ Λ 3 n b 2 − n eff 2 ,
( K 0 ( k ⊥ r 1 ⁄ 2 ) K 0 ( k ⊥ ρ ) ) 2 = 0.5 ,

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