Abstract

The cause of fundamental core-mode leakage in a tapered photonic crystal fiber is examined in terms of modal coupling from the core-mode to the ring modes. Experimental data are compared to predictions. The main features of the transmission are convincingly explained by the proposed model.

©2007 Optical Society of America

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References

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  1. P. V. Kaiser and H. W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal, 53,1021–1039 (1974).
  2. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21,1547–1549 (1996).
    [Crossref] [PubMed]
  3. B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9,698–713 (2001) http://www.opticsexpress.org/abstract.cfm?id=66901.
    [Crossref] [PubMed]
  4. H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
    [Crossref]
  5. J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
    [Crossref]
  6. G. E Town and J. T. Lizier, “Tapered holey fibers for spot-size and numerical-aperture conversion,” Opt. Lett. 26,1042–1044 (2001).
    [Crossref]
  7. H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Mägi, R. C. McPhedran, and B. J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30,1123–1125 (2005).
    [Crossref] [PubMed]
  8. B. T. Kuhlmey, H. C. Nguyen, M. J. Steel, and B. J. Eggleton, “Confinement loss in adiabatic photonic crystal fiber tapers,” J. Opt. Soc. Am. B 23,1965–1974 (2006).
    [Crossref]
  9. M. Koshiba and K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29,1739–1741 (2004).
    [Crossref] [PubMed]
  10. A. W. Snyder and J. D. Love, Optical waveguide theory, (Chapman and Hall, London, 1983).
  11. A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical couplers,” Electron. Lett. 21,864–865 (1985).
    [Crossref]
  12. S. Kawakami and S. Nishida, “Characteritics of a doubly clad optical fiber with a low-index inner cladding,” IEEE J. Quantum Electron. 10,879–887 (1974).
    [Crossref]
  13. J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).
  14. D. T. Cassidy, D. C. Johnson, and K. O. Hill, “Wavelength-dependent transmission of monomode optical fiber tapers,” Appl. Opt. 24,945–950 (1985).
    [Crossref] [PubMed]
  15. S. Lacroix, R. Bourbonnais, F. Gonthier, and J. Bures, “Tapered monomode optical fibers: understanding large power transfer,” Appl. Opt. 25,4421–4425 (1986).
    [Crossref] [PubMed]

2006 (1)

2005 (2)

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Mägi, R. C. McPhedran, and B. J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30,1123–1125 (2005).
[Crossref] [PubMed]

H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
[Crossref]

2004 (1)

2001 (3)

1996 (1)

1991 (1)

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

1986 (1)

1985 (2)

A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical couplers,” Electron. Lett. 21,864–865 (1985).
[Crossref]

D. T. Cassidy, D. C. Johnson, and K. O. Hill, “Wavelength-dependent transmission of monomode optical fiber tapers,” Appl. Opt. 24,945–950 (1985).
[Crossref] [PubMed]

1974 (2)

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

P. V. Kaiser and H. W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal, 53,1021–1039 (1974).

Astle, H. W.

P. V. Kaiser and H. W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal, 53,1021–1039 (1974).

Atkin, D. M.

Birks, T. A.

Black, R. J.

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

Boucouvalas, A. C.

A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical couplers,” Electron. Lett. 21,864–865 (1985).
[Crossref]

Bourbonnais, R.

Bures, J.

Cassidy, D. T.

Chandalia, J. K.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

Domachuk, P.

H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
[Crossref]

Eggleton, B. J.

Georgiou, G.

A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical couplers,” Electron. Lett. 21,864–865 (1985).
[Crossref]

Gonthier, F.

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

S. Lacroix, R. Bourbonnais, F. Gonthier, and J. Bures, “Tapered monomode optical fibers: understanding large power transfer,” Appl. Opt. 25,4421–4425 (1986).
[Crossref] [PubMed]

Hale, A.

Henry, W. M.

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

Hill, K. O.

Johnson, D. C.

Kaiser, P. V.

P. V. Kaiser and H. W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal, 53,1021–1039 (1974).

Kawakami, S.

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

Kerbage, C.

Knight, J. C.

Koshiba, M.

Kosinski, S. G.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

Kuhlmey, B. T.

Lacroix, S.

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

S. Lacroix, R. Bourbonnais, F. Gonthier, and J. Bures, “Tapered monomode optical fibers: understanding large power transfer,” Appl. Opt. 25,4421–4425 (1986).
[Crossref] [PubMed]

Liu, X.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

Lizier, J. T.

Love, J. D.

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

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

Mägi, E. C.

H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
[Crossref]

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Mägi, R. C. McPhedran, and B. J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30,1123–1125 (2005).
[Crossref] [PubMed]

McPhedran, R. C.

Nguyen, H. C.

Nishida, S.

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

Russell, P. St. J.

Saitoh, K.

Smith, C. L.

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Mägi, R. C. McPhedran, and B. J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30,1123–1125 (2005).
[Crossref] [PubMed]

H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
[Crossref]

Snyder, A. W.

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

Steel, M. J.

Stewart, W. J

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

Town, G. E

Westbrook, P. S.

Windeler, R. S.

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9,698–713 (2001) http://www.opticsexpress.org/abstract.cfm?id=66901.
[Crossref] [PubMed]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

Xu, C.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

H. C. Nguyen, B. T. Kuhlmey, E. C. Mägi, M. J. Steel, P. Domachuk, C. L. Smith, and B. J. Eggleton “Tapered photonic crystal fibres: properties, characterisation and applications,” Appl. Phys. B 81,377–387 (2005).
[Crossref]

Electron. Lett. (1)

A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical couplers,” Electron. Lett. 21,864–865 (1985).
[Crossref]

IEE Proc-J (1)

J. D. Love, W. M. Henry, W. J Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices, Part 1 : Adiabacity criteria,” IEE Proc-J 138,343–357 (1991).

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Tech. Lett. (1)

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu, “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photon. Tech. Lett. 13,52–54 (2001).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (4)

The Bell System Technical Journal (1)

P. V. Kaiser and H. W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal, 53,1021–1039 (1974).

Other (1)

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

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Figures (5)

Figure 1.
Figure 1. (a) SEM photograph of the Photonic Crystal Fiber (PCF) used in our experiments. The largest dimension of the fiber is measured to be 121μm; (b) Index profile of the equivalent Depressed Inner Cladding (DIC) fiber used for calculations.

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Figure 2.
Figure 2. (a) Effective indices n eff and (b) adiabacity criteria versus ITR for the DIC fiber profile shown in Fig. 1.(b). The calculations were made at λ=1550nm in the scalar approximation [10] using a finite difference scheme.

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Figure 3.
Figure 3. Photonic Crystal Fiber modal parameters: (a) index profile of the fiber used for calculation; (b) effective indices neff as function of the ITR parameter; (c) modal field profiles; (d) adiabacity criterion delineation curves as functions of the ITR parameter. The calculations used a finite difference scheme and were made at λ=1550nm.

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Figure 4.
Figure 4. (a) Transmission for the K, “L”, G, F, E and D modes calculated using the coupled equations formalism after propagation through the taper whose longitudinal profile is shown in (b).

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Figure 5.
Figure 5. (a) Transmission of a taper made from the PCF shown on Fig. 1.(a) versus elongation at 1550nm; (b) Transmission versus λ after the completion of the stretching process of that same taper; (c) Longitudinal profile and (d) the cleaved endface at the waist of the taper in (b).

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Equations (4)

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

C ¯ jℓ = k 2 2 ∣ β j β ℓ ∣ 1 2 ( β j − β ℓ ) ∫ A ∞ ( ∂ n 2 ∂ x x + ∂ n 2 ∂ y y ) ϕ ̂ j * ϕ ̂ ℓ dA
C jℓ = 1 ρ dρ dz C ¯ jℓ .
1 ρ dρ dz ≪ β j − β ℓ C ¯ jℓ .
d A F dz = 2 πi λ ( n eff ) F A F + C FG A G − C FE A E

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