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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  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. M¨agi, 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. M¨agi, 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)

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.

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]

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]

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]

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).

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]

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, 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. M¨agi, 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]

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.

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.

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.

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).

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).

Equations (4)

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C ¯ jℓ = k 2 2 β j β 1 2 ( β j β ) A ( n 2 x x + n 2 y y ) ϕ ̂ j * ϕ ̂ dA
C jℓ = 1 ρ dz C ¯ jℓ .
1 ρ dz β j β 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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