Abstract

We investigate the evolution of the propagation mode and the group velocity dispersion in the taper region and analyze its contribution to the nonlinearity of tapered fibers, which is important for a comprehensive understanding of the light propagation characteristics and the mechanisms supporting the supercontinuum generation in tapered fibers.

© 2004 Optical Society of America

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References

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  1. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, �??Supercontinuum generation in tapered fibers,�?? Opt. Lett. 25, 1415-1417 (2000).
    [CrossRef]
  2. J. M. Harbold, F. �?. Ilday, F. W. Wise, T. A. Birks, W. J. Wadsworth, and Z. Chen, �??Long-wavelength continuum generation about the second dispersion zero of a tapered fiber,�?? Opt. Lett. 27, 1558-1560 (2002).
    [CrossRef]
  3. A.V. Husakou and J. Herrmann, �??Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,�?? Phys. Rev. Lett. 85, 203901 (2001).
    [CrossRef]
  4. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, �??Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,�?? Phys. Rev. Lett. 88, 173901 (2002).
    [CrossRef] [PubMed]
  5. J. Teipel, K. Franke, D. Tuerke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, �??Characteristics of supercontinuum generation in tapered fibers using femtosecond laser pulses,�?? Appl. Phys. B 77, 245-250 (2003).
    [CrossRef]
  6. R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, �??Group velocity dispersion of tapered fibers immersed in different liquids,�?? Opt. Express 12, 1700-1708 (2004).
    [CrossRef] [PubMed]
  7. J. Teipel and H. Giessen, �??Tapered fiber femtosecond optical parametric oscillator,�?? presented at CLEO/QELS, Baltimore, Maryland, USA, 1-6 June (2003), Paper CMO3.
  8. A. W. Snyder, and J. D. Love, �??Optical waveguide theory,�?? (London, 1983). Chapter 12-15.
  9. 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: Adiabaticity Criteria,�?? IEEE Proceedings-J, 138, 343-354 (1991) .
  10. M. Monerie, �??Propagation in Doubly Clad Single-mode Fibers,�?? IEEE Trans. Microwave Theory Techniques MTT-30, 381-388 (1982).
    [CrossRef]
  11. A. J. Fielding, K. Edinger, and C. C. Davis, �??Experimental Observation of Mode Evolution in Single-Mode Tapered Optical Fibers,�?? J. Lightwave Technol. 17, 1649-1656 (1999).
    [CrossRef]
  12. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, �??Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,�?? J. Opt. Soc. Am. B 19, 2148-2155 (2002).
    [CrossRef]
  13. F. Warken and H. Giessen, �??Fast profile measurement of micrometer-sized tapered fibers with better than 50-nm accuracy,�?? Opt. Lett. 29, 1727-1729 (2004).
    [CrossRef] [PubMed]
  14. R. J. Black and R. Bourbonnais, �??Core-mode cutoff for finite-cladding lightguides,�?? IEEE Proceedings-J, 133, 377-384 (1986).
  15. G. P. Agrawal, Nonlinear Fiber Optics �?? Optics and Photonics, Third Edition, 2001, Academic Press.

Appl. Phys. B

J. Teipel, K. Franke, D. Tuerke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, �??Characteristics of supercontinuum generation in tapered fibers using femtosecond laser pulses,�?? Appl. Phys. B 77, 245-250 (2003).
[CrossRef]

IEEE 1991

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: Adiabaticity Criteria,�?? IEEE Proceedings-J, 138, 343-354 (1991) .

IEEE Trans. Microwave Theory Techniques

M. Monerie, �??Propagation in Doubly Clad Single-mode Fibers,�?? IEEE Trans. Microwave Theory Techniques MTT-30, 381-388 (1982).
[CrossRef]

IEEE-J 1986

R. J. Black and R. Bourbonnais, �??Core-mode cutoff for finite-cladding lightguides,�?? IEEE Proceedings-J, 133, 377-384 (1986).

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A.V. Husakou and J. Herrmann, �??Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,�?? Phys. Rev. Lett. 85, 203901 (2001).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, �??Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,�?? Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Other

J. Teipel and H. Giessen, �??Tapered fiber femtosecond optical parametric oscillator,�?? presented at CLEO/QELS, Baltimore, Maryland, USA, 1-6 June (2003), Paper CMO3.

A. W. Snyder, and J. D. Love, �??Optical waveguide theory,�?? (London, 1983). Chapter 12-15.

G. P. Agrawal, Nonlinear Fiber Optics �?? Optics and Photonics, Third Edition, 2001, Academic Press.

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Figures (7)

Fig. 1.
Fig. 1.

Radial profile along the input tapered fiber.

Fig. 2.
Fig. 2.

The evolution of the radial distribution of intensity along the input taper region of SMF 28 fused silica tapered fiber (at 800 nm).

Fig. 3.
Fig. 3.

The evolution of the radial distribution of intensity along the taper at (a) 500 nm and (b)1064 nm.

Fig. 4.
Fig. 4.

The evolution of (a) effective area and (b) nonlinear parameter γ along the SMF 28 fused silica fiber.

Fig. 5.
Fig. 5.

The evolution of (a) effective area and (b) nonlinear parameter γ, obtained by the variational calculation and the calculation of standard Bessel differential equation, respectively.

Fig. 6.
Fig. 6.

The evolution of the GVD along a tapered SMF 28 fused silica fiber, with a wai diameter of 1.8 µm, pumped at (a) 1024 nm, (b) 880 nm and (c) 800 nm. The black d

Fig. 7.
Fig. 7.

The evolution of GVD, estimated by (a) the vector Maxwell equation (solid) and the scalar equation (dotted) and (b) the cladding-air vector equation (dotted) and the core-cladding-air vector equation (solid). The hatched area denotes the region where the difference between the equations is less than 1% and the wavelength is 800 nm.

Equations (8)

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r 2 2 ψ r 2 + r ψ r + [ r 2 ( n 2 k 0 2 n eff 2 k 0 2 ) m 2 ] ψ = 0 ,
r cladding ( μ m ) = 1.9 + 67.8 · exp ( z 4.7 ) ,
1 = r core 2 k 0 2 e ( r core w ) 2 ( n core 2 n cladding 2 ) + r 2 2 k 0 2 e ( r cladding w ) 2 ( n cladding 2 n air 2 ) ,
D = 2 π c λ 2 d 2 β d ω 2 ,
( E z 1 H z 1 ) = ( A 1 A 2 ) J m ( k 0 n core 2 n eff 2 · r ) ( sin m ϕ cos m ϕ ) ,
( E z 2 H z 2 ) = ( B 1 B 2 ) I m ( k 0 n eff 2 n cladding 2 · r ) ( sin m ϕ cos m ϕ ) + ( C 1 C 2 ) K m ( k 0 n eff 2 n cladding 2 · r ) ( sin m ϕ cos m ϕ ) .
( E z 2 H z 2 ) = ( B 1 B 2 ) J m ( k 0 n cladding 2 n eff 2 · r ) ( sin m ϕ cos m ϕ ) + ( C 1 C 2 ) Y m ( k 0 n cladding 2 n eff 2 · r ) ( sin m ϕ cos m ϕ ) ,
( E z 3 H z 3 ) = ( D 1 D 2 ) K m ( k 0 n eff 2 n air 2 · r ) ( sin m ϕ cos m ϕ ) ,

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