Abstract

We present a generalized heat-brush tapering approach in which the ratio of the feed and draw velocities changes within each tapering sweep. This approach allows for controlled and precise shaping of tapers with an arbitrary waist profile and dissimilar transition regions as demonstrated experimentally. A quantitative analysis of the mismatch error after each tapering sweep is also provided.

© 2011 OSA

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References

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  1. P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, and G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett.18, 1996–1998 (1993).
    [CrossRef] [PubMed]
  2. C. Baker and M. Rochette, “Highly nonlinear hybrid AsSe-PMMA microtapers,” Opt. Express18, 12391–12398 (2010).
    [CrossRef] [PubMed]
  3. A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical fibre coupler,” Electron. Lett.21, 864–865 (1985).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett.22, 320–321 (1986).
    [CrossRef]
  6. S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron.18, 1580–1583 (1982).
    [CrossRef]
  7. J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986).
    [CrossRef]
  8. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
    [CrossRef]
  9. T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992).
    [CrossRef]
  10. F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.
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    [CrossRef]
  12. Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992).
    [CrossRef]
  13. H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.
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    [CrossRef]
  15. L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
    [CrossRef]
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    [CrossRef]
  17. J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. A. Alkadery and M. Rochette, “Widely tunable soliton shifting for mid-infrared applications,” in IEEE Photonics Conference 2011 (IPC2011) (2011).
  26. N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
    [CrossRef]
  27. S. Chapra and R. Canale, Numerical Methods for Engineers, 5th ed. (McGraw-Hill, 2005).
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    [CrossRef]
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2011

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

2010

2009

2008

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

2007

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

S. Xue, M. van Eijkelenborg, G. W. Barton, and P. Hambley, “Theoretical, numerical, and experimental analysis of optical fiber tapering,” J. Lightwave Technol.25, 1169–1176 (2007).
[CrossRef]

2006

2004

1998

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in co laser processing of optical fibres,” Opt. Commun.152, 324–328 (1998).
[CrossRef]

1993

1992

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992).
[CrossRef]

Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992).
[CrossRef]

1991

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991).
[CrossRef]

1989

J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
[CrossRef]

1986

J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986).
[CrossRef]

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett.22, 320–321 (1986).
[CrossRef]

1985

1982

S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

1976

F. Geyling, “Basic fluid dynamic consideration in the drawing of optical fibers,” Bell Sys. Tech. J.55, 1011–1056 (1976).

1972

Alkadery, A.

A. Alkadery and M. Rochette, “Widely tunable soliton shifting for mid-infrared applications,” in IEEE Photonics Conference 2011 (IPC2011) (2011).

Baker, C.

Bang, O.

Barton, G. W.

Bilodeau, F.

F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.

Birks, T.

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express12, 2864–2869 (2004).
[CrossRef] [PubMed]

Birks, T. A.

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992).
[CrossRef]

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991).
[CrossRef]

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. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

Boucouvalas, A. C.

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

Brambilla, G.

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

Broderick, N.

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

Bures, J.

Canale, R.

S. Chapra and R. Canale, Numerical Methods for Engineers, 5th ed. (McGraw-Hill, 2005).

Chapra, S.

S. Chapra and R. Canale, Numerical Methods for Engineers, 5th ed. (McGraw-Hill, 2005).

Cormen, T. H.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

de Sterke, C. M.

Dewynne, J.

J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
[CrossRef]

Dumais, P.

Eggleton, B. J.

Faucher, S.

F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.

George, A. K.

Georgiou, G.

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

Geyling, F.

F. Geyling, “Basic fluid dynamic consideration in the drawing of optical fibers,” Bell Sys. Tech. J.55, 1011–1056 (1976).

Giessen, H.

Gonthier, F.

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, and G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett.18, 1996–1998 (1993).
[CrossRef] [PubMed]

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

Grellier, A. J. C.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in co laser processing of optical fibres,” Opt. Commun.152, 324–328 (1998).
[CrossRef]

Guay, F.

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

Hambley, P.

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. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986).
[CrossRef]

Hill, K.

F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.

Hill, K. O.

Jensen, S.

S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

Johnson, D.

F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.

Johnson, D. C.

Judge, A. C.

Kashima, Y.

H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.

Kashyap, R.

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

Kenny, R. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991).
[CrossRef]

Kito, C.

Knight, J. C.

Kudlinski, A.

Kuhlmey, B. T.

Lacroix, S.

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, and G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett.18, 1996–1998 (1993).
[CrossRef] [PubMed]

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

Lamont, R. G.

Leiserson, C. E.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

Leon-Saval, S.

Li, Y. W.

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992).
[CrossRef]

Liao, M.

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. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986).
[CrossRef]

Mägi, E. C.

Mason, M.

Mori, A.

Noda, J.

Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992).
[CrossRef]

Oakley, K. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991).
[CrossRef]

Ockendon, J. R.

J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
[CrossRef]

Ohishi, Y.

Ozcan, L. C.

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

Pannell, C. N.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in co laser processing of optical fibres,” Opt. Commun.152, 324–328 (1998).
[CrossRef]

Pant, R.

Petrovich, M.

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

Popov, S. V.

Pricking, S.

Qin, G.

Rivest, R. L.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

Rochette, M.

C. Baker and M. Rochette, “Highly nonlinear hybrid AsSe-PMMA microtapers,” Opt. Express18, 12391–12398 (2010).
[CrossRef] [PubMed]

A. Alkadery and M. Rochette, “Widely tunable soliton shifting for mid-infrared applications,” in IEEE Photonics Conference 2011 (IPC2011) (2011).

Rulkov, A. B.

Russell, P. S. J.

Sasaki, Y.

H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.

Snyder, A. W.

Stegeman, G. I.

Stein, C.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

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. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

Sugai, E.

H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.

Sun, W.

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

Suzuki, T.

Takeuchi, Y.

Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992).
[CrossRef]

Taylor, J. R.

Travers, J. C.

Treanton, V.

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

van Eijkelenborg, M.

Villeneuve, A.

Vukovic, N.

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

Wadsworth, W.

Wigley, P. G. J.

Wilmott, P.

J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
[CrossRef]

Wright, J. V.

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett.22, 320–321 (1986).
[CrossRef]

Xue, S.

Yan, X.

Yokota, H.

H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.

Yuan, M.

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

Zayer, N. K.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in co laser processing of optical fibres,” Opt. Commun.152, 324–328 (1998).
[CrossRef]

Zeng, X.

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

Appl. Opt.

Bell Sys. Tech. J.

F. Geyling, “Basic fluid dynamic consideration in the drawing of optical fibers,” Bell Sys. Tech. J.55, 1011–1056 (1976).

Electron. Lett.

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

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett.22, 320–321 (1986).
[CrossRef]

J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986).
[CrossRef]

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991).
[CrossRef]

IEE Proc.-J: Optoelectron.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” IEE Proc.-J: Optoelectron.138, 343–354 (1991).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Quantum Electron.

S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

Opt. Commun.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in co laser processing of optical fibres,” Opt. Commun.152, 324–328 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Optoelectron. Lett.

W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett.7, 154–157 (2011).
[CrossRef]

Photon. Technol. Lett.

L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett.19, 656–658 (2007).
[CrossRef]

Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992).
[CrossRef]

N. Vukovic, N. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” Photon. Technol. Lett.20, 1264–1266 (2008).
[CrossRef]

SIAM J. Appl. Math.

J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989).
[CrossRef]

Other

H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.

F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in Optical Fiber Sensors, (Optical Society of America, 1988), p. ThCC10.

S. Chapra and R. Canale, Numerical Methods for Engineers, 5th ed. (McGraw-Hill, 2005).

A. Alkadery and M. Rochette, “Widely tunable soliton shifting for mid-infrared applications,” in IEEE Photonics Conference 2011 (IPC2011) (2011).

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

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Figures (13)

Fig. 1
Fig. 1

Schematic of a fiber taper with a uniform waist and similar transition regions.

Fig. 2
Fig. 2

(a) A taper profile and (b) the resulting tapering function.

Fig. 3
Fig. 3

Flow-chart of the simulation program for the single-sweep tapering setup presented in Section 2.3. In this flow-chart, x is the displacement of both translation stages extending the fiber, y is the displacement of the heater translation stage, xprevious and yprevious are state variables, δ is a differential feed step, s is the tapering function, ld is the drawing length, and Δz is the longitudinal separation between any two consecutive diameter sampling points.

Fig. 4
Fig. 4

Single-sweep simulation schematics of (a) shifting the hot-zone by Δz, and (b) extension of the fiber by 2Δz.

Fig. 5
Fig. 5

Simulation of step-taper fabrication using the single-sweep tapering method.

Fig. 6
Fig. 6

(a) Percent overshoot, and (b) settling distance dependence on the inverse tapering ratio at different hot-zone lengths for the step-taper.

Fig. 7
Fig. 7

Simulated fabrication results of taper profiles with linear transition regions at different slopes using the single-sweep tapering method.

Fig. 8
Fig. 8

Schematic of the experimental implementation of the single-sweep tapering method.

Fig. 9
Fig. 9

Experimentally measured profiles of (a) a step taper, and (b) an arbitrary taper fabricated using the single-sweep tapering method.

Fig. 10
Fig. 10

Schematic of taper profile evolution using the multi-sweep tapering method.

Fig. 11
Fig. 11

Dividing the taper into sections for the determination of the tapering function of each tapering stage.

Fig. 12
Fig. 12

Percent overshoot and maximum percent overshoot versus the number of tapering sweeps n for a step-taper with ρ = 0.4 using Lhz = 3 mm.

Fig. 13
Fig. 13

Experimental results showing the profile of an As2Se3 taper fabricated using the multi-sweep tapering method with n = 24.

Equations (13)

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s ( l d ) = ϕ 2 ( z ) ϕ 0 2 | z = l d .
z ( 3 μ A u z ) = 0 ,
A t + z ( u A ) = 0 ,
[ F i 0.25 ( F i + 1 F i 1 ) ] u ¯ i 1 2 F i u ¯ i + [ F i + 0.25 ( F i + 1 F i 1 ) ] u ¯ i + 1 = 0
A i n e w = A i [ A i ( u ¯ i + 1 u ¯ i 1 ) + u ¯ i ( A i + 1 A i 1 ) ]
v y ( l d ) = v d ( l d ) + v f ( l d ) 2 = α 2 [ 1 s ( l d ) + 1 ] ,
v x ( l d ) = v w ( l d ) = v d ( l d ) v f ( l d ) 2 = α 2 [ 1 s ( l d ) 1 ] .
L j = z j l e f t z j r i g h t ϕ 2 ( z ) d z ϕ j 2 ,
ϕ o s ( j ) = [ 1 ɛ o s ( ρ j ) / 100 % ] × ρ j × ϕ o s ( j 1 )
ϕ o s ( 1 ) = [ 1 ɛ o s ( ρ 1 ) / 100 % ] × ρ 1 × ϕ 0 ,
ϕ o s ( j ) = [ 1 ɛ o s ( t ) / 100 % ] j × r j × ϕ 0 ,
ɛ o s , m a x ( n ) = [ 1 ( 1 ɛ o s ( r ) / 100 % ) n ] × 100 % ,
T = L 0 v f m a x × 1 ρ 2 1 ρ 2 / n ,

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