Abstract

This work reports a modified flame-brush technique to fabricate fiber tapers with arbitrary waist profiles. The flame-brush approach is used to produce small step reductions in the fiber diameter, or step-tapers, with a constant speed flame brush sweep, while the fiber is uniformly stretched. Arbitrary waist profiles in tapers are fabricated by approximating the taper diameter function to any monotonic function of the fiber length while combining a superposition of step-tapers. This method to produce the arbitrary profiles is described and a set of tapers with dissimilar transition regions are fabricated for its validation.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. 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]
  21. 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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2012 (2)

2011 (2)

C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express6, 1065–1076 (2011).
[CrossRef]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (1)

2007 (2)

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]

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]

2006 (2)

2004 (1)

2003 (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

2002 (1)

1998 (1)

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]

1996 (1)

R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys.80, 4804–4812 (1996).
[CrossRef]

1992 (1)

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

1989 (1)

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

1988 (1)

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

1981 (1)

Andersen, T. V.

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Baker, C.

C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express6, 1065–1076 (2011).
[CrossRef]

Bang, O.

S. T. Sørensen, U. Møller, C. Larsen, P. M. Moselund, C. Jakobsen, J. Johansen, T. V. Andersen, C. L. Thomsen, and O. Bang, “Deep-blue supercontinnum sources with optimum taper profiles – verification of GAM,” Opt. Express20, 10635–10645 (2012).
[CrossRef] [PubMed]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

Barton, G. W.

Bilodeau, F.

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

Birks, T. A.

Brambilla, G.

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]

Duan, Z.

Faucher, S.

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

Feng, X.

Finazzi, V.

Flannery, B. P.

William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, 2007).

Gao, W.

Garcia-Fernandez, R.

Gattass, R. R.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

George, A. K.

Giessen, H.

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.

He, S.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Hill, K. O.

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

B. S. Kawasaki, K. O. Hill, and R. G. Lamont, “Biconical-taper single-mode fiber coupler,” Opt. Lett.6, 327–328 (1981).
[CrossRef] [PubMed]

Horak, P.

Jakobsen, C.

Johansen, J.

Johnson, D. C.

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

Judge, A.

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

Jung, Y.

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]

Kawasaki, B. S.

Knight, J. C.

Koizumi, F.

Koukharenko, E.

Kudlinski, A.

Lamont, R. G.

Larsen, C.

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.

Lou, J.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Man, T. P. M.

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Miles, M. J.

R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys.80, 4804–4812 (1996).
[CrossRef]

Møller, U.

Moselund, P. M.

Murugan, G. S.

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.

Ortigosa-Blanch, A.

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]

Popov, S. V.

Press, William H.

William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, 2007).

Pricking, S.

Rauschenbeutel, A.

Richardson, D.

Richardson, D. J.

Rochette, M.

C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express6, 1065–1076 (2011).
[CrossRef]

Rulkov, A. B.

Russell, P. St. J.

Sessions, N. P.

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Sørensen, S. T.

S. T. Sørensen, U. Møller, C. Larsen, P. M. Moselund, C. Jakobsen, J. Johansen, T. V. Andersen, C. L. Thomsen, and O. Bang, “Deep-blue supercontinnum sources with optimum taper profiles – verification of GAM,” Opt. Express20, 10635–10645 (2012).
[CrossRef] [PubMed]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

Stiebeiner, A.

Suzuki, T.

Taylor, J. R.

Teukolsky, S. A.

William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, 2007).

Thomsen, C. L.

S. T. Sørensen, U. Møller, C. Larsen, P. M. Moselund, C. Jakobsen, J. Johansen, T. V. Andersen, C. L. Thomsen, and O. Bang, “Deep-blue supercontinnum sources with optimum taper profiles – verification of GAM,” Opt. Express20, 10635–10645 (2012).
[CrossRef] [PubMed]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

Tong, L.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

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.

Vetterling, W. T.

William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, 2007).

Wadsworth, W. J.

Wilkinson, J. S.

Williamson, R. L.

R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys.80, 4804–4812 (1996).
[CrossRef]

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]

Xu, F.

Xue, S.

Yan, X.

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]

Adv. Opt. Photon. (1)

Electron. Lett (1)

G. Brambilla, F. Xu, and X. Feng, “Fabrication of optical fibre nanowires and their optical and mechanical characterisation,” Electron. Lett42, 517–519 (2006).
[CrossRef]

J. Appl. Phys. (1)

R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys.80, 4804–4812 (1996).
[CrossRef]

J. Lightwave Technol. (3)

F. Bilodeau, K. O. Hill, S. Faucher, and D. C. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” J. Lightwave Technol.6, 1476–1482 (1988).
[CrossRef]

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

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

Nature (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426, 816–818 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

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 (7)

Opt. Lett (1)

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett36, 816–818. (2011).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Mater. Express (1)

C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express6, 1065–1076 (2011).
[CrossRef]

Photon. Technol. Lett. (1)

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]

SIAM J. Appl. Math. (1)

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 (1)

William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, 2007).

Supplementary Material (2)

» Media 1: MOV (2989 KB)     
» Media 2: MOV (6561 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Scheme representing the translation stages in the tapering process, with the velocities, VFB (flame-brush stage), VSL (left stretching stage) and VSR (right stretching stage) and black arrows showing their directions.

Fig. 2.
Fig. 2.

Normalized areas of the taper as a function of its length for step-tapers produced with a single flame-brush sweep at a speed of 7.5mm/s to the right, while the left stretching translation stage moves to the left with a speed of VSL of 12mm/min, 24mm/min, 48mm/min and 140mm/min.

Fig. 3.
Fig. 3.

Schematic diagram representing the taper with a linear transition and the variables used in the process, xn, x0, ZR and ZL, from which the distance law can be inferred.

Fig. 4.
Fig. 4.

The Fig. (a), (c) and (e) show the measured taper radius points (black scattered), and designed taper profile function (continuous line in blue) for the exponential-Gaussian, quadratic-sinusoidal and arc-sinusoidal-arc-sinusoidal taper profiles, respectively. The flame-brush length progression curves, Ln, are depicted on the right side of the corresponding taper profiles (continuous blue line) in Fig. (b), (d) and (f).

Fig. 5.
Fig. 5.

In (a), quadratic-arc-sinusoidal taper profile function produced with the data logged by the taper rig software using the stepwise method simulated with a sequence of step-tapers ( Media 1); in (b), simulation of the stepwise method by the algorithm using the fluid-dynamic model ( Media 2). Simulations use the parameters Lw = 30mm and rw = 31.25μm.

Fig. 6.
Fig. 6.

Measured and simulated errors as a function of the taper length for the left (a) and right (b) arc-sinusoidal-arc-sinusoidal transitions. The error is the difference between the designed function and the resulting simulated or measured values.

Tables (1)

Tables Icon

Table 1: Statistics of the error for the measured/simulated arc-sinusoidal-arc-sinusoidal taper.

Equations (15)

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

z ( 3 μ A u z ) = 0
A t + z ( u A ) = 0
x n = { x 0 + ( V S R + V S L ) T n 1 Z R ( A n ) Z L ( A n 1 ) , when flame - brush is moving to the right ; x 0 + ( V S R + V S L ) T n 1 Z L ( A n ) Z R ( A n 1 ) , when flame - brush is moving to the left .
L n = { x n + V S R Δ T ( L n ) , when flame - brush is moving to the right ; x n + V S L Δ T ( L n ) , when flame - brush is moving to the left .
Δ T ( L ) = t a + t d + ( L L a L d ) / V F B
A n = { ( V F B V S R V F B + V S L ) A n 1 , when flame - brush moves to the right ; ( V F B V S L V F B + V S R ) A n 1 , when flame - brush moves to the left .
L w n = { L n + V S L Δ T ( L n ) , when flame - brush moves to the right ; L n + V S R Δ T ( L n ) , when flame - brush moves to the left .
x 0 = Z L ( A w ) + Z R ( A w ) + L w
x 0 = x 0 = ( L w L w ) A w / A 0
z left ( r ) = 50 * ln ( r r 0 ) ln ( r w r 0 ) , for the left side transition .
z right ( r ) = 50 * [ ln ( r r 0 ) ln ( r w r 0 ) ] 0.5 , for the right side transition ;
z left ( r ) = 50 * ( 1 r r 0 ) 0.5 , for the left side transition .
z right ( r ) = 18 π 3 [ 6 π r r w r 0 r w + sin ( 4 π r r w r 0 r w ) ] , for the right side transition ;
z left ( r ) = 24 π 4 [ 6 π r r w r 0 r w + sin ( 4 π r r w r 0 r w ) ] , for the left side transition .
z right ( r ) = 15 π 2.5 [ 6 π r r w r 0 r w sin ( 4 π r r w r 0 r w ) ] , for the right side transition ;

Metrics