## Stepwise fabrication of arbitrary fiber optic tapers |

Optics Express, Vol. 20, Issue 18, pp. 19893-19904 (2012)

http://dx.doi.org/10.1364/OE.20.019893

Acrobat PDF (1864 KB)

### 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.

© 2012 OSA

## 1. Introduction

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

9. G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon. **1**, 107–161 (2009). [CrossRef]

10. 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]

11. A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express **14**, 5715–5722 (2006). [CrossRef] [PubMed]

12. S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express **18**, 20151–20163 (2010). [CrossRef] [PubMed]

12. S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express **18**, 20151–20163 (2010). [CrossRef] [PubMed]

13. A. Stiebeiner, R. Garcia-Fernandez, and A. Rauschenbeutel, “Design and optimization of broadband tapered optical fibers with a nanofiber waist,” Opt. Express **18**, 22677–22685 (2010). [CrossRef] [PubMed]

6. 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. Express **20**, 10635–10645 (2012). [CrossRef] [PubMed]

14. 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. Lett **36**, 816–818. (2011). [CrossRef] [PubMed]

17. C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express **6**, 1065–1076 (2011). [CrossRef]

## 2. Methodology

### 2.1. Experimental setup

*V*. The arrows in Fig. 1 indicate the possible directions of the movements performed by the translation stages.

_{FB}### 2.2. From the step-taper to the arbitrary taper

*s*, is defined as the ratio between the feed velocity,

*v*=

_{f}*V*−

_{FB}*V*, and the draw velocity,

_{SR}*v*=

_{d}*V*+

_{FB}*V*, where

_{SL}*V*and

_{SR}*V*are the constant speeds of the left and right translation stages (with pre-determined directions to the left and to the right, respectively) in the tapering process.

_{SL}17. C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express **6**, 1065–1076 (2011). [CrossRef]

#### 2.2.1. Tapering simulation

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]

*μ*=

*μ*(

*z*,

*t*), was considered as a function of the taper length,

*z*, assumed to have been calculated from an uncoupled heat transfer model. Such an assumption is only valid when the Nusselt number divided by the Péclet number is large, that is, when radiative heat loss dominates convection and conduction, that is the case in the tapering process. The model employed in the tapering simulation uses: The Eq. (1) describes the balance of forces in terms of the stress in the fiber, and the conservation is described in terms of continuity Eq. (2), where

*u*=

*u*(

*z*,

*t*) is the axial speed distribution and

*A*=

*A*(

*z*,

*t*) is the cross-sectional area of the hot-zone. The spatial coordinate was discretized using a previously proposed scheme[17

17. C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express **6**, 1065–1076 (2011). [CrossRef]

### 2.3. Modeling the tapering process

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

*V*, changing its direction after each

_{FB}*n*–th sweep and traveling a length of

*L*. The initial sweep has a length of

_{n}*L*

_{0}, and uses a length of fiber,

*x*

_{0}, that must provide a fiber volume which is sufficient for the taper fabrication. Its initialization is explained in the following sections.

*Z*(

_{R}*A*) and

*Z*(

_{L}*A*), determine the tapers transitions and return the distances from the transition beginning, which has a cross sectional area

*A*

_{0}and the point in the transition having cross sectional area

*A*, for the right and left transitions, respectively. They are used to elaborate the distance law for asymmetrical tapers. The cross sectional area of the flame-brushed fiber is

*A*after the

_{n}*n*–th flame-brush sweep. Thus, the burner starts its

*n*–th sweep in one of the transitions at the point having cross sectional area

*A*

_{n}_{−1}that is just leaving the waist region and entering the transition, and ends at a point in the other transition which must have final cross sectional area

*A*. The distance law can then be stated through Eq. (3):

_{n}15. T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. **10**, 432–438 (1992). [CrossRef]

*Z*(

_{R}*A*) and

*Z*(

_{L}*A*), and depends on the direction of the flame-brush movement.

*T*

_{n−1}is the duration of the first (

*n*− 1) flame-brush sweeps.

*x*

_{0}is initialized with a valid value and the direction of the first sweep is known, all subsequent movements of the flame-brush can be determined.

*x*

_{0}·

*A*

_{0}determines the volume of the fabricated taper, however only the shape of the transitions, the waist length and the waist diameter are given as input parameters. Firstly, it is considered that the volume of the transitions is constant and that the excess of volume outside the transition is the waist volume. By using

*x*′

_{0}as in Eq. (8), one can obtain a taper with waist length

*L*′

*, by using Eq. (3) to Eq. (7): This length is a final designed taper length, as a consequence this chosen*

_{w}*x*′

_{0}corresponds to a fiber that has a volume larger than the necessary volume to produce a taper with a given waist length

*L*. Now, a length of fiber

_{w}*x*

_{0}can be calculated that produces a taper with the designed waist length, namely: Since

*L*is given and

_{w}*x*′

_{0}was calculated by using once the algorithm, Eq. (9) produces an acceptable initialization to the free parameter

*x*

_{0}, that corresponds to a volume of a taper with input waist length

*L*.

_{w}### 2.4. The designed tapers

*z*(

_{right}*r*) or

*z*(

_{left}*r*), that are functions of the fiber radius,

*r*. After calculating the next area profile, from which the radius is obtained using Eq. (6), the distance that the flame-brush travels is calculated for the next sweep using Eq. (4) and the

*z*(

_{right}*r*) or

*z*(

_{left}*r*) function. It is clear that, for a cylindrical fiber,

*A*=

*πr*

^{2}, which gives

*z*(

_{right}*r*) =

*Z*(

_{R}*πr*

^{2}) and

*z*(

_{left}*r*) =

*Z*(

_{L}*πr*

^{2}). The resulting taper profiles were measured with a 2D Coordinate Measurement Geometry Calculation System (QM-DATA 200 - MITUTOYO).

#### 2.4.1. The Gaussian-exponential taper

*V*= 2.5mm/min towards the right while the left stretching stage was static. The taper had as input parameters a final waist length

_{SR}*L*= 20mm and a uniform waist radius

_{w}*r*= 12.5

_{w}*μ*m.

#### 2.4.2. The quadratic-arc-sinusoidal taper

*V*= 5mm/min towards the right while the left side stretching stage was static. The taper input parameters were a waist length of

_{SR}*L*= 15mm and a waist radius of

_{w}*r*= 12.5

_{w}*μ*m.

#### 2.4.3. The arc-sinusoidal-arc-sinusoidal taper

*z*(

_{left}*r*) and

*z*(

_{right}*r*) given by: The right translation stage had a speed value of

*V*= 2.5mm/min while the left stretching stage was static. The taper input parameters were a waist length of

_{SR}*L*= 10mm and a waist radius of

_{w}*r*= 12.5

_{w}*μ*m.

## 3. Results and discussion

*μ*m. The apparent outliers in the data set that deviate more than the uncertainty are supposedly corresponding to imperfections in the taper holders used to fix the fiber and translate it under the microscope objective lenses.

*r*= 31.25

_{w}*μ*m and their profile curves are shown in Fig. 5(a) and Fig. 5(b). In the video corresponding to Fig. 5(a) ( Media 1), the superposition of step-tapers is illustrated while creating the desired taper transition functions. The video used the same sequences of flame-brush sweeps with the calculated lengths as to produce the required taper. The superposition of single flame-brush sweeps was simulated by using the fluid-dynamic model ( Media 2) [21

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]

### 3.1. Errors in the fabrication

*ε*, obtained from the difference between the value of the designed transition function and the measured or simulated radii was calculated as a function of the taper length for the previously fabricated arc-sinusoidal-arc-sinusoidal taper. The error curves depicted in Fig. 6(a) and Fig. 6(b) have the statistics summarized in Table 1. The table contains the mean error

*ε̄*for the measured points, the ideal stepwise method and the fluid-dynamic model simulations, and also their corresponding standard deviations,

*σ*, for the left and right transitions.

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

*μ*m were fabricated with the used taper rig having losses of less than 0.5% in the transmitted signal. The exponential and linear profiles had the envelope of the

*L*functions as predicted by the ordinary flame-brush technique, namely constant and linearly increasing

_{n}*L*, with the addition that the course of the flame-brush was shifted towards the moving stretching stage.

_{n}*μ*m, decreasing with the diameter of the transition, as shown in Fig. 6(a) and Fig. 6(b) and summarized in Table 1. The measurement of the transition was performed using the 2D microscope which has an uncertainty larger than the standard deviation of the measured error. Its statistics shows a standard deviation around 1

*μ*m, therefore one would not be able to isolate the errors produced in the measurement with the microscope from the errors in the fabrication process. The theoretical results obtained from simulations indicate that the fabrication errors would be below 1

*μ*m on average for an oscillating transition function. The statistics from the simulated ideal method and the fluid dynamic model shows a much lower average error and standard deviation. It is important to notice that the error in fabrication decreases with the designed diameter and has peaks at the oscillations of the transition functions. This is an indication that transition functions that do not oscillate can be fabricated with smaller errors.

## 4. Conclusion

## Acknowledgments

## References and links

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. |

2. | B. S. Kawasaki, K. O. Hill, and R. G. Lamont, “Biconical-taper single-mode fiber coupler,” Opt. Lett. |

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,” Nature |

4. | G. Brambilla, V. Finazzi, and D. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express |

5. | G. Brambilla, F. Xu, and X. Feng, “Fabrication of optical fibre nanowires and their optical and mechanical characterisation,” Electron. Lett |

6. | 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. Express |

7. | M. Liao, W. Gao, Z. Duan, X. Yan, T. Suzuki, and Y. Ohishi, “Directly draw highly nonlinear tellurite microstructured fiber with diameter varying sharply in a short fiber length,”Opt. Express |

8. | R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys. |

9. | G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon. |

10. | 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 |

11. | A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express |

12. | S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express |

13. | A. Stiebeiner, R. Garcia-Fernandez, and A. Rauschenbeutel, “Design and optimization of broadband tapered optical fibers with a nanofiber waist,” Opt. Express |

14. | 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. Lett |

15. | T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. |

16. | L. C. Ozcan, V. Treanton, F. Guay, and R. Kashyap, “Highly symmetric optical fiber tapers fabricated with a CO2 laser,” Photon. Technol. Lett. |

17. | C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express |

18. | S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express |

19. | A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat transfer modelling in CO laser processing of optical fibres,” Opt. Commun. |

20. | S. Xue, M. van Eijkelenborg, G. W. Barton, and P. Hambley, “Theoretical, numerical, and experimental analysis of optical fiber tapering,” J. Lightwave Technol. |

21. | J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math. |

22. | William H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2310) Fiber optics and optical communications : Fiber optics

(060.2340) Fiber optics and optical communications : Fiber optics components

(060.2370) Fiber optics and optical communications : Fiber optics sensors

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: April 26, 2012

Revised Manuscript: July 2, 2012

Manuscript Accepted: July 6, 2012

Published: August 15, 2012

**Citation**

Alexandre Felipe, Guilherme Espíndola, Hypolito J. Kalinowski, José A. S. Lima, and Aleksander S. Paterno, "Stepwise fabrication of arbitrary fiber optic tapers," Opt. Express **20**, 19893-19904 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-19893

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### References

- 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]
- 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]
- G. Brambilla, V. Finazzi, and D. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express12, 2258–2263 (2004). [CrossRef] [PubMed]
- G. Brambilla, F. Xu, and X. Feng, “Fabrication of optical fibre nanowires and their optical and mechanical characterisation,” Electron. Lett42, 517–519 (2006). [CrossRef]
- 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]
- M. Liao, W. Gao, Z. Duan, X. Yan, T. Suzuki, and Y. Ohishi, “Directly draw highly nonlinear tellurite microstructured fiber with diameter varying sharply in a short fiber length,”Opt. Express20, 1141–1150 (2012). [CrossRef] [PubMed]
- R. L. Williamson and M. J. Miles, “Melt-drawn scanning near-field optical microscopy probe profiles,” J. Appl. Phys.80, 4804–4812 (1996). [CrossRef]
- G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon.1, 107–161 (2009). [CrossRef]
- 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. B19, 2148–2155 (2002). [CrossRef]
- A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express14, 5715–5722 (2006). [CrossRef] [PubMed]
- S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express18, 20151–20163 (2010). [CrossRef] [PubMed]
- A. Stiebeiner, R. Garcia-Fernandez, and A. Rauschenbeutel, “Design and optimization of broadband tapered optical fibers with a nanofiber waist,” Opt. Express18, 22677–22685 (2010). [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]
- T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992). [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]
- 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. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express18, 3426–3437 (2010). [CrossRef] [PubMed]
- 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]
- 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. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989). [CrossRef]
- 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).

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