## A generalized heat-brush approach for precise control of the waist profile in fiber tapers |

Optical Materials Express, Vol. 1, Issue 6, pp. 1065-1076 (2011)

http://dx.doi.org/10.1364/OME.1.001065

Acrobat PDF (1251 KB)

### 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

## 1. Introduction

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. Express **18**, 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]

4. R. G. Lamont, D. C. Johnson, and K. O. Hill, “Power transfer in fused biconical-taper single-mode fiber couplers: dependence on external refractive index,” Appl. Opt. **24**, 327–332 (1985). [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]

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

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

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

_{2}Laser [13–15

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]

16. 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]

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]

18. S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express **18**, 3426–3437 (2010). [CrossRef] [PubMed]

19. 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]

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]

*s*=

*v*/

_{f}*v*, where

_{d}*v*is the feed velocity and

_{f}*v*is the draw velocity, is constant throughout each tapering sweep. A constant

_{d}*s*limits the lowest inverse tapering ratio

*ϕ*is the waist diameter after sweep

_{j}*j*, that can be used in each sweep [21

21. S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express **12**, 2864–2869 (2004). [CrossRef] [PubMed]

*ρ*is less than 0.97 [11

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

*s*to change as the heater sweeps along the brushing-zone, and hence, the taper shape is carved within each sweep rather than having a sudden change in diameter. Just as in the heat-brush approach, the generalized heat-brush approach allows for precise shaping of the transition regions [11

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

21. S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express **12**, 2864–2869 (2004). [CrossRef] [PubMed]

*ρ*in each sweep as well as controlled fabrication of tapers with an arbitrary waist profile and dissimilar transition regions [18

18. S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express **18**, 3426–3437 (2010). [CrossRef] [PubMed]

*ρ*in each sweep reduces the number of sweeps required in the tapering process, and hence, reduces the taper fabrication duration. Replacing the uniform waist profile by one that follows an arbitrary function provides additional freedom in taper design and widens the range of taper applications. For example, a nonuniform waist profile in tapered fibers shifts the zero-dispersion wavelength along the microtaper waist for extended and flat supercontinuum generation [22

22. 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]

23. G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Zero-dispersion-wavelength-decreasing tellurite microstructured fiber for wide and flattened supercontinuum generation,” Opt. Lett. **35**, 136–138 (2010). [CrossRef] [PubMed]

24. A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B **26**, 2064–2071 (2009). [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]

_{2}Se

_{3}chalcogenide taper with a linearly decreasing waist profile and dissimilar transition regions.

## 2. Single-sweep tapering

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]

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]

*ϕ*(

*t*) is the taper diameter,

*ϕ*

_{0}is the initial fiber diameter, and

*s*(

*t*) =

*v*(

_{f}*t*)/

*v*(

_{d}*t*) is the tapering function. To draw a taper with a predefined profile

*ϕ*(

*z*), the tapering function

*s*(

*t*) must be determined accordingly. The replacement of the time variable

*t*by the drawing length

*v*(

_{d}*l*) =

_{d}*v*(

_{f}*l*)/

_{d}*s*(

*l*). In this case, the tapering function

_{d}*s*(

*l*) is calculated from the taper profile

_{d}*ϕ*(

*z*) using Figure 2 provides an arbitrary taper profile

*ϕ*(

*z*) and its corresponding tapering function

*s*(

*l*).

_{d}### 2.1. Single-sweep tapering simulations

*L*) [17

_{hz}**49**, 983–990 (1989). [CrossRef]

*μ*(

*z,t*) is the viscosity distribution,

*u*(

*z,t*) is the axial velocity distribution, and

*A*(

*z,t*) is the cross-sectional area in the hot-zone [17

**49**, 983–990 (1989). [CrossRef]

*μ*is independent of

*u*, and hence, Eq. (1) leads to

*∂ū*/

*∂z*×

*∂F/∂z*+

*F*×

*∂*

^{2}

*ū*/

*∂z*

^{2}= 0, where

*ū*=

*u/v*is the normalized axial velocity and

_{d}*F*=

*μA*. Using the centered differentiation formulas [27]

*∂F/∂z*= (

*F*

_{i}_{+1}–

*F*

_{i–}_{1})/2Δ

*z*,

*∂ū*/

*∂z*= (

*ū*

_{i}_{+1}–

*ū*

_{i−1})/2Δ

*z*, and

*∂*

^{2}

*ū*/

*∂z*

^{2}= (

*ū*

_{i+1}− 2

*ū*

_{i}+

*ū*

_{i−1})/Δ

*z*

^{2}leads to the finite difference form of Eq. (1) where

*F*=

_{i}*F*(

*l*,

_{d}*z*),

_{i}*ū*=

_{i}*ū*(

*l*,

_{d}*z*), and Δ

_{i}*z*is the separation between any two consecutive

*z*. Changing the variable

_{i}*t*to

*l*in Eq. (2) leads to the equation

_{d}*v*+

_{d}∂A/∂l_{d}*∂*(

*uA*)/

*∂z*= 0, which is expanded and divided by

*v*to obtain

_{d}*∂A/∂l*+

_{d}*A∂ū*/

*∂z*+

*ū∂A/∂z*= 0. Using the centered differentiation formulas

*∂ū*/

*∂z*= (

*ū*

_{i+1}−

*ū*

_{i−1})/2Δ

*z*,

*∂A/∂z*= (

*A*

_{i+1}–

*A*

_{i−1})/2Δ

*z*and the forward differentiation formula [27]

*l*= 2Δ

_{d}*z*is given by where

*A*=

_{i}*A*(

*l*,

_{d}*z*),

_{i}*ϕ*taken at points

_{k}*z*with any two consecutive points separated by Δ

_{k}*z*. The hot-zone is a subarray of the taper array and the starting point of the hot-zone subarray can change to simulate a moving heater as illustrated in Fig. 4(a). The cross-section area in the hot-zone is given by

*A*where

_{i}*i*= 1, 2,...,

*N*and the cross-section area of the extended hot-zone that results from drawing the hot-zone, as illustrated in Fig. 4(b), is calculated as follows: first, Eq. (3) is used with the boundary conditions

*ū*

_{i=0}= −1/2 and

*ū*

_{i=N+1}= 1/2 to calculate the normalized axial velocity distribution

*ū*in the hot-zone, and then, Eq. (4) is used to calculate the extended hot-zone profile. In the simulations that follow, the hot-zone is assumed to have a uniform viscosity distribution.

_{i}*ɛ*(

*z*) = [

*ϕ*(

_{r}*z*) –

*ϕ*(

_{t}*z*)]/

*ϕ*(

_{t}*z*) × 100% where

*ϕ*is the resulting taper diameter and

_{r}*ϕ*is the targeted taper diameter. The transient response is quantified by the percent overshoot

_{t}*ɛ*= (

_{os}*ϕ*–

_{t}*ϕ*)/

_{os}*ϕ*× 100% where

_{t}*ϕ*is the overshoot diameter, and by the settling distance

_{os}*z*defined as the distance between the beginning of the waist and the point where the envelope of the absolute percent error is less than

_{s}*ɛ*= 2%.

_{s}*ɛ*and

_{os}*z*represent the closeness of the of the resulting taper shape to the taper design, and the overall mismatch is reduced by reducing

_{s}*ɛ*and

_{os}*z*. Step-taper simulation results in Fig. 6 show

_{s}*ɛ*and

_{os}*z*as a function of

_{s}*L*and the inverse tapering ratio

_{hz}*ρ*=

*ϕ*/

_{min}*ϕ*

_{0}, where

*ϕ*is the minimum taper diameter. As expected,

_{min}*ɛ*and

_{os}*z*decrease with increasing

_{s}*ρ*(≤ 1) and shortening

*L*. With respect to optical propagation in the taper, the overshoot in the waist diameter acts as a perturbation that may lead to coupling between the fundamental mode and higher order modes, radiation modes, or reflection modes [28

_{hz}28. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. **62**, 1267–1277 (1972). [CrossRef]

*ɛ*and

_{os}*z*also represents the strength and the length of the perturbation region; therefore, a lower

_{s}*ɛ*and a shorter

_{os}*z*reduces the perturbation impact.

_{s}### 2.2. Single-sweep tapering optimization

*ɛ*and

_{os}*z*decrease when

_{s}*ρ*→ 1 and

*L*→ 0 mm. However, applications such as the enhancement of the waveguide nonlinearity or the sensitivity require microtapers with a waist diameter on the order of 1 μm drawn from fibers with a diameter on the order of 100 μm leading to

_{hz}*ρ*∼ 0.01. Also,

*L*is on the order of 1 mm and is limited by the temperature distribution in the fiber and the heater dimensions. Moreover, it turns out that

_{hz}*ɛ*and

_{os}*z*decrease when the taper slope decreases. As an example, Fig. 7 shows that as the slope decreases from 0.0105 to 0.0035,

_{s}*ɛ*decreases from 8.8% to 3.8% and

_{os}*z*decreases from 13.5 mm to 11.65 mm. In most cases, however, it is desirable to use the largest slope allowed by the adiabaticity criteria because using a small taper slope to reduce

_{s}*ɛ*and

_{os}*z*leads to a long transition region and consequently increases the sensitivity of the taper to environmental variations [9

_{s}9. T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. **10**, 432–438 (1992). [CrossRef]

*ɛ*and

_{os}*z*are reduced by tapering a fiber over multiple sweeps leading to an implementation of the generalized heat-brush approach.

_{s}### 2.3. Experimental setup

*v*and two other translation stages pull the fiber from opposite directions at equal velocities

_{y}*v*and

_{w}*v*. Using

_{x}*v*=

_{d}*v*+

_{y}*v*and

_{w}*v*=

_{f}*v*–

_{y}*v*=

_{x}*α*, where

*α*is a constant, the velocities of the heater and the translation stages pulling on the fiber at a drawing length

*l*=

_{d}*y*+

*w*are

### 2.4. Single-sweep tapering experimental results

_{2}Se

_{3}fiber with an initial diameter of 170 μm using a 5 mm long resistive heater at 210° C with

*v*=0.72 mm/min and

_{f}## 3. Multi-sweep tapering

*n*sweeps, the taper profile is divided into subsections as shown in Fig. 11, where

*ϕ*is the minimum taper diameter, and

_{n}*ϕ*

_{1}to

*ϕ*

_{n–1}are the waist diameters for all intermediate tapering sweeps and are calculated using

*ϕ*=

_{j}*rϕ*

_{j−1}with

*r*=

*ρ*

^{1/n}and

*ρ*=

*ϕ*

_{n}/

*ϕ*

_{0}. For every sweep

*j*<

*n*, the stage tapering function

*s*

^{(j)}(

*l*) is calculated from the stage taper profile

_{p}*ϕ*

^{(j)}(

*z*) composed of a left transition region extracted from

*ϕ*(

*z*) between

*ϕ*(

*z*) between

*L*makes the mass volume of the waist at stage

_{j}*j*equal to the mass volume required to draw the taper section between

*ϕ*

^{(}

^{n}^{)}(

*z*) is extracted from

*ϕ*(

*z*) between

*s*

^{(}

^{n}^{)}(

*l*). Finally, for each stage

_{p}*j*, a single tapering sweep is performed using the calculated stage tapering function and then the heater is moved back a distance

### 3.1. Quantitative analysis of multi-sweep tapering

*j*is estimated using the recurrence relation where

*ɛ*(

_{os}*ρ*) is provided in Fig. 6(a). By setting the inverse tapering ratio for all sweeps to

_{j}*r*, the worst-case overshoot diameter becomes and the maximum percent overshoot at the end of tapering is which is simplified to

*ɛ*(

_{os}*r*) ≤ 1%. It is clear from Fig. 6(a) that

*n*increases. For, example, the fabrication of a step-taper with

*ρ*= 0.5 over a single sweep using a 4 mm long hot-zone leads to

*ɛ*(0.5) = 17%. However, when tapering is performed over 6 sweeps with

_{os}*r*= 0.89 and

*ɛ*(0.89) = 0.5%, the maximum percent overshoot is

_{os}*j*is

*n*sweeps is which is reduced by increasing

*n*. In general, to keep the tapering duration at a minimum,

*n*is selected to be the minimum number of sweeps required to keep

*ɛ*bellow a certain prescribed value.

_{os}### 3.2. Reduced mismatch in the transition regions using multi-sweep tapering

*ϕ*, the diameter step is Δ

*ϕ*= (1 –

*ρ*)

*ϕ*and the taper slope is approximated by

*∂ϕ*/

*∂z*≈ Δ

*ϕ*/Δ

*z*leading to Δ

*z*≈ (1 −

*ρ*)

*ϕ*/(

*∂ϕ*/

*∂z*). Setting

*L*≪ |Δ

_{hz}*z*| does not decrease the mismatch because the diameter steps in the transition region become more prominent; in fact, setting

*L*≳ |Δ

_{hz}*z*| is practical to keep the transition region smooth. For example, if the length of the brushing-zone is a constant

*L*

_{0}, then the taper profile is given by

*ϕ*(

*z*) =

*ϕ*

_{0}

*exp*(−

*z*/

*L*

_{0}) [9

**10**, 432–438 (1992). [CrossRef]

*z*| ≈ (1−

*ρ*)

*L*

_{0}. Using typical values of

*ρ*= 0.97 and

*L*

_{0}= 2.0 cm leads to |Δ

*z*| ≈ 0.6 mm, which requires

*L*≳ 0.6 mm. In contrast, the diameter steps are eliminated in the multi-sweep tapering method because the transition region is carved within each tapering sweep; therefore, shortening

_{hz}*L*always reduces the mismatch between the resulting taper and the design.

_{hz}### 3.3. Multi-sweep tapering simulation

*L*= 3 mm for a step-taper with

_{hz}*ρ*= 0.4 show that the percent overshoot

*n*increases. Also shown in Fig. 12 is the worst-case percent overshoot,

*n*reduces

*ɛ*,

_{os}*L*must also be shortened to ensure that |

_{hz}*ɛ*(

*z*)| is less than a prescribed value

*ɛ*. Shortening

_{target}*L*is critical when the taper profile incorporates fine details such as a large

_{hz}*∂ϕ*/

*∂z*, a large change in

*∂ϕ*/

*∂z*, or a short waist. For example, if the taper waist length is of the same order as

*L*, then the details of the waist can not be precisely shaped. The value of

_{hz}*L*that ensures |

_{hz}*ɛ*(

*z*)| <

*ɛ*for a given taper profile can be determined through simulations.

_{target}### 3.4. Multi-sweep tapering experimental results

_{2}Se

_{3}taper with an initial fiber diameter of 170 μm, dissimilar left and right transition regions, and a nonuniform waist with a diameter decreasing linearly from 15 μm to 10 μm over a waist length of 2.0 cm. The taper is experimentally fabricated over 24 sweeps using the same resistive heater in the single-sweep experiment in Subsection 2.4 at 210° C with

*v*= 3.56 mm/min and

_{f}## 4. Conclusion

_{2}Se

_{3}chalcogenide taper with dissimilar transition regions and a waist diameter decreasing linearly from 15 μm to 10 μm over 2.0 cm was fabricated using the multi-sweep tapering method showing good agreement between the targeted and the measured taper profiles.

## References

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. |

2. | C. Baker and M. Rochette, “Highly nonlinear hybrid AsSe-PMMA microtapers,” Opt. Express |

3. | A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical fibre coupler,” Electron. Lett. |

4. | R. G. Lamont, D. C. Johnson, and K. O. Hill, “Power transfer in fused biconical-taper single-mode fiber couplers: dependence on external refractive index,” Appl. Opt. |

5. | J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett. |

6. | S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron. |

7. | J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett. |

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. |

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

10. | F. Bilodeau, K. Hill, S. Faucher, and D. Johnson, “Low-loss highly overcoupled fused couplers: Fabrication and sensitivity to external pressure,” in |

11. | R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. |

12. | Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett. |

13. | H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in |

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

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

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

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

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

19. | W. Sun, M. Yuan, X. Zeng, and T. Birks, “Theoretical shape analysis of tapered fibers using a movable large-zone furnace,” Optoelectron. Lett. |

20. | F. Geyling, “Basic fluid dynamic consideration in the drawing of optical fibers,” Bell Sys. Tech. J. |

21. | S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express |

22. | 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 |

23. | G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Zero-dispersion-wavelength-decreasing tellurite microstructured fiber for wide and flattened supercontinuum generation,” Opt. Lett. |

24. | A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B |

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. |

27. | S. Chapra and R. Canale, |

28. | A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. |

29. | T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, |

**OCIS Codes**

(220.4610) Optical design and fabrication : Optical fabrication

(230.4000) Optical devices : Microstructure fabrication

**ToC Category:**

Materials for Fiber Optics

**History**

Original Manuscript: July 22, 2011

Revised Manuscript: August 18, 2011

Manuscript Accepted: August 29, 2011

Published: September 2, 2011

**Citation**

Chams Baker and Martin Rochette, "A generalized heat-brush approach for precise control of the waist profile in fiber tapers," Opt. Mater. Express **1**, 1065-1076 (2011)

http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-6-1065

Sort: Year | Journal | Reset

### References

- 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]
- C. Baker and M. Rochette, “Highly nonlinear hybrid AsSe-PMMA microtapers,” Opt. Express18, 12391–12398 (2010). [CrossRef] [PubMed]
- A. C. Boucouvalas and G. Georgiou, “Biconical taper coaxial optical fibre coupler,” Electron. Lett.21, 864–865 (1985). [CrossRef]
- R. G. Lamont, D. C. Johnson, and K. O. Hill, “Power transfer in fused biconical-taper single-mode fiber couplers: dependence on external refractive index,” Appl. Opt.24, 327–332 (1985). [CrossRef] [PubMed]
- J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett.22, 320–321 (1986). [CrossRef]
- S. Jensen, “The nonlinear coherent coupler,” J. Quantum Electron.18, 1580–1583 (1982). [CrossRef]
- J. D. Love and W. M. Henry, “Quantifying loss minimisation in single-mode fibre tapers,” Electron. Lett.22, 912–914 (1986). [CrossRef]
- 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]
- T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol.10, 432–438 (1992). [CrossRef]
- 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.
- R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett.27, 1654–1656 (1991). [CrossRef]
- Y. Takeuchi and J. Noda, “Novel fiber coupler tapering process using a microheater,” Photon. Technol. Lett.4, 465–467 (1992). [CrossRef]
- H. Yokota, E. Sugai, Y. Kashima, and Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” in Optical Fiber Sensors, (OSA, 1996), p. Th319.
- 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]
- 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]
- J. Dewynne, J. R. Ockendon, and P. Wilmott, “On a mathematical model for fiber tapering,” SIAM J. Appl. Math.49, 983–990 (1989). [CrossRef]
- S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express18, 3426–3437 (2010). [CrossRef] [PubMed]
- 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]
- F. Geyling, “Basic fluid dynamic consideration in the drawing of optical fibers,” Bell Sys. Tech. J.55, 1011–1056 (1976).
- 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]
- 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]
- G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Zero-dispersion-wavelength-decreasing tellurite microstructured fiber for wide and flattened supercontinuum generation,” Opt. Lett.35, 136–138 (2010). [CrossRef] [PubMed]
- A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B26, 2064–2071 (2009). [CrossRef]
- A. Alkadery and M. Rochette, “Widely tunable soliton shifting for mid-infrared applications,” in IEEE Photonics Conference 2011 (IPC2011) (2011).
- 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]
- S. Chapra and R. Canale, Numerical Methods for Engineers, 5th ed. (McGraw-Hill, 2005).
- A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am.62, 1267–1277 (1972). [CrossRef]
- T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. (MIT Press, 2001).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1 |
Fig. 2 |
Fig. 3 |

Fig. 4 |
Fig. 5 |
Fig. 6 |

Fig. 7 |
Fig. 8 |
Fig. 9 |

Fig. 10 |
Fig. 11 |
Fig. 12 |

Fig. 13 |
||

« Previous Article | Next Article »

OSA is a member of CrossRef.