Abstract

We construct a fluid mechanics model of the drawing of microstructured optical fibres (‘holey fibres’). This model can be used to understand and quantify methods for controlling the fibre geometry. The effects of preform rotation are included to examine methods for reducing fibre birefringence. Asymptotic numerical-solutions are obtained and applied to two typical microstructured-fibres and a number of practical suggestions are made for achieving sub-mm spin pitches without damaging the microstructure within.

© 2004 Optical Society of America

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References

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  2. T.M. Monro, D.J. Richardson, N.G.R. Broderick, P.J. Bennett, �??Holey optical fibers: An efficient modal model,�?? J. Lightwave Technol. 17, 1093�??1102 (1999).
    [CrossRef]
  3. T. M. Monro, D. J. Richardson, P. J. Bennett, �??Developing holey fibres for evanescent field devices,�?? Elect. Lett. 35, 1188�??1189 (1999).
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    [CrossRef]
  7. M. Fuochi, J. R. Hayes, K. Furusawa, W. Belardi, J. C. Baggett, T. M. Monro, D. J. Richardson, �??Polarization mode dispersion reduction in spun large mode area silica holey fibres,�?? Opt. Express 9, 1972�??1977 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1972">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1972</a>.
    [CrossRef]
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  10. J. R. Hayes, Optoelectronics Research Centre, University of Southampton, University Road, Southampton, Hampshire, SO17 1BJ, U.K. (personal communication, 2003).
  11. A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, �??Modelling the fabrication of hollow fibers: capillary drawing,�?? J. Lightwave Technol. 31, 1924�??31 (2001).
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  12. A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, D. J. Richardson, �??The mathematical modelling of capillary drawing for holey fibre manufacture,�?? J. Eng. Math. 43, 201�??227 (2002).
    [CrossRef]
  13. C. J. Voyce, School of Mathematics, University of Southampton, Southampton, SO17 1BJ, U.K., A. D. Fitt and T. M. Monro are preparing a manuscript to be called �??The mathematical modelling of spun capillaries.�??
  14. R.H. Doremus, �??Viscosity of silica,�?? J. Appl. Phys. 92, 7619-7629 (2002).
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  15. T. M. Monro, K. Furusawa, J. H. Lee, J. H. V. Price, Z. Yusoff, J. C. Baggett, D. J. Richardson, �??Advances in holey fibers,�?? in Advances in Fiber Lasers, L.N. Durvasula, ed., Proc. SPIE 4974, 83�??95 (2003).
  16. P. K. A. Wai, W. L. Kath, C. R. Menyuk, J. W. Zhang, �??Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence,�?? J. Opt. Soc. Am. B 14, 2967�??2979 (1997).
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  17. U. C. Paek, �??Free Drawing and Polymer Coating of Silica Glass Optical Fibers,�?? ASME Journal of Heat Transfer 121, 774�??789 (1999).
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  18. P. Petropoulous, H. Ebendorff�??Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, T. M. Monro, �??Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,�?? Opt. Express 11, 3568�??3573 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3568">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3568</a>.
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  19. C. J. Voyce, A. D. Fitt, T. M.Monro, �??Mathematical modelling of the drawing of spun capillary tubes,�?? in Progress in Industrial Mathematics at ECMI 2002, A. Buikis, R. Ciegis, A. D. Fitt, eds. (Springer-Verlag, Berlin, 2004), pp. 387�??391.

Applied Optics (1)

A. J. Barlow, J. J. Ramskov-Hansen, D. N. Payne, �??Birefringence and polarization mode dispersion in spun singlemode fibres,�?? Applied Optics 30, 2962�??68 (1981).
[CrossRef]

ASME Journal of Heat Transfer (1)

U. C. Paek, �??Free Drawing and Polymer Coating of Silica Glass Optical Fibers,�?? ASME Journal of Heat Transfer 121, 774�??789 (1999).
[CrossRef]

Elect. Lett. (1)

T. M. Monro, D. J. Richardson, P. J. Bennett, �??Developing holey fibres for evanescent field devices,�?? Elect. Lett. 35, 1188�??1189 (1999).
[CrossRef]

J. Appl. Phys. (1)

R.H. Doremus, �??Viscosity of silica,�?? J. Appl. Phys. 92, 7619-7629 (2002).
[CrossRef]

J. Eng. Math. (1)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, D. J. Richardson, �??The mathematical modelling of capillary drawing for holey fibre manufacture,�?? J. Eng. Math. 43, 201�??227 (2002).
[CrossRef]

J. Lightwave Technol (1)

T.M. Monro, D.J. Richardson, N.G.R. Broderick, P.J. Bennett, �??Holey optical fibers: An efficient modal model,�?? J. Lightwave Technol. 17, 1093�??1102 (1999).
[CrossRef]

J. Lightwave Technol. (2)

A. D. Fitt, K. Furusawa, T. M. Monro, C. P. Please, �??Modelling the fabrication of hollow fibers: capillary drawing,�?? J. Lightwave Technol. 31, 1924�??31 (2001).
[CrossRef]

R.E. Schuh, X. Shan, A. Shamim Siddiqui, �??Polarization Mode Dispersion in Spun Fibers with Different Linear Birefringence and Spinning Parameters,�?? J. Lightwave Technol. 16, 1583�??1588 (1998).
[CrossRef]

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

Opt. Express (2)

M. Fuochi, J. R. Hayes, K. Furusawa, W. Belardi, J. C. Baggett, T. M. Monro, D. J. Richardson, �??Polarization mode dispersion reduction in spun large mode area silica holey fibres,�?? Opt. Express 9, 1972�??1977 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1972">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1972</a>.
[CrossRef]

P. Petropoulous, H. Ebendorff�??Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, T. M. Monro, �??Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,�?? Opt. Express 11, 3568�??3573 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3568">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3568</a>.
[CrossRef]

Opt. Lett. (3)

PNAS (1)

J. P. Gordon, H. Kogelnik, �??PMD Fundamentals: Polarization mode dispersion in optical fibers,�?? PNAS 97 (9), 4541�??4550 (2000).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. M. Monro, K. Furusawa, J. H. Lee, J. H. V. Price, Z. Yusoff, J. C. Baggett, D. J. Richardson, �??Advances in holey fibers,�?? in Advances in Fiber Lasers, L.N. Durvasula, ed., Proc. SPIE 4974, 83�??95 (2003).

Progress in Industrial Mathematics (1)

C. J. Voyce, A. D. Fitt, T. M.Monro, �??Mathematical modelling of the drawing of spun capillary tubes,�?? in Progress in Industrial Mathematics at ECMI 2002, A. Buikis, R. Ciegis, A. D. Fitt, eds. (Springer-Verlag, Berlin, 2004), pp. 387�??391.

Other (2)

C. J. Voyce, School of Mathematics, University of Southampton, Southampton, SO17 1BJ, U.K., A. D. Fitt and T. M. Monro are preparing a manuscript to be called �??The mathematical modelling of spun capillaries.�??

J. R. Hayes, Optoelectronics Research Centre, University of Southampton, University Road, Southampton, Hampshire, SO17 1BJ, U.K. (personal communication, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

(Left) The cross-section of a type-one holey fibre. (Right) The cross-section of a type-two holey fibre.

Fig. 2.
Fig. 2.

Problem geometry and nomenclature.

Fig. 3.
Fig. 3.

The effects of preform rotation on outer capillary radius. The diagram shows the outer radius h 2 for fibre pulls with and without rotation. The thin-walled tube has h 1(0)=0.01m, h 2(0)=0.015m and the thick-walled tube has h 1(0)=0.01m, h 2(0)=0.02m. (Draw length L=0.03m, temperature T=2200C, draw speed Wd =25m/min, feed speed Wf =15mm/min, rotation rate Ω=35rad/s.)

Fig. 4.
Fig. 4.

The destructive effects of preform rotation on the microstructure of type-two fibres. Dashed lines show holey cladding and jacket radii of preform without rotation and solid lines show the radii with rotation.

Equations (10)

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ρ ( h 2 2 h 1 2 ) ( w 0 t + w 0 w 0 z g ) = [ 3 μ ( h 2 2 h 1 2 ) w 0 z + γ ( h 1 + h 2 ) + ρ 4 ( h 2 4 h 1 4 ) B 2 ] z ,
( h 1 2 ) t + ( h 1 2 w 0 ) z = 2 p 0 h 1 2 h 2 2 2 γ h 1 h 2 ( h 1 + h 2 ) + ρ h 1 2 h 2 2 B 2 ( h 2 2 h 1 2 ) 2 μ ( h 2 2 h 1 2 ) ,
( h 2 2 ) t + ( h 2 2 w 0 ) z = 2 p 0 h 1 2 h 2 2 2 γ h 1 h 2 ( h 1 + h 2 ) + ρ h 1 2 h 2 2 B 2 ( h 2 2 h 1 2 ) 2 μ ( h 2 2 h 1 2 ) ,
μ ( ( h 2 4 h 1 4 ) B z ) z = ρ [ h 2 2 ( h 2 2 B ) t h 1 2 ( h 1 2 B ) t ] + ρ w 0 [ h 2 2 ( h 2 2 B ) z h 1 2 ( h 1 2 B ) z ]
ρ γ B μ ( h 1 2 h 2 + h 2 2 h 1 ) + ρ 2 B 3 2 μ ( h 1 2 h 2 4 h 2 2 h 1 4 ) + ρ μ p 0 B h 1 2 h 2 2 ,
d ( z ) = 2 π w 0 ( z ) ϕ t .
ϕ t + w 0 ( z ) ϕ z = B ( z ) ,
d ( L ) = 2 π W d ϕ t z = L = 2 π W d B ( 0 ) .
3 μ ̅ ( h ̅ 2 2 w ̅ 0 z ̅ ) z ̅ 1 4 R e S 2 ( h ̅ 2 4 B ̅ 2 ) Z ̅ ,
Ω 3 2 h 3 μ ̅ μ 0 W L ρ .

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