Abstract

The driving mechanism of a scanning mirror can cause significant impairment of expanded beam properties, which we investigated for several scanning waveforms. Engineering on the scanning waveform is then carried out by a scanned CO2 laser beam technique to enlarge the uniform heating region for stretching and sintering of silica fibers. Details of the derivation are given. A simple thermal model is presented to account for the relationship between the scanning beam profile and the taper shape. Fusion profiles are also compared for various scanning waveforms. The corresponding scanned beam power distributions are determined experimentally, which enables us to determine precise power density conditions for CO2 laser fusion.

© 2005 Optical Society of America

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  1. B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
    [CrossRef]
  2. Y. Takeuchi, M. Huriguchi, “Microheater control of wavelength-flattened fiber coupler properties,” Appl. Opt. 33, 1029–1034 (1994).
    [CrossRef] [PubMed]
  3. H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
    [CrossRef]
  4. T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
    [CrossRef]
  5. A. Grellier, “Characterisation of optical fibre tapering using a CO2laser,” Ph. D. dissertation (University of Kent, Canterbury, UK, 2000).
  6. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, F. Gonthier, “Tapered single-mode fibres and devices. I. Adiabaticity criteria,” IEE Proc. Optoelectron. 138, 343–354 (1991).
    [CrossRef]
  7. T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Light-wave Technol. 10, 432–438 (1992).
    [CrossRef]
  8. A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
    [CrossRef]
  9. G. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley-Interscience, 1983).
  10. A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
    [CrossRef]
  11. S. Lacroix, F. Gonthier, J. Bures, “Modeling of symmetric 2 × 2 fused-fiber couplers,” Appl. Opt. 33, 8361–8369 (1994).
    [CrossRef] [PubMed]
  12. J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
    [CrossRef] [PubMed]
  13. E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
    [CrossRef] [PubMed]

2004 (2)

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
[CrossRef] [PubMed]

2003 (1)

B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
[CrossRef]

1999 (1)

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

1998 (1)

A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
[CrossRef]

1997 (1)

H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
[CrossRef]

1994 (2)

1992 (1)

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

1991 (1)

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

1989 (1)

J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
[CrossRef] [PubMed]

Bayle, F.

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Birks, T. A.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

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

Black, R. J.

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

Bohren, G. F.

G. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley-Interscience, 1983).

Bures, J.

Chaudhuri, P. R.

B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
[CrossRef]

Daxhelet, X.

E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
[CrossRef] [PubMed]

Dimmick, T. E.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

Fang, Z.

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Gonthier, F.

S. Lacroix, F. Gonthier, J. Bures, “Modeling of symmetric 2 × 2 fused-fiber couplers,” Appl. Opt. 33, 8361–8369 (1994).
[CrossRef] [PubMed]

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

Grellier, A.

A. Grellier, “Characterisation of optical fibre tapering using a CO2laser,” Ph. D. dissertation (University of Kent, Canterbury, UK, 2000).

Grellier, A. J. C.

A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
[CrossRef]

Henry, W. M.

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

Huffman, D. R.

G. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley-Interscience, 1983).

Huriguchi, M.

Kakarantzas, G.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

Lacroix, S.

E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, J. Bures, “Modeling of symmetric 2 × 2 fused-fiber couplers,” Appl. Opt. 33, 8361–8369 (1994).
[CrossRef] [PubMed]

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

Li, Y. W.

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

Lin, Z. Q.

J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
[CrossRef] [PubMed]

Love, J. D.

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

Luo, A.

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Mao, Z. M.

J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
[CrossRef] [PubMed]

Marin, E.

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Meunier, J. P.

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Pal, B. P.

B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
[CrossRef]

Pannell, C. N.

A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
[CrossRef]

Pone, E.

E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
[CrossRef] [PubMed]

Russell, J.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

Sasaki, Y.

H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
[CrossRef]

Shenoy, M. R.

B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
[CrossRef]

St, P.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

Stewart, W. J.

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

Sugai, E.

H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
[CrossRef]

Takeuchi, Y.

Yokota, H.

H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
[CrossRef]

Zayer, N. K.

A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
[CrossRef]

Zhang, J. L.

J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
[CrossRef] [PubMed]

Appl. Opt. (2)

T. E. Dimmick, G. Kakarantzas, T. A. Birks, P. St, J. Russell, “Carbon dioxide laser fabrication of fused-fiber couplers and tapers,” Appl. Opt. 38, 6845–6848 (1999).
[CrossRef]

J. L. Zhang, Z. M. Mao, Z. Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
[CrossRef] [PubMed]

Appl. Opt. (2)

Fiber Integr. Opt. (1)

B. P. Pal, P. R. Chaudhuri, M. R. Shenoy, “Fabrication and modeling of fused biconical tapered fiber couplers,” Fiber Integr. Opt. 22, 97–117 (2003).
[CrossRef]

IEE Proc. Optoelectron. (1)

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

J. Light-wave Technol. (1)

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

Opt. Express (1)

E. Pone, X. Daxhelet, S. Lacroix, “Refractive index profile of fused-fiber couplers cross-section,” Opt. Express 12, 1036–1044 (2004).
[CrossRef] [PubMed]

Opt. Commun. (2)

A. J. C. Grellier, N. K. Zayer, C. N. Pannell, “Heat transfer modelling in CO2 laser processing of optical fibres,” Opt. Commun. 152, 324–328 (1998).
[CrossRef]

A. Luo, F. Bayle, E. Marin, J. P. Meunier, Z. Fang, “Influence of Bragg grating position and length on spectral response in conventional hydrogenated 2 × 2 fused tapered couplers,” Opt. Commun. 231, 191–198 (2004).
[CrossRef]

Opt. Rev. (1)

H. Yokota, E. Sugai, Y. Sasaki, “Optical irradiation method for fiber coupler fabrications,” Opt. Rev. 4, 104–107 (1997).
[CrossRef]

Other (2)

A. Grellier, “Characterisation of optical fibre tapering using a CO2laser,” Ph. D. dissertation (University of Kent, Canterbury, UK, 2000).

G. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley-Interscience, 1983).

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Figures (21)

Fig. 1
Fig. 1

(a) Scanned beam method for CO2 laser irradiation. The optional lens is cylindrical (focal length, 30 cm at 10.6 μm) and scanned along its axis. (b) Experimental setup for scanning beam shape analysis.

Fig. 2
Fig. 2

Longitudinal brightness profiles induced by a CO2 laser irradiation beam scanned along a 2 mm thick silica rod for three sawtoothed waveform frequencies: (a) 4 Hz, (b) 40 Hz, and (c) 80 Hz with the same amplitude voltage in steady-state conditions.

Fig. 3
Fig. 3

Longitudinal brightness profiles induced by a CO2 laser beam scanned along a 2 mm thick silica rod for two sinusoidal waveform frequencies: (a) 40 Hz, (b) 80 Hz. Other experimental conditions, parameters, and scales are the same as in Fig. 2.

Fig. 4
Fig. 4

(a) 100 Hz sawtoothed driving waveform and (b) resultant angular velocity of the scanning mirror.

Fig. 5
Fig. 5

Distribution of power along (a) an unscanned beam and (b) a scanned beam driven by a 100 Hz sawtoothed waveform.

Fig. 6
Fig. 6

Division of the scanning length into N local subsections.

Fig. 7
Fig. 7

Dependence on time of A, position and B, velocity for the scanning motion resulting from the optimized waveform.

Fig. 8
Fig. 8

Flattened scanning beam distribution of power obtained by tuning of the scanner’s driving waveform.

Fig. 9
Fig. 9

Variation of the elongation of a Corning SMF28 fiber with CO2 laser power by use of the optimized scanning beam.

Fig. 10
Fig. 10

Microscope analysis of the fiber tapers obtained with (a), (b) a 100 Hz sawtoothed waveform and (c) an optimized scanning waveform.

Fig. 11
Fig. 11

Evolution of the optical transmission of the taper with stretching time, at 1550 nm, for pulling conditions of 2 × 0.01 mm/s: (a) 100 Hz sawtoothed waveform, (b) optimized waveform.

Fig. 12
Fig. 12

Taper profile for optimized scanning beam and constant speed pulling conditions (2 × 0.01 mm/s).

Fig. 13
Fig. 13

Elliptical laser beam with wx and wy FWMH impinging upon an optical fiber of diameter d.

Fig. 14
Fig. 14

Half-view representation of x-symmetrical (a) temperature variations along an optical fiber irradiated with (b) a gaussian laser power distribution (wx = wy = 2.3 mm and Ptot = 31 W).

Fig. 15
Fig. 15

Microscope photograph of two fused Corning SMF28 fibers.

Fig. 16
Fig. 16

Cross-section parameters of 2 × 2 fused fibers. The origins of the axes are taken at the symmetry point of the fusion region (Fig. 15).

Fig. 17
Fig. 17

Longitudinal fusion profile for several scanning waveforms.

Fig. 18
Fig. 18

Microscope photograph of a region of two fused fibers obtained with an optimized scanning beam profile (Fig. 8).

Fig. 19
Fig. 19

Optical transmission during fusion.

Fig. 20
Fig. 20

Effect of a 14 W sawtooth scanning CO2 beam, with 1.5 cm amplitude, on two Corning SMF28 fibers hold in contact.

Fig. 21
Fig. 21

Core separation of fused-fiber regions under different scanning waveforms with the same amplitude.

Tables (2)

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Table 1 Nomenclature for Thermal Equation (1)

Tables Icon

Table 2 Experimental Conditions for Fusing Two Fibers

Equations (4)

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d 2 T d x 2 = 4 H d K ( T - T air ) - q ( x ) K ,
q ( x ) = η 2 2 P total w x π 1.5 d 2 erf ( 2 d w y ) exp ( - 2 x 2 w x 2 ) ,
T = T air + 2 π / ( 4 b w x 2 γ ) { exp ( b 2 / 4 + b u ) × [ 1 - erf ( u + b 2 ) ] + exp ( b 2 / 4 - b u ) × [ 1 + erf ( u - b 2 ) ] } ,
a = 4 H / ( d K ) , γ = η P total erf ( 2 d / w y ) / ( K w x d 2 ) , b 2 = w x 2 a / 2 , u = 2 x / w x .

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