Abstract

In considering the wavelength-dependent transmission of tapered fibers we provide an observation of the fringe that shows the least response to variations in wavelength and that is, by definition, the achromatic fringe. This is a manifestation of the equalization of the HE11–HE12 group velocity occurring at V = 4.4. The fact that it was observed in a tapered single-mode fiber confers some particular features that are discussed and compared with those of other two-mode guides with regard to sensor applications.

© 1988 Optical Society of America

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References

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  1. D. T. Cassidy, D. C. Johnson, K. O. Hill, Appl. Opt. 24, 945 (1985).
    [CrossRef] [PubMed]
  2. S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, Appl. Opt. 25, 2468 (1986).
    [CrossRef] [PubMed]
  3. S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.
  4. S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).
  5. S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, Appl. Opt. 25, 4421 (1986).
    [CrossRef] [PubMed]
  6. F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
    [CrossRef] [PubMed]
  7. R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.
  8. F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).
  9. B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, Opt. Lett. 12, 729 (1987).
    [CrossRef] [PubMed]
  10. J. N. Blake, S. Y. Huang, B. Y. Kim, H. J. Shaw, Opt. Lett. 12, 732 (1987).
    [CrossRef] [PubMed]
  11. S. Lacroix, F. Gonthier, J. Bures, Ann. Telecommun. (to be published).
  12. A. C. Boucouvalas, S. C. Robertson, Electron. Lett. 23, 215 (1987).
    [CrossRef]
  13. S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 14.
  15. S. Lacroix, F. Gonthier, J. Bures, Opt. Lett. 11, 671 (1986).
    [CrossRef] [PubMed]
  16. F. Bilodeau, K. O. Hill, D. C. Johnson, S. Faucher, Opt. Lett. 12, 634 (1987).
    [CrossRef] [PubMed]
  17. Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).
  18. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7.3.5.

1987

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, Opt. Lett. 12, 729 (1987).
[CrossRef] [PubMed]

J. N. Blake, S. Y. Huang, B. Y. Kim, H. J. Shaw, Opt. Lett. 12, 732 (1987).
[CrossRef] [PubMed]

A. C. Boucouvalas, S. C. Robertson, Electron. Lett. 23, 215 (1987).
[CrossRef]

F. Bilodeau, K. O. Hill, D. C. Johnson, S. Faucher, Opt. Lett. 12, 634 (1987).
[CrossRef] [PubMed]

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

1986

1985

Bilodeau, F.

Black, R. J.

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, Appl. Opt. 25, 2468 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.

Blake, J. N.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7.3.5.

Boucouvalas, A. C.

A. C. Boucouvalas, S. C. Robertson, Electron. Lett. 23, 215 (1987).
[CrossRef]

Bourbonnais, R.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, Appl. Opt. 25, 4421 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

Bures, J.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

S. Lacroix, F. Gonthier, J. Bures, Opt. Lett. 11, 671 (1986).
[CrossRef] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, Appl. Opt. 25, 4421 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.

S. Lacroix, F. Gonthier, J. Bures, Ann. Telecommun. (to be published).

Cassidy, D. T.

Faucher, S.

Gonthier, F.

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, Appl. Opt. 25, 4421 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

S. Lacroix, F. Gonthier, J. Bures, Opt. Lett. 11, 671 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, J. Bures, Ann. Telecommun. (to be published).

S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

Hill, K. O.

Huang, S. Y.

Johnson, D. C.

Kim, B. Y.

Lacroix, S.

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, Appl. Opt. 25, 4421 (1986).
[CrossRef] [PubMed]

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, Appl. Opt. 25, 2468 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

S. Lacroix, F. Gonthier, J. Bures, Opt. Lett. 11, 671 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, J. Bures, Ann. Telecommun. (to be published).

S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

Lapierre, J.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, Appl. Opt. 25, 2468 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 14.

Robertson, S. C.

A. C. Boucouvalas, S. C. Robertson, Electron. Lett. 23, 215 (1987).
[CrossRef]

Shaw, H. J.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 14.

Veilleux, C.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, Appl. Opt. 26, 444 (1987).
[CrossRef] [PubMed]

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, Appl. Opt. 25, 2468 (1986).
[CrossRef] [PubMed]

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7.3.5.

Ann. Assoc. Can. Fr. Avance. Sci.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 54, 342 (1986).

F. Gonthier, S. Lacroix, J. Bures, J. Lapierre, Ann. Assoc. Can. Fr. Avance. Sci. 55, 284 (1987).

Appl. Opt.

Electron. Lett.

A. C. Boucouvalas, S. C. Robertson, Electron. Lett. 23, 215 (1987).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

Theoretical results showing the contrast between the two types of responses are given in Fig. 4.1 of R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, Proc. Soc. Photo-Opt. Instrum. Eng. 839, 2 (1987).

Other

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7.3.5.

S. Lacroix, F. Gonthier, R. J. Black, J. Bures, in 13th European Conference on Optical Communication, Technical Digest I (Consulting Committee of the Professional Electroengineers’ Organizations, Helsinki, 1987), p. 219.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 14.

S. Lacroix, F. Gonthier, C. Veilleux, R. Bourbonnais, J. Bures, J. Lapierre, “Propriétés des fibres optiques effilées,” presented at the 54th meeting of the Association Canadienne-Française pour l’Avancement des Sciences, 1986.

S. Lacroix, F. Gonthier, J. Bures, Ann. Telecommun. (to be published).

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, in Technical Digest, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communications Engineers of Japan, Tokyo, 1986), paper PD-3.

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Figures (2)

Fig. 1
Fig. 1

Profile of the tapered fiber used for experiment. Note the long quasi-cylindrical central region. The experimental radius measurement error is evaluated to be 0.25 μm in this region and 0.5 μm in the untapered region.

Fig. 2
Fig. 2

Tapered fiber transmission as a function of wavelength when immersed in oils of different indices. As the external index augments, the numerical aperture of the guide decreases and so do the HE12 cutoff and HE11–HE12 equalization wavelengths. Note that in all three cases the equalization point λ0 is far easier to evaluate than the cutoff λc and that the ratio λc/λ0 remains constant and equal to 1.10. (a) n25D = 1.420, t = 28.2°C, λc = 1625 nm, λ0 = 1480 nm. (b) n25D = 1.424, t = 27.7°C, λc = 1550 nm, λ0 = 1400 nm. (c) n25D = 1.428, t = 27.5°C, λc = 1460 nm, λ0 = 1325 nm.

Equations (9)

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I = I 1 + I 2 + 2 I 1 I 2 cos ϕ ,
ϕ = δ β L
ϕ = 0 L δβ d z
δ β = λ 4 π ρ 2 n ( U 2 2 U 1 2 ) ,
1 2 Λ ( λ ) = 1 2 π d ϕ d λ = L 2 π d ( δ β ) d λ .
d ϕ d λ = L / 2 + L / 2 d ( δ β ) d λ dz = 2 0 + L / 2 d ( δ β ) d λ d z .
V e = 2 π λ 0 ρ e NA = 4 . 4
V c = 2 π λ c ρ w NA = 3 . 8 ,
λ 0 = ρ e ρ w 3 . 8 4 . 4 λ c > 3 . 8 4 . 4 λ c = λ e ,

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