Abstract

An abruptly tapered fiber can be essentially divided into three different regions: one beating region in its central, quasi-cylindrical part, lying between two coupling regions, where the slopes are large. In this paper we report two experiments which help to visualize and analyze the beating region. We show that, in this region, there are principally two modes present, HE11 and HE12, both excited with large amplitudes.

© 1987 Optical Society of America

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References

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  1. D. T. Cassidy, D. C. Johnson, K. O. Hill, “Wavelength-dependent transmission of monomode optical fiber tapers,” Appl. Opt. 24, 945 (1985).
    [Crossref] [PubMed]
  2. A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Coupler Filter,” Electron. Lett. 21, 1034 (1986).
  3. A. C. Boucouvalas, G. Georgiou, “External Refractive-Index Response of Tapered Coaxial Couplers,” Opt. Lett. 11, 257 (1986).
    [Crossref] [PubMed]
  4. W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
    [Crossref]
  5. S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, “Tapered Single-Mode Fibers: External Refractive-Index Dependence,” Appl. Opt. 25, 2468 (1986).
    [Crossref] [PubMed]
  6. S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.
  7. C. Veilleux, J. Lapierre, J. Bures, “Liquid-Crystal Clad Tapered Fibers,” to be published.
  8. S. Lacroix, F. Gonthier, J. Bures, “All-Fiber Wavelength Filter from Successive Biconical Tapers,” Opt. Lett. 11, 671 (1986).
    [Crossref] [PubMed]
  9. W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibers,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication–Eleventh European Conference on Optical Communication, Venice (1985), pp. 559–562.
  10. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 412.
  11. R. J. Black, R. Bourbonnais, “Core-Mode Cutoff for Doubly-Clad Lightguides,” IEE proc. J. Opto-electronics, in press.
  12. R. J. Black, J. Lapierre, J. Bures, “Field Evolution in Doubly-Clad Lightguides,” IEE Proc. J. Opto-electronics, in press.
  13. S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, “Tapered Monomode Optical Fibers: Understanding Large Power Transfer,” Appl. Opt. Vol. 25, pp. 4421–4425 (1986).
    [Crossref] [PubMed]
  14. Ref. 10, pp. 313 and 318.
  15. R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

1986 (6)

1985 (1)

Abebe, M.

W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
[Crossref]

Black, R. J.

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, “Tapered Single-Mode Fibers: External Refractive-Index Dependence,” Appl. Opt. 25, 2468 (1986).
[Crossref] [PubMed]

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

R. J. Black, R. Bourbonnais, “Core-Mode Cutoff for Doubly-Clad Lightguides,” IEE proc. J. Opto-electronics, in press.

R. J. Black, J. Lapierre, J. Bures, “Field Evolution in Doubly-Clad Lightguides,” IEE Proc. J. Opto-electronics, in press.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

Boucouvalas, A. C.

A. C. Boucouvalas, G. Georgiou, “External Refractive-Index Response of Tapered Coaxial Couplers,” Opt. Lett. 11, 257 (1986).
[Crossref] [PubMed]

A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Coupler Filter,” Electron. Lett. 21, 1034 (1986).

Bourbonnais, R.

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, “Tapered Monomode Optical Fibers: Understanding Large Power Transfer,” Appl. Opt. Vol. 25, pp. 4421–4425 (1986).
[Crossref] [PubMed]

R. J. Black, R. Bourbonnais, “Core-Mode Cutoff for Doubly-Clad Lightguides,” IEE proc. J. Opto-electronics, in press.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

Bures, J.

S. Lacroix, F. Gonthier, J. Bures, “All-Fiber Wavelength Filter from Successive Biconical Tapers,” Opt. Lett. 11, 671 (1986).
[Crossref] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, “Tapered Monomode Optical Fibers: Understanding Large Power Transfer,” Appl. Opt. Vol. 25, pp. 4421–4425 (1986).
[Crossref] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

C. Veilleux, J. Lapierre, J. Bures, “Liquid-Crystal Clad Tapered Fibers,” to be published.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

R. J. Black, J. Lapierre, J. Bures, “Field Evolution in Doubly-Clad Lightguides,” IEE Proc. J. Opto-electronics, in press.

Burns, W. K.

W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
[Crossref]

Cassidy, D. T.

Georgiou, G.

A. C. Boucouvalas, G. Georgiou, “External Refractive-Index Response of Tapered Coaxial Couplers,” Opt. Lett. 11, 257 (1986).
[Crossref] [PubMed]

A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Coupler Filter,” Electron. Lett. 21, 1034 (1986).

Gonthier, F.

S. Lacroix, F. Gonthier, J. Bures, “All-Fiber Wavelength Filter from Successive Biconical Tapers,” Opt. Lett. 11, 671 (1986).
[Crossref] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, “Tapered Monomode Optical Fibers: Understanding Large Power Transfer,” Appl. Opt. Vol. 25, pp. 4421–4425 (1986).
[Crossref] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

Hill, K. O.

Johnson, D. C.

Lacroix, S.

S. Lacroix, F. Gonthier, J. Bures, “All-Fiber Wavelength Filter from Successive Biconical Tapers,” Opt. Lett. 11, 671 (1986).
[Crossref] [PubMed]

S. Lacroix, R. Bourbonnais, F. Gonthier, J. Bures, “Tapered Monomode Optical Fibers: Understanding Large Power Transfer,” Appl. Opt. Vol. 25, pp. 4421–4425 (1986).
[Crossref] [PubMed]

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, “Tapered Single-Mode Fibers: External Refractive-Index Dependence,” Appl. Opt. 25, 2468 (1986).
[Crossref] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

Lapierre, J.

S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, “Tapered Single-Mode Fibers: External Refractive-Index Dependence,” Appl. Opt. 25, 2468 (1986).
[Crossref] [PubMed]

C. Veilleux, J. Lapierre, J. Bures, “Liquid-Crystal Clad Tapered Fibers,” to be published.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

R. J. Black, J. Lapierre, J. Bures, “Field Evolution in Doubly-Clad Lightguides,” IEE Proc. J. Opto-electronics, in press.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 412.

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibers,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication–Eleventh European Conference on Optical Communication, Venice (1985), pp. 559–562.

Moeller, R. P.

W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
[Crossref]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 412.

Stewart, W. J.

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibers,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication–Eleventh European Conference on Optical Communication, Venice (1985), pp. 559–562.

Veilleux, C.

Villarruel, C. A.

W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
[Crossref]

Appl. Opt. (3)

Electron. Lett. (1)

A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Coupler Filter,” Electron. Lett. 21, 1034 (1986).

IEEE/OSA J. Lightwave Technol. (1)

W. K. Burns, M. Abebe, C. A. Villarruel, R. P. Moeller, “Loss Mechanisms in Single-Mode Fiber Tapers,” IEEE/OSA J. Lightwave Technol. LT-4, 608 (1986).
[Crossref]

Opt. Lett. (2)

Other (8)

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibers,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication–Eleventh European Conference on Optical Communication, Venice (1985), pp. 559–562.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 412.

R. J. Black, R. Bourbonnais, “Core-Mode Cutoff for Doubly-Clad Lightguides,” IEE proc. J. Opto-electronics, in press.

R. J. Black, J. Lapierre, J. Bures, “Field Evolution in Doubly-Clad Lightguides,” IEE Proc. J. Opto-electronics, in press.

S. Lacroix, F. Gonthier, R. Bourbonnais, R. J. Black, J. Bures, J. Lapierre, “Abruptly Tapered Fibers,” in Technical Digest, Twelfth European Conference on Optical Communication, Barcelona (1986), pp. 191–194.

C. Veilleux, J. Lapierre, J. Bures, “Liquid-Crystal Clad Tapered Fibers,” to be published.

Ref. 10, pp. 313 and 318.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly Tapered Fibers: Index Response for Sensor Application,” in Technical Digest, Post-Deadline Papers, 4th International Conference on Optical Fiber Sensors, Tokyo (1986), pp. PD-3-1–PD-3-4.

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Figures (9)

Fig. 1
Fig. 1

(a) Typical slope profile of an abrupt biconical taper (Newport fiber); (b) the Stewart and Love limit curve. Normalization is obtained with respect to the radius of either the core or the cladding of the untapered fiber.

Fig. 2
Fig. 2

Measured geometric profile of a tapered fiber: regions A, adiabatic monomode region, B, beating region, and C, coupling region are obtained from the cross-points of the slope profile with the limit curve of Fig. 1.

Fig. 3
Fig. 3

Representation of the power distribution in a multimode guide in which only the HE11 and HE12 modes propagate. The power density is represented by the darkness of the drawing. The drawing is not to scale; in our experiments (λ = 633 nm), we have 15 < zb/ρ < 100.

Fig. 4
Fig. 4

Photographs of taper 1 immersed in three different solutions for which n = 1.468, 1.547, and 1.635 at × 633 nm. Photographs are shown together with the corresponding geometric profile.

Fig. 5
Fig. 5

Photographs of taper 2 obtained in the same conditions as the ones described in Fig. 4.

Fig. 6
Fig. 6

Fiber and the soap film perturbation. The refractive indices of the film and of the fiber cladding are identical. The film is held by a small loop and moved along the tapered fiber to obtain Figs. 6 and 7.

Fig. 7
Fig. 7

Taper 3: power transmission vs position of the film. The origin of the z axis in Figs. 68 is at the waist.

Fig. 8
Fig. 8

Taper 4: power transmission vs position of the film.

Fig. 9
Fig. 9

Comparison for taper 3 of (a) the profile measured under microscope, and (b) the profile deduced from a beating analysis.

Tables (2)

Tables Icon

Table I Fiber Parameters

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Table II Biconical Taper Characteristics

Equations (6)

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| d ρ d z | ρ z b ,
z b = 2 π / Δ β
| d ρ d z | = ρ z b .
β i = 2 π λ n c l [ 1 - ( λ U i 2 π ρ n c l ) 2 ] 1 / 2 ,
Δ β = β j - β i λ 4 π ρ 2 n c l ( U i 2 - U j 2 ) .
ρ = | λ ( U i 2 - U j 2 ) 8 π 2 n c l z b | 1 / 2 .

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