Abstract

Oscillatory transmission of biconically tapered monomode fibers is related to the nonadiabaticity of the process. In this paper, we show that large power transfer from HE11 to other modes, thus large amplitude in the oscillations, cannot be predicted by a formalism using only two coupled local mode equations. A new model based on successive use of the sudden approximation and the adiabatic approximation is considered. Its predictions show good agreement with experimental results.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918 (1983).
    [CrossRef] [PubMed]
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 19.
  4. S. Lacroix, R. J. Black, C. Veilleux, J. Lapierre, “Tapered Single-Mode Fibers: External Refractive Index Dependence,” Appl. Opt. 25, 2468 (1986).
    [CrossRef] [PubMed]
  5. A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Optical Fiber Coupler,” Electron. Lett. 21, 864 (1985).
    [CrossRef]
  6. A. C. Boucouvalas, G. Georgiou, “Biconical Coaxial Coupler Filter,” Electron. Lett. 21, 1033 (1985).
    [CrossRef]
  7. A. C. Boucouvalas, G. Georgiou, “External Refractive-Index Response of Tapered Coaxial Couplers,” Opt. Lett. 11, 257 (1986).
    [CrossRef] [PubMed]
  8. S. Lacroix, F. Gonthier, J. Bures, “All-Fiber Wavelength Filter from Successive Biconical Tapers,” Opt. Lett. 11, 671 (1986).
    [CrossRef] [PubMed]
  9. 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), Vol. 1, pp. 191–194.
  10. W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibres,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication-Eleventh European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1985), Vol. 1, pp. 559–562.
  11. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (29-8).
  12. F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

1986 (3)

1985 (3)

D. T. Cassidy, D. C. Johnson, K. O. Hill, “Wavelength-Dependent Transmission of Monomode Optical Fiber Tapers,” Appl. Opt. 24, 945 (1985).
[CrossRef] [PubMed]

A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Optical Fiber Coupler,” Electron. Lett. 21, 864 (1985).
[CrossRef]

A. C. Boucouvalas, G. Georgiou, “Biconical Coaxial Coupler Filter,” Electron. Lett. 21, 1033 (1985).
[CrossRef]

1983 (1)

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), Vol. 1, pp. 191–194.

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 Optical Fiber Coupler,” Electron. Lett. 21, 864 (1985).
[CrossRef]

A. C. Boucouvalas, G. Georgiou, “Biconical Coaxial Coupler Filter,” Electron. Lett. 21, 1033 (1985).
[CrossRef]

Bourbonnais, R.

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), Vol. 1, 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]

J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918 (1983).
[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), Vol. 1, pp. 191–194.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

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 Optical Fiber Coupler,” Electron. Lett. 21, 864 (1985).
[CrossRef]

A. C. Boucouvalas, G. Georgiou, “Biconical Coaxial Coupler Filter,” Electron. Lett. 21, 1033 (1985).
[CrossRef]

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, 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), Vol. 1, pp. 191–194.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

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

J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918 (1983).
[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), Vol. 1, pp. 191–194.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

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]

J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918 (1983).
[CrossRef] [PubMed]

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

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), Vol. 1, pp. 191–194.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 19.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (29-8).

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibres,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication-Eleventh European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1985), Vol. 1, pp. 559–562.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (29-8).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 19.

Stewart, W. J.

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibres,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication-Eleventh European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1985), Vol. 1, pp. 559–562.

Veilleux, C.

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

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

Appl. Opt. (3)

Electron. Lett. (2)

A. C. Boucouvalas, G. Georgiou, “Biconical Taper Coaxial Optical Fiber Coupler,” Electron. Lett. 21, 864 (1985).
[CrossRef]

A. C. Boucouvalas, G. Georgiou, “Biconical Coaxial Coupler Filter,” Electron. Lett. 21, 1033 (1985).
[CrossRef]

Opt. Lett. (2)

Other (5)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 19.

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), Vol. 1, pp. 191–194.

W. J. Stewart, J. D. Love, “Design Limitation on Tapers and Couplers in Single Mode Fibres,” in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fiber Communication-Eleventh European Conference on Optical Communication (Instituto Internazionale delle Communicazioni, Genova, Italy, 1985), Vol. 1, pp. 559–562.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (29-8).

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, J. Bures, “Investigation of Power Oscillations along Tapered Monomode Fibers,” to be published in Applied Optics.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Local modes of a varying waveguide: Δβ(z) = β1(z) − β2(z). In each slice of thickness δz, there is a widening of β obeying the uncertainty relation δβδz ≥ 1.

Fig. 2
Fig. 2

Comparison of (a) Stewart-Love limit curve with (b) local mode validity cirterion; (c) represents the slope of the taper for experiment. Taper slope /dz and radius ρ have been normalized to the untapered fiber radius ρ0.

Fig. 3
Fig. 3

(a) Schematic taper profile; (b) schematic taper profile used for calculations. Coupling occurs in large taper slope regions (ρB < ρ < ρA). Elsewhere (ρ < ρB and ρ > ρA) there is only a beating between excited local modes

Fig. 4
Fig. 4

Measured biconical taper profile. Radii ρA and ρB at which overlap integral coefficients are calculated correspond to the intersections of the Stewart-Love limit curve and the taper profile (see Fig. 2).

Fig. 5
Fig. 5

(a) Experimental wavelength response of the taper in air (nex = 1). The upper curve is the normalization factor (system response). (b) Theoretical wavelength response of the same taper.

Fig. 6
Fig. 6

(a) Experimental and (b) theoretical external refractive-index response of the taper (λ = 633 nm). Theoretical mode cutoff indices are: HE11 = 1.4574; HE12 = 1.4527; HE13 = 1.4416.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

F 2 ~ 4 | 1 ρ d ρ d z | 2 4 | 1 ρ d ρ d z | 2 + ( 2 π z b ) 2 = 1 1 + π 2 ~ 10 % .
δ β δ z 1.
| β z | δ β δ z
| β z | = sup ( | β 1 z | , | β 2 z | ) .
Δ β 2 δ β .
β z = β V V ρ d ρ d z = β V V ρ d ρ d z ,
β V V ρ | d ρ d z | δ β δ z δ β 2 Δ β 2 4 = π 2 z b 2 , | d ρ d z | 1 β V ρ V π 2 z b 2 .
ψ ( z = 0 ) = HE 11 A = m a m 0 HE 1 m B
ψ ( z = L ) = m a m 0 HE 1 m B exp [ - i 0 L β m ( z ) d z ] .
HE 11 ψ ( z = L ) A = m a m 0 a m L exp [ - i 0 L β m ( z ) d z ] ,
| m a m 0 a m L exp [ - i 0 L β m ( z ) d z ] | 2 = m n a m 0 a m L a n 0 a n L cos ϕ m n = m ( a m 0 a m L ) 2 + 2 m > n a m 0 a m L a n 0 a n L cos ϕ m n ,
ϕ m n = 0 L β m n ( z ) d z ,
I = m I m + 2 m > n I m I n cos ϕ m n .

Metrics