Abstract

Internal fields in fused couplers have been investigated for the first time by measuring the near field and far field patterns at different cross sections of the couplers. Detailed information concerning the internal fields in the couplers provides experimental evidence for the validity of the hybrid mode theory of fused couplers.

© 1989 Optical Society of America

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References

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  1. J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel a fibres optiques monomodes fusionnees,” Appl. Opt. 22, 1918–1922 (1983).
    [CrossRef] [PubMed]
  2. R. G. Lamont, D. C. Johnson, K. O. Hill, “Power Transfer in Fused Biconical-Taper Single-Mode Fiber Couplers: Dependence on External Refractive Index,” Appl. Opt. 24, 327–332 (1985).
    [CrossRef] [PubMed]
  3. A. W. Snyder, X. H. Zheng, “Optical Fibers of Arbitrary Cross Sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
    [CrossRef]
  4. X. H. Zheng, “Finite-Element Analysis for Fused Couplers,” Electron. Lett. 22, 804 (1986).
    [CrossRef]
  5. X. H. Zheng, A. W. Snyder, “Fused Couplers: Condition for Insensitivity to External Refractive Index,” Electron. Lett. 23, 182 (1987).
    [CrossRef]
  6. A. W. Snyder, X. H. Zheng, “Fused Couplers of Arbitrary Cross-Section,” Electron. Lett. 21, 1079 (1985).
    [CrossRef]
  7. K. S. Chiang, “Analysis of Fused Couplers by the Effective-Index Method,” Electron. Lett. 22, 1221 (1986).
    [CrossRef]
  8. K. S. Chiang, “Perturbation Analysis of Fused Tapered Single-Mode Fiber Couplers,” Electron. Lett. 23, 717 (1987).
    [CrossRef]
  9. K. S. Chiang, “Birefringent-Fibre Polarisation Splitters,” Electron. Lett. 23, 908 (1987).
    [CrossRef]
  10. 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, 608–613 (1986).
    [CrossRef]
  11. F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
    [CrossRef]
  12. F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).
  13. J. D. Love, M. Hall, “Polarisation Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 407.
    [CrossRef]
  15. B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, “Use of Highly Elliptical Core Fibers for Two-Mode Fiber Devices,” Opt. Lett. 12, 729–731 (1987).
    [CrossRef] [PubMed]
  16. J. N. Blake, S. Y. Huang, B. Y. Kim, H. J. Shaw, “Strain Effects on Highly Elliptical Core Two-Mode Fibers,” Opt. Lett. 12, 732–734 (1987).
    [CrossRef] [PubMed]
  17. S. Y. Huang, Shanghai Jiao Tong University; private communication.

1987

X. H. Zheng, A. W. Snyder, “Fused Couplers: Condition for Insensitivity to External Refractive Index,” Electron. Lett. 23, 182 (1987).
[CrossRef]

K. S. Chiang, “Perturbation Analysis of Fused Tapered Single-Mode Fiber Couplers,” Electron. Lett. 23, 717 (1987).
[CrossRef]

K. S. Chiang, “Birefringent-Fibre Polarisation Splitters,” Electron. Lett. 23, 908 (1987).
[CrossRef]

B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, “Use of Highly Elliptical Core Fibers for Two-Mode Fiber Devices,” Opt. Lett. 12, 729–731 (1987).
[CrossRef] [PubMed]

J. N. Blake, S. Y. Huang, B. Y. Kim, H. J. Shaw, “Strain Effects on Highly Elliptical Core Two-Mode Fibers,” Opt. Lett. 12, 732–734 (1987).
[CrossRef] [PubMed]

1986

A. W. Snyder, X. H. Zheng, “Optical Fibers of Arbitrary Cross Sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
[CrossRef]

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, 608–613 (1986).
[CrossRef]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

X. H. Zheng, “Finite-Element Analysis for Fused Couplers,” Electron. Lett. 22, 804 (1986).
[CrossRef]

K. S. Chiang, “Analysis of Fused Couplers by the Effective-Index Method,” Electron. Lett. 22, 1221 (1986).
[CrossRef]

1985

A. W. Snyder, X. H. Zheng, “Fused Couplers of Arbitrary Cross-Section,” Electron. Lett. 21, 1079 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).

J. D. Love, M. Hall, “Polarisation Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).

R. G. Lamont, D. C. Johnson, K. O. Hill, “Power Transfer in Fused Biconical-Taper Single-Mode Fiber Couplers: Dependence on External Refractive Index,” Appl. Opt. 24, 327–332 (1985).
[CrossRef] [PubMed]

1983

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, 608–613 (1986).
[CrossRef]

Blake, J. N.

Bures, J.

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, 608–613 (1986).
[CrossRef]

Chiang, K. S.

K. S. Chiang, “Perturbation Analysis of Fused Tapered Single-Mode Fiber Couplers,” Electron. Lett. 23, 717 (1987).
[CrossRef]

K. S. Chiang, “Birefringent-Fibre Polarisation Splitters,” Electron. Lett. 23, 908 (1987).
[CrossRef]

K. S. Chiang, “Analysis of Fused Couplers by the Effective-Index Method,” Electron. Lett. 22, 1221 (1986).
[CrossRef]

Finegan, T.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

Hall, M.

J. D. Love, M. Hall, “Polarisation Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).

Hill, K. O.

Huang, S. Y.

Hussey, C. D.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).

Johnson, D. C.

Kim, B. Y.

Lacroix, S.

Lamont, R. G.

Lapierre, J.

Love, J. D.

J. D. Love, M. Hall, “Polarisation Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 407.
[CrossRef]

Mears, R. J.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

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, 608–613 (1986).
[CrossRef]

Payne, F. P.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).

Shaw, H. J.

Snyder, A. W.

X. H. Zheng, A. W. Snyder, “Fused Couplers: Condition for Insensitivity to External Refractive Index,” Electron. Lett. 23, 182 (1987).
[CrossRef]

A. W. Snyder, X. H. Zheng, “Optical Fibers of Arbitrary Cross Sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
[CrossRef]

A. W. Snyder, X. H. Zheng, “Fused Couplers of Arbitrary Cross-Section,” Electron. Lett. 21, 1079 (1985).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 407.
[CrossRef]

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, 608–613 (1986).
[CrossRef]

Yataki, M. S.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).

Zheng, X. H.

X. H. Zheng, A. W. Snyder, “Fused Couplers: Condition for Insensitivity to External Refractive Index,” Electron. Lett. 23, 182 (1987).
[CrossRef]

X. H. Zheng, “Finite-Element Analysis for Fused Couplers,” Electron. Lett. 22, 804 (1986).
[CrossRef]

A. W. Snyder, X. H. Zheng, “Optical Fibers of Arbitrary Cross Sections,” J. Opt. Soc. Am. A 3, 600–609 (1986).
[CrossRef]

A. W. Snyder, X. H. Zheng, “Fused Couplers of Arbitrary Cross-Section,” Electron. Lett. 21, 1079 (1985).
[CrossRef]

Appl. Opt.

Electron. Lett.

X. H. Zheng, “Finite-Element Analysis for Fused Couplers,” Electron. Lett. 22, 804 (1986).
[CrossRef]

X. H. Zheng, A. W. Snyder, “Fused Couplers: Condition for Insensitivity to External Refractive Index,” Electron. Lett. 23, 182 (1987).
[CrossRef]

A. W. Snyder, X. H. Zheng, “Fused Couplers of Arbitrary Cross-Section,” Electron. Lett. 21, 1079 (1985).
[CrossRef]

K. S. Chiang, “Analysis of Fused Couplers by the Effective-Index Method,” Electron. Lett. 22, 1221 (1986).
[CrossRef]

K. S. Chiang, “Perturbation Analysis of Fused Tapered Single-Mode Fiber Couplers,” Electron. Lett. 23, 717 (1987).
[CrossRef]

K. S. Chiang, “Birefringent-Fibre Polarisation Splitters,” Electron. Lett. 23, 908 (1987).
[CrossRef]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of Fused Taper Couplers on External Refractive Index,” Electron. Lett. 22, 1207 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modeling Fused Single-Mode Fibre Couplers,” Electron. Lett. 21, 461 (1985).

J. D. Love, M. Hall, “Polarisation Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).

IEEE/OSA J. Lightwave Technol.

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, 608–613 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 407.
[CrossRef]

S. Y. Huang, Shanghai Jiao Tong University; private communication.

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Figures (7)

Fig. 1
Fig. 1

(a) Dumbbell coupler cross section with the aspect ratio a/b and two center points L and R. (b) Phase relation between the fields at the two center points in the coupler cross section; Δθ is the phase difference between E11 and E01 at coupling Length z.

Fig. 2
Fig. 2

Phase difference Δϕ between E L and E R (solid curve) and the intensity coupling ratio R C = I L /(I L + I R ) (dotted curve) vs Δθ.

Fig. 3
Fig. 3

Characteristics of the coupling section of the couplers: (a) dimension b; (b) measured and calculated intensity coupling ratio R C ; (c) the aspect ratio a/b vs the coupling length z for the coupler with 0.33-dB excess loss; (d) general characteristics of another coupler with 1.2-dB excess loss. In (a), a, b, c, d, e, f, g, h are eight measured points, the near field and far field patterns of which are shown in Figs. 4 and 5: ——, dimension b;------, measured R C ; ............, calculated R C ; –···, aspect ratio a/b.

Fig. 4
Fig. 4

(a) Normal single-mode fiber, (b)–(h) Near field (left) and far field (right) patterns at different points in the coupler.

Fig. 5
Fig. 5

Determination of the forward direction by the principle of symmetry. (a) Far field patterns of point d in Fig. 3(a). Δα is the deviation angle of the maximum lobe of the far field patterns from the forward direction. (b) Far field patterns of point a in Fig. 3(a). Light is launched into the left tail (dotted curve) and the right tail (solid curve).

Fig. 6
Fig. 6

Deviation angle Δα from the experiments (solid curve) and the phase difference Δϕ in Fig. 2 (dashed curve) vs the intensity coupling ratio.

Fig. 7
Fig. 7

Relation between the near field patterns and the far field patterns of a two-mode fiber under stretch.

Equations (5)

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

E 01 = e 01 ( x , y , z ) exp { j 0 z β 01 ( z ) d z } ,
E 11 = e 11 ( x , y , z ) exp { j 0 z β 11 ( z ) d z } ,
E i = E 01 i + E 11 i ,
I L = ( E L ) 2 = 4 A 2 cos 2 { 0 z C ( z ) d z } ,
I R = ( E R ) 2 = 4 A 2 sin 2 { 0 z C ( z ) d z } ,

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