Abstract

The power-splitting ratio of fused tapered single-mode fiber couplers can be reversibly tuned by axial twisting without affecting loss. The twist-tuning behavior of a range of different tapered couplers is described. A simple expression for twist-tuning can be derived by representing the effects of twist by a change in the refractive index profile. Good agreement between this expression and experimental results is demonstrated. Repeated tuning over tens of thousands of cycles is found not to degrade coupler performance, and a number of practical applications, including a freely tunable tapered coupler, are described.

© 1989 Optical Society of America

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References

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  1. T. Bricheno and A. Fielding, "Stable Low-Loss Single-Mode Coupler," Electron. Lett. 20, 230–232 (1984).
    [CrossRef]
  2. B. S. Kawasaki, K. O. Hill, and R. G. Lamont, "Biconical-Taper Single-Mode Fiber Coupler," Opt. Lett. 6, 327–328 (1981).
    [CrossRef] [PubMed]
  3. S. P. Shipley and A. El Fatatry, "All Single-Mode Optical Fibre Wavelength-Tunable WDM with Very Narrow Pass/Stopband Separations," Electron. Lett. 23, 523–524 (1987).
    [CrossRef]
  4. M. B. J. Diemeer and W. J. DeVries, "Fused Coupler Switch Using a Thermo Optic Cladding," Electron. Lett. 24, 457–458 (1988).
    [CrossRef]
  5. R. G. Lamont, D. C. Johnson, and 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]
  6. F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
    [CrossRef]
  7. B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A Single-Mode-Fiber Coupler with a Variable Coupling Ratio," IEEE/OSA J. Lightwave Technol. LT-1, 176–178 (1983).
    [CrossRef]
  8. D. C. Johnson and K. O. Hill, "Control of Wavelength Selectivity of Power Transfer in Fused Biconical Monomode Directional Couplers," Appl. Opt. 25, 3800–3803 (1986).
    [CrossRef] [PubMed]
  9. S. Celaschi, J. T. De Jesus, and F. M. Smolka, "All-Fiber Tunable Beam Splitter" in Technical Digest, Conference on Lasers and ElectroOptics (Optical Society of America, Washington, DC, 1988), paper THM43.
  10. M. J. F. Digonnet and H. J. Shaw, "Analysis of a Tunable Single Mode Optical Fiber Coupler," IEEE J. Quantum Electron. QE-18, 746–754 (1982).
    [CrossRef]
  11. T. A Birks, "Practical Tuning Mechanism for Fused-Tapered Couplers," Opt. Lett. 13, 1126–1128 (1988).
    [CrossRef] [PubMed]
  12. F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
    [CrossRef]
  13. T. A. Birks and C. D. Hussey, "Control of Power-Splitting Ratio in Asymmetric Fused-Tapered Single-Mode Fiber Couplers," Opt. Lett. 13, 681–683 (1988).
    [CrossRef] [PubMed]
  14. F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).
  15. R. Ulrich and A. Simon, "Polarization Optics of Twisted Single-Mode Fibers," Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  16. M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
    [CrossRef]
  17. T. Bricheno and V. Baker, "All-Fibre Polarisation Splitter/Combiner," Electron. Lett. 21, 251–252 (1985).
    [CrossRef]
  18. D. Marcuse, "Field Deformation and Loss Caused by Curvature of Optical Fibers," J. Opt. Soc. Am. 66, 311–320 (1976).
    [CrossRef]
  19. A. W. Snyder and X. H. Zheng, "Optical Fibers of Arbitrary Cross Sections," J. Opt. Soc. Am. A 3, 600–609 (1986).
    [CrossRef]
  20. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 283–284.
  21. M. R. Spiegel, Mathematical Handbook (McGraw-Hill, New York, 1986), p. 125.
  22. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 5.
  23. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 229.
  24. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 218.
  25. E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983), pp. 369–378.
  26. Reference 20, pp. 567–575.
  27. Reference 20, p. 376.
  28. M. N. McLandrich, "Core Dopant Profiles in Weakly Fused Single-Mode Fibres," Electron. Lett. 24, 8–10 (1988).
    [CrossRef]
  29. M. H. Slonecker, S. E. Goodman, and J. C. Williams, "Low-Loss Environmentally Stable Single-Mode Optical Coupler for 1300-nm Operation," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984).
  30. M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).
  31. P. R. Morkel, U. Southampton; private communication.

1988 (4)

M. B. J. Diemeer and W. J. DeVries, "Fused Coupler Switch Using a Thermo Optic Cladding," Electron. Lett. 24, 457–458 (1988).
[CrossRef]

M. N. McLandrich, "Core Dopant Profiles in Weakly Fused Single-Mode Fibres," Electron. Lett. 24, 8–10 (1988).
[CrossRef]

T. A. Birks and C. D. Hussey, "Control of Power-Splitting Ratio in Asymmetric Fused-Tapered Single-Mode Fiber Couplers," Opt. Lett. 13, 681–683 (1988).
[CrossRef] [PubMed]

T. A Birks, "Practical Tuning Mechanism for Fused-Tapered Couplers," Opt. Lett. 13, 1126–1128 (1988).
[CrossRef] [PubMed]

1987 (1)

S. P. Shipley and A. El Fatatry, "All Single-Mode Optical Fibre Wavelength-Tunable WDM with Very Narrow Pass/Stopband Separations," Electron. Lett. 23, 523–524 (1987).
[CrossRef]

1986 (3)

1985 (5)

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).

M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
[CrossRef]

T. Bricheno and V. Baker, "All-Fibre Polarisation Splitter/Combiner," Electron. Lett. 21, 251–252 (1985).
[CrossRef]

R. G. Lamont, D. C. Johnson, and 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]

1984 (1)

T. Bricheno and A. Fielding, "Stable Low-Loss Single-Mode Coupler," Electron. Lett. 20, 230–232 (1984).
[CrossRef]

1983 (1)

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A Single-Mode-Fiber Coupler with a Variable Coupling Ratio," IEEE/OSA J. Lightwave Technol. LT-1, 176–178 (1983).
[CrossRef]

1982 (1)

M. J. F. Digonnet and H. J. Shaw, "Analysis of a Tunable Single Mode Optical Fiber Coupler," IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

1981 (1)

1979 (1)

1976 (1)

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 5.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 218.

Baker, V.

T. Bricheno and V. Baker, "All-Fibre Polarisation Splitter/Combiner," Electron. Lett. 21, 251–252 (1985).
[CrossRef]

Birks, T. A

Birks, T. A.

T. A. Birks and C. D. Hussey, "Control of Power-Splitting Ratio in Asymmetric Fused-Tapered Single-Mode Fiber Couplers," Opt. Lett. 13, 681–683 (1988).
[CrossRef] [PubMed]

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Bricheno, T.

T. Bricheno and V. Baker, "All-Fibre Polarisation Splitter/Combiner," Electron. Lett. 21, 251–252 (1985).
[CrossRef]

T. Bricheno and A. Fielding, "Stable Low-Loss Single-Mode Coupler," Electron. Lett. 20, 230–232 (1984).
[CrossRef]

Celaschi, S.

S. Celaschi, J. T. De Jesus, and F. M. Smolka, "All-Fiber Tunable Beam Splitter" in Technical Digest, Conference on Lasers and ElectroOptics (Optical Society of America, Washington, DC, 1988), paper THM43.

DeVries, W. J.

M. B. J. Diemeer and W. J. DeVries, "Fused Coupler Switch Using a Thermo Optic Cladding," Electron. Lett. 24, 457–458 (1988).
[CrossRef]

Diemeer, M. B. J.

M. B. J. Diemeer and W. J. DeVries, "Fused Coupler Switch Using a Thermo Optic Cladding," Electron. Lett. 24, 457–458 (1988).
[CrossRef]

Digonnet, M. J. F.

M. J. F. Digonnet and H. J. Shaw, "Analysis of a Tunable Single Mode Optical Fiber Coupler," IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

Farries, M. C.

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Fatatry, A. El

S. P. Shipley and A. El Fatatry, "All Single-Mode Optical Fibre Wavelength-Tunable WDM with Very Narrow Pass/Stopband Separations," Electron. Lett. 23, 523–524 (1987).
[CrossRef]

Fielding, A.

T. Bricheno and A. Fielding, "Stable Low-Loss Single-Mode Coupler," Electron. Lett. 20, 230–232 (1984).
[CrossRef]

Finegan, T.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

Goodman, S. E.

M. H. Slonecker, S. E. Goodman, and J. C. Williams, "Low-Loss Environmentally Stable Single-Mode Optical Coupler for 1300-nm Operation," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984).

Hill, K. O.

Hussey, C. D.

T. A. Birks and C. D. Hussey, "Control of Power-Splitting Ratio in Asymmetric Fused-Tapered Single-Mode Fiber Couplers," Opt. Lett. 13, 681–683 (1988).
[CrossRef] [PubMed]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).

Jesus, J. T. De

S. Celaschi, J. T. De Jesus, and F. M. Smolka, "All-Fiber Tunable Beam Splitter" in Technical Digest, Conference on Lasers and ElectroOptics (Optical Society of America, Washington, DC, 1988), paper THM43.

Johnson, D. C.

Kawachi, M.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A Single-Mode-Fiber Coupler with a Variable Coupling Ratio," IEEE/OSA J. Lightwave Technol. LT-1, 176–178 (1983).
[CrossRef]

Kawasaki, B. S.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A Single-Mode-Fiber Coupler with a Variable Coupling Ratio," IEEE/OSA J. Lightwave Technol. LT-1, 176–178 (1983).
[CrossRef]

B. S. Kawasaki, K. O. Hill, and R. G. Lamont, "Biconical-Taper Single-Mode Fiber Coupler," Opt. Lett. 6, 327–328 (1981).
[CrossRef] [PubMed]

Kreyszig, E.

E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983), pp. 369–378.

Laming, R. I.

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Lamont, R. G.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 229.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 283–284.

Marcuse, D.

McLandrich, M. N.

M. N. McLandrich, "Core Dopant Profiles in Weakly Fused Single-Mode Fibres," Electron. Lett. 24, 8–10 (1988).
[CrossRef]

Mears, R. J.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

Morkel, P. R.

P. R. Morkel, U. Southampton; private communication.

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Payne, D. N.

M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
[CrossRef]

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Payne, F. P.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).

Shaw, H. J.

M. J. F. Digonnet and H. J. Shaw, "Analysis of a Tunable Single Mode Optical Fiber Coupler," IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

Shipley, S. P.

S. P. Shipley and A. El Fatatry, "All Single-Mode Optical Fibre Wavelength-Tunable WDM with Very Narrow Pass/Stopband Separations," Electron. Lett. 23, 523–524 (1987).
[CrossRef]

Simon, A.

Slonecker, M. H.

M. H. Slonecker, S. E. Goodman, and J. C. Williams, "Low-Loss Environmentally Stable Single-Mode Optical Coupler for 1300-nm Operation," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984).

Smolka, F. M.

S. Celaschi, J. T. De Jesus, and F. M. Smolka, "All-Fiber Tunable Beam Splitter" in Technical Digest, Conference on Lasers and ElectroOptics (Optical Society of America, Washington, DC, 1988), paper THM43.

Snyder, A. W.

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

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 283–284.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 229.

Spiegel, M. R.

M. R. Spiegel, Mathematical Handbook (McGraw-Hill, New York, 1986), p. 125.

Tarbox, E. J.

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

Ulrich, R.

Varnham, M. P.

M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
[CrossRef]

Williams, J. C.

M. H. Slonecker, S. E. Goodman, and J. C. Williams, "Low-Loss Environmentally Stable Single-Mode Optical Coupler for 1300-nm Operation," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984).

Yataki, M. S.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).

M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
[CrossRef]

Zheng, X. H.

Appl. Opt. (3)

Electron. Lett. (9)

M. S. Yataki, D. N. Payne, and M. P. Varnham, "All-Fibre Polarising Beamsplitter," Electron. Lett. 21, 249–251 (1985).
[CrossRef]

T. Bricheno and V. Baker, "All-Fibre Polarisation Splitter/Combiner," Electron. Lett. 21, 251–252 (1985).
[CrossRef]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, and C. D. Hussey, "Dependence of Fused Taper Couplers on External Refractive Index," Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

T. Bricheno and A. Fielding, "Stable Low-Loss Single-Mode Coupler," Electron. Lett. 20, 230–232 (1984).
[CrossRef]

S. P. Shipley and A. El Fatatry, "All Single-Mode Optical Fibre Wavelength-Tunable WDM with Very Narrow Pass/Stopband Separations," Electron. Lett. 23, 523–524 (1987).
[CrossRef]

M. B. J. Diemeer and W. J. DeVries, "Fused Coupler Switch Using a Thermo Optic Cladding," Electron. Lett. 24, 457–458 (1988).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Polarisation Analysis of Strongly Fused and Weakly Fused Tapered Couplers," Electron. Lett. 21, 561–563 (1985).
[CrossRef]

M. N. McLandrich, "Core Dopant Profiles in Weakly Fused Single-Mode Fibres," Electron. Lett. 24, 8–10 (1988).
[CrossRef]

F. P. Payne, C. D. Hussey, and M. S. Yataki, "Modelling Fused Single-Mode-Fibre Couplers," Electron. Lett. 21, 461–462 (1985).

IEEE J. Quantum Electron. (1)

M. J. F. Digonnet and H. J. Shaw, "Analysis of a Tunable Single Mode Optical Fiber Coupler," IEEE J. Quantum Electron. QE-18, 746–754 (1982).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A Single-Mode-Fiber Coupler with a Variable Coupling Ratio," IEEE/OSA J. Lightwave Technol. LT-1, 176–178 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (3)

Other (12)

M. H. Slonecker, S. E. Goodman, and J. C. Williams, "Low-Loss Environmentally Stable Single-Mode Optical Coupler for 1300-nm Operation," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984).

M. C. Farries, R. I. Laming, P. R. Morkel, T. A. Birks, D. N. Payne, and E. J. Tarbox, "Efficient High-Gain Erbium-Doped Fiber Amplifier Pumped with a Frequency-Doubled Nd:YAG Laser," in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1989).

P. R. Morkel, U. Southampton; private communication.

S. Celaschi, J. T. De Jesus, and F. M. Smolka, "All-Fiber Tunable Beam Splitter" in Technical Digest, Conference on Lasers and ElectroOptics (Optical Society of America, Washington, DC, 1988), paper THM43.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 283–284.

M. R. Spiegel, Mathematical Handbook (McGraw-Hill, New York, 1986), p. 125.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 5.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 229.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 218.

E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983), pp. 369–378.

Reference 20, pp. 567–575.

Reference 20, p. 376.

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Figures (12)

Fig. 1
Fig. 1

Variation of the power-splitting ratio [= 10 log10(Pc/Pt), where Pc and Pt are the coupled and throughput output powers, respectively] at 870 nm of the 1-cycle coupler A as a function of the axial twist angle.

Fig. 2
Fig. 2

Spectral power-splitting ratio of coupler A under progressively increasing amounts of twist: (a) 0°; (b) 240°; and (c) 480°.

Fig. 3
Fig. 3

Variation of the power-splitting ratio at 810 nm of the 10-cycle coupler C as a function of the number of axial twist revolutions.

Fig. 4
Fig. 4

Variation of the power-splitting ratio at 825 nm of the 5-cycle coupler D as a function of the number of axial twist revolutions.

Fig. 5
Fig. 5

Number of twist revolutions required to decouple couplers E1−E4 through 0.5 cycles as a function of the degree of fusion.

Fig. 6
Fig. 6

Effective index profile neff across a section XX′ of a coupler before (solid line) and after (broken line) being twisted. The residual fiber cores are ignored.

Fig. 7
Fig. 7

Experimental (points) and predicted (solid line) variations of the number of twist revolutions T with the number of coupling cycles decoupled through (N0N) for the 10-cycle coupler C on a log–log scale.

Fig. 8
Fig. 8

Number of twist revolutions required to tune coupler F from N0 = 2.25 coupling cycles to N = 1.75 (□) and N = 1.25 (○) coupling cycles as the operating wavelength is changed.

Fig. 9
Fig. 9

Experimental (points) and predicted (solid line) variation of the number of twist revolutions T with the number of coupling cycles decoupled through (N0−N) for the 0.75-cycle coupler G on a log–log scale.

Fig. 10
Fig. 10

Variation of the loss of coupler G with the number of imposed twist revolutions T.

Fig. 11
Fig. 11

Spectral-splitting ratio of coupler H with 3 coupling cycles at 980 nm where this occurs during tapering (broken line) and after twisting the fully tapered coupler (solid line).

Fig. 12
Fig. 12

Construction of a simple tunable coupler package.

Equations (27)

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

N = C l π .
2 E 0 x 2 + 2 E 0 y 2 + ( k 2 n 0 2 β 0 2 ) E 0 = 0 ,
x = x cos ( b z ) y sin ( b z ) ,
y = x sin ( b z ) + y cos ( b z ) ,
z = z ,
2 E x 2 + 2 E y 2 + ( k 2 n 0 2 β 2 ) E + ( x 2 + y 2 ) β 2 h 2 b 2 E + 1 h 2 b 2 ( x x + y y ) E = 0 ,
h 2 = x 2 b 2 + y 2 b 2 + 1 .
h 2 1 .
2 E x 2 + 2 E y 2 + ( k 2 n eff 2 β 2 ) E = 0 ,
n eff 2 = [ 1 + ( x 2 + y 2 ) b 2 ] n 0 2
n eff = n 0 δ s δ z ,
n eff = n 0 [ 1 + r R cos ( ϕ ) ] ,
n eff 2 = [ 1 + ( x 2 + y 2 ) b 2 ] n 0 2
E 10 = 1 a 2 cos ( π x 4 a ) cos ( π y 2 a ) ,
E 20 = 1 a 2 sin ( π x 2 a ) cos ( π y 2 a ) ,
β p 0 2 = k 2 n 0 2 ( 4 + p 2 ) π 2 16 a 2 ; p = 1 , 2 ,
Δ n eff 2 = ( x 2 + y 2 ) b 2 n 0 2
β p 2 = β p 0 2 + k 2 E p 0 2 Δ n eff 2 dxdy
Δ β = Δ β 0 9 32 b 2 Δ β 0 ,
Δ β 0 = 3 π 2 32 a 2 k n 0 ,
N = Δ β Δ β 0 N 0
l = 2 π N 0 Δ β 0 ,
T = l 2 π b = N 0 Δ β 0 b .
N = ( 1 9 T 2 32 N 0 2 ) N 0 ,
T 2 = 32 9 ( N 0 N ) .
d N d T = 9 T 16 N 0 ,
T neg = 4 2 3 N 0

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