Abstract

The effect of twist on fused couplers is discussed theoretically. We find that the twist, large or small, introduced unintentionally in fused couplers may deteriorate the extinction ratio of polarization splitting when devices are used as polarization beam splitters, and that the modulation period of the spectral response of fused couplers can be tuned by controlling the twist rate when they are used as wavelength filters.

© 1988 Optical Society of America

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References

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  1. A. C. Boucouvalas, C. Georgiou, “Method for Fine-Tuning the Wavelength Response of Single-Mode Optical-Fiber Taper Filters,” Electron. Lett. 23, 410 (1987).
    [CrossRef]
  2. J. D. Love, M. Hall, “Polarization Modulation in Long Couplers,” Electron. Lett. 21, 519 (1985).
  3. F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling Fused Single-Mode-Fibre Couplers,” Electron. Lett. 21, 461 (1985).
  4. F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarization Analysis of Strongly Fused and Weakly Fused Tapered Couplers,” Electron. Lett. 21, 561 (1985).
    [CrossRef]
  5. K. S. Chiang, “Birefringent-Fiber Polarization Splitters,” Electron. Lett. 23, 908 (1987).
    [CrossRef]
  6. Y. Chen, “Behaviour of Polarization Beam Splitters made from Different Types of Fiber,” Appl. Phys. B 45, 17 (1988).
    [CrossRef]
  7. K. S. Chiang, “Effects of Cores in Fused Tapered Single-Mode Fiber Couplers,” Opt. Lett. 12, 431 (1987).
    [CrossRef] [PubMed]
  8. X-H. Zheng, “Finite-Element Analysis for Fused Couplers,” Electron. Lett. 22, 804 (1986).
    [CrossRef]
  9. C. L. Chen, W. K. Burn, “Polarization Characteristics of Single-Mode Fiber Couplers,” IEEE J. Quantum Electron. QE-18, 1589 (1982).
    [CrossRef]
  10. R. Ulrich, A. Simon, “Polarization Optics of Twisted Single-Moded Fibers,” Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]

1988 (1)

Y. Chen, “Behaviour of Polarization Beam Splitters made from Different Types of Fiber,” Appl. Phys. B 45, 17 (1988).
[CrossRef]

1987 (3)

K. S. Chiang, “Effects of Cores in Fused Tapered Single-Mode Fiber Couplers,” Opt. Lett. 12, 431 (1987).
[CrossRef] [PubMed]

A. C. Boucouvalas, C. Georgiou, “Method for Fine-Tuning the Wavelength Response of Single-Mode Optical-Fiber Taper Filters,” Electron. Lett. 23, 410 (1987).
[CrossRef]

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

1986 (1)

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

1985 (3)

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

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

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

1982 (1)

C. L. Chen, W. K. Burn, “Polarization Characteristics of Single-Mode Fiber Couplers,” IEEE J. Quantum Electron. QE-18, 1589 (1982).
[CrossRef]

1979 (1)

Boucouvalas, A. C.

A. C. Boucouvalas, C. Georgiou, “Method for Fine-Tuning the Wavelength Response of Single-Mode Optical-Fiber Taper Filters,” Electron. Lett. 23, 410 (1987).
[CrossRef]

Burn, W. K.

C. L. Chen, W. K. Burn, “Polarization Characteristics of Single-Mode Fiber Couplers,” IEEE J. Quantum Electron. QE-18, 1589 (1982).
[CrossRef]

Chen, C. L.

C. L. Chen, W. K. Burn, “Polarization Characteristics of Single-Mode Fiber Couplers,” IEEE J. Quantum Electron. QE-18, 1589 (1982).
[CrossRef]

Chen, Y.

Y. Chen, “Behaviour of Polarization Beam Splitters made from Different Types of Fiber,” Appl. Phys. B 45, 17 (1988).
[CrossRef]

Chiang, K. S.

K. S. Chiang, “Effects of Cores in Fused Tapered Single-Mode Fiber Couplers,” Opt. Lett. 12, 431 (1987).
[CrossRef] [PubMed]

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

Georgiou, C.

A. C. Boucouvalas, C. Georgiou, “Method for Fine-Tuning the Wavelength Response of Single-Mode Optical-Fiber Taper Filters,” Electron. Lett. 23, 410 (1987).
[CrossRef]

Hall, M.

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

Hussey, C. D.

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

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

Love, J. D.

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

Payne, F. P.

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

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

Simon, A.

Ulrich, R.

Yataki, M. S.

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

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

Zheng, X-H.

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

Appl. Opt. (1)

Appl. Phys. B (1)

Y. Chen, “Behaviour of Polarization Beam Splitters made from Different Types of Fiber,” Appl. Phys. B 45, 17 (1988).
[CrossRef]

Electron. Lett. (6)

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

A. C. Boucouvalas, C. Georgiou, “Method for Fine-Tuning the Wavelength Response of Single-Mode Optical-Fiber Taper Filters,” Electron. Lett. 23, 410 (1987).
[CrossRef]

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

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

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

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

IEEE J. Quantum Electron. (1)

C. L. Chen, W. K. Burn, “Polarization Characteristics of Single-Mode Fiber Couplers,” IEEE J. Quantum Electron. QE-18, 1589 (1982).
[CrossRef]

Opt. Lett. (1)

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Figures (4)

Fig. 1
Fig. 1

Rectangular model.

Fig. 2
Fig. 2

Extinction ratio as a function of twist rate for a = 9 μm, L = 188.4 mm, n2 = 1.458, n3 = 1, λ0 = 1.3015 μm.

Fig. 3
Fig. 3

Spectral response of fused couplers with L = 125 mm, a = 9 μm, n2 = 1.458, n3 = 1; the solid line is for an untwisted coupler and the dashed line is for a twisted coupler.

Fig. 4
Fig. 4

Fractional shift of modulation wavelength response vs twist rate for n2 = 1.458 and n3 = 1.

Equations (40)

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P 1 x = ¼ [ 1 + A 1 cos ( C x + C y ) L - A 2 sin ( C x + C y ) L ] ,
P 1 y = ¼ [ 1 + A 1 cos ( C x + C y ) L + A 2 sin ( C x + C y ) L ] ,
P 2 x = ¼ [ 1 - A 1 cos ( C x + C y ) L + A 2 sin ( C x + C y ) L ] ,
P 2 y = ¼ [ 1 - A 1 cos ( C x + C y ) L - A 2 sin ( C x + C y ) L ] ,
C x + C y = 3 π λ 32 n 2 a 2 ,
A 1 = cos Q 1 L cos Q 2 L + 1 Q 1 Q 2 ( Δ β 1 Δ β 2 4 + ξ 2 ) sin Q 1 L sin Q 2 L ,
A 2 = 1 2 ( Δ β 1 Q 1 sin Q 1 L cos Q 2 L - Δ β 2 Q 2 sin Q 2 L cos Q 1 L ) ,
Q 1 = [ ( ½ Δ β 1 ) 2 + ξ 2 ] ½ ,
Q 2 = [ ( ½ Δ β 2 ) 2 + ξ 2 ] 1 / 2 ,
α = g τ .
Δ β 1 = π λ 4 n 2 ( 1 - n 3 2 n 2 2 ) ( 4 b 2 V b - 1 2 a 2 V a ) ,
Δ β 2 = π λ 4 n 2 ( 1 - n 3 2 n 2 2 ) ( 4 b 2 V b - 1 2 a 2 V a ) ,
V a = 2 z a λ n 2 2 - n 3 2 ,             V b = 2 π b λ n 2 2 - n 3 2 .
A 1 cos ( C x + C y ) L = 0 ,
A 2 sin ( C x + C y ) L = 1
C x L = ( n + m + 1 ) π 2 ,
C y L = ( n - m ) π 2 ,
E 1 = 10 | log P 1 x P 1 y | ,             E 2 = 10 | log P 2 y P 2 x | ,
E 1 ( λ 0 ) = E 2 ( λ 0 ) = | log 1 - A 2 1 + A 2 | ,
P 1 = ½ [ 1 + A 1 cos ( C x + C y ) L ] ,
P 2 = ½ [ 1 - A 1 cos ( C x + C y ) L ] ,
E = cos θ x ^ + sin θ exp ( - j ϕ y ^ )
P 1 x = ¼ [ 1 + A 6 + O 1 + cos ( C x + C y ) L - O 2 + sin ( C x + C y ) L ] ,
P 1 y = ¼ [ 1 - A 6 + O 1 - cos ( C x + C y ) L + O 2 - sin ( C x + C y ) L ] ,
P 2 x = ¼ [ 1 + A 6 - O 1 + cos ( C x + C y ) L + O 2 + sin ( C x + C y ) L ] ,
P 2 y = ¼ [ 1 - A 6 - O 1 - cos ( C x + C y ) L - O 2 - sin ( C x + C y ) L ] ,
O 1 ± = A 1 ± A 4 cos 2 θ ± [ A 3 cos ϕ + ξ ( Δ β 1 + Δ β 2 ) 2 Q 1 Q 2 × sin Q 1 L sin Q 2 L sin ϕ ] sin 2 θ ,
O 2 ± = A 2 ± A 5 ,
A 3 = ξ Q 1 cos Q 2 L sin Q 1 L + ξ Q 2 cos Q 1 L sin Q 2 L ,
A 4 = cos Q 1 L cos Q 2 L + 1 Q 1 Q 2 ( Δ β 1 Δ β 2 4 - ξ 2 ) sin Q 1 L sin Q 2 L ,
A 5 = A 2 cos 2 θ + [ Δ β 1 - Δ β 2 2 Q 1 Q 2 ξ sin Q 1 L sin Q 2 L cos ϕ + ( ξ Q 1 sin Q 1 L cos Q 2 L - ξ Q 2 sin Q 2 L cos Q 1 L ) sin ϕ ] sin 2 θ ,
A 6 = ( 1 - ξ 2 Q 1 2 sin 2 Q 1 L - ξ 2 Q 2 2 sin 2 Q 2 L ) cos 2 θ + [ cos ϕ ( ξ Q 1 cos Q 1 L sin Q 1 L + ξ Q 2 cos Q 2 L sin Q 2 L ) + 0.5 ξ sin ϕ ( Δ β 1 Q 1 2 sin 2 Q 1 L + Δ β 2 Q 2 2 sin 2 Q 2 L ) ] sin 2 θ ,
P 1 x = P 2 y = ½ ,             P 2 x = P 1 y = 0 ,
P 1 x = P 2 y = 0 ,             P 2 x = P 1 y = ½ ,
E 1 ( λ 0 ) = 10 | log 1 + A 6 - O 2 + 1 - A 6 + O 2 - | ,
E 2 ( λ 0 ) = 10 | log 1 - A 6 - O 2 - 1 + A 6 + O 2 + | ,
P 1 = ½ [ 1 + A 1 cos ( C x + C y ) L - A 5 sin ( C x + C y ) L ] ,
P 2 = ½ [ 1 - A 1 cos ( C x + C y ) L + A 5 sin ( C x + C y ) L ] .
P i = 1 2 { 1 ± A 1 2 + A 5 2 cos [ ( C x + C y ) L + tan - 1 A 5 A 1 ] } ,
tan - 1 A 5 - A 1 cos 2 θ tan - 1 ( C x - C y ) L A 1 + A 5 cos 2 θ tan - 1 ( C x - C y ) L

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