Abstract

Random polarization coupling with a broadband source in birefringent polarization-maintaining fibers is carefully studied. The effect of the broad bandwidth of light on cross talk is formulated in the mode-coupling parameter by means of the autocorrelation function of the light electric field. It is shown that, for light with a Lorentzian-shaped spectrum, cross talk increases as the spectral width becomes larger but is invariant for light with a Gaussian-shaped spectrum.

© 1985 Optical Society of America

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References

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  1. Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
    [CrossRef]
  2. R. Ulrich, M. Johnson, “Fiber-ring interferometer: polarization analysis,” Opt. Lett. 4, 152–154 (1979).
    [CrossRef] [PubMed]
  3. I. Jeunhome, M. Monerie, “Polarisation-maintaining single-mode fiber cable design,” Electron. Lett. 17, 388–389 (1981).
  4. T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
    [CrossRef]
  5. V. Ramaswamy, W. G. French, R. D. Standley, “Polarization characteristics of noncircular core single-mode fibers,” Appl. Opt. 17, 3014–3017 (1978).
    [CrossRef] [PubMed]
  6. T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
    [CrossRef]
  7. R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
    [CrossRef]
  8. S. C. Rashleigh, W. K. Burns, R. P. Moeller, R. Ulrich, “Polarization holding in birefringent single-mode fibers,” Opt. Lett. 7, 40–42 (1982).
    [CrossRef] [PubMed]
  9. I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
    [CrossRef]
  10. K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
    [CrossRef]
  11. J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
    [CrossRef]
  12. C. J. Nielson, “Impulse response of single-mode fibers with polarization mode coupling,”J. Opt. Soc. Am. 73, 1603–1611 (1983).
    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).
  14. K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
    [CrossRef] [PubMed]
  15. E. D. Hinkley, C. Freed, “Direct observation of the Lorentzian line shape as limited by quantum phase noise in a laser above threshold,” Phys. Rev. Lett. 23, 277–280 (1969).
    [CrossRef]
  16. W. K. Burns, R. P. Moeller, “Measurement of polarization mode dispersion in high-birefringence fibers,” Opt. Lett. 8, 195–197 (1983).
    [CrossRef] [PubMed]
  17. W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

1983 (2)

1982 (5)

K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
[CrossRef] [PubMed]

R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
[CrossRef]

S. C. Rashleigh, W. K. Burns, R. P. Moeller, R. Ulrich, “Polarization holding in birefringent single-mode fibers,” Opt. Lett. 7, 40–42 (1982).
[CrossRef] [PubMed]

K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
[CrossRef]

J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
[CrossRef]

1981 (5)

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

I. Jeunhome, M. Monerie, “Polarisation-maintaining single-mode fiber cable design,” Electron. Lett. 17, 388–389 (1981).

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
[CrossRef]

1979 (1)

1978 (1)

1969 (1)

E. D. Hinkley, C. Freed, “Direct observation of the Lorentzian line shape as limited by quantum phase noise in a laser above threshold,” Phys. Rev. Lett. 23, 277–280 (1969).
[CrossRef]

Birch, R.

R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Burns, W. K.

Edahiro, T.

K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
[CrossRef] [PubMed]

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

Freed, C.

E. D. Hinkley, C. Freed, “Direct observation of the Lorentzian line shape as limited by quantum phase noise in a laser above threshold,” Phys. Rev. Lett. 23, 277–280 (1969).
[CrossRef]

French, W. G.

Hinkley, E. D.

E. D. Hinkley, C. Freed, “Direct observation of the Lorentzian line shape as limited by quantum phase noise in a laser above threshold,” Phys. Rev. Lett. 23, 277–280 (1969).
[CrossRef]

Hosaka, T.

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

Jeunhome, I.

I. Jeunhome, M. Monerie, “Polarisation-maintaining single-mode fiber cable design,” Electron. Lett. 17, 388–389 (1981).

Johnson, M.

Kaminov, I. P.

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Katsuyama, T.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
[CrossRef]

Kimura, T.

J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
[CrossRef]

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

Machida, S.

J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
[CrossRef]

Magnus, W.

W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

Matsumura, H.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
[CrossRef]

Miya, T.

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

Moeller, R. P.

Monerie, M.

I. Jeunhome, M. Monerie, “Polarisation-maintaining single-mode fiber cable design,” Electron. Lett. 17, 388–389 (1981).

Nielson, C. J.

Oberhettinger, F.

W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

Okamoto, K.

K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
[CrossRef] [PubMed]

K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
[CrossRef]

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

Payne, D.

R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
[CrossRef]

Ramaswamy, V.

Rashleigh, S. C.

Sakai, J.

J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
[CrossRef]

Sasaki, Y.

K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
[CrossRef]

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

Shibata, N.

K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
[CrossRef]

K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
[CrossRef] [PubMed]

Standley, R. D.

Suganuma, T.

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
[CrossRef]

Tricomi, F. G.

W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

Ulrich, R.

Varnham, M. P.

R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Yamamoto, Y.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (4)

T. Katsuyama, H. Matsumura, T. Suganuma, “Low-loss single polarisation fibres,” Electron. Lett. 17, 473–479 (1981).
[CrossRef]

R. Birch, D. Payne, M. P. Varnham, “Fabrication of polarisation maintaining fibres using gas-phase etching,” Electron. Lett. 18, 1036–1037 (1982).
[CrossRef]

I. Jeunhome, M. Monerie, “Polarisation-maintaining single-mode fiber cable design,” Electron. Lett. 17, 388–389 (1981).

T. Hosaka, K. Okamoto, T. Miya, Y. Sasaki, T. Edahiro, “Low loss single polarisation fibres with asymmetric strain birefringence,” Electron. Lett. 17, 530–531 (1981).
[CrossRef]

IEEE J. Quantum Electron. (4)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

K. Okamoto, Y. Sasaki, N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. QE-18, 1890–1899 (1982).
[CrossRef]

J. Sakai, S. Machida, T. Kimura, “Degree of polarization in anisotropic single-mode optical fibers: theory,” IEEE J. Quantum Electron. QE-18, 488–495 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

E. D. Hinkley, C. Freed, “Direct observation of the Lorentzian line shape as limited by quantum phase noise in a laser above threshold,” Phys. Rev. Lett. 23, 277–280 (1969).
[CrossRef]

Other (2)

W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

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Figures (8)

Fig. 1
Fig. 1

Polarization-maintaining fiber with random perturbations.

Fig. 2
Fig. 2

Schematic diagram of the autocorrelation functions of R(u) and F(Du).

Fig. 3
Fig. 3

Deformation of stress-applying part that is due to angle deformation in the clockwise direction.

Fig. 4
Fig. 4

Comparison of autocorrelation function for four spectral-density shapes with single peak intensity. Δν is the angular half-width at half-maximum intensity; τ is group-delay-time difference.

Fig. 5
Fig. 5

Mode-coupling parameter as a function of the spectral width Δν for a Lorentzian spectrum.

Fig. 6
Fig. 6

Mode-coupling parameter as a function of the spectral width Δν for a Gaussian spectrum.

Fig. 7
Fig. 7

Mode-coupling parameter as a function of the spectral width Δν for a sinc spectrum.

Fig. 8
Fig. 8

Schematic diagram of light propagation in the excited (HE11x) and the coupled (HE11y) modes. Ω is a part of the statistically independent ensembles resulting from the dephasing process.

Equations (33)

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η ( z ) = tanh ( h z ) ,
h = - + R ( u ) exp ( - j Δ β u ) d u ,
E ˜ ( r , t ) = μ = x , y C μ ( z , t ) E μ ( r ) ,
H ˜ ( r , t ) = μ = x , y C μ ( z , t ) H μ ( r ) ,
C μ ( z , t ) = 0 + H μ ( z , ω ) e j ω t d ω .
d H μ ( z , ω ) d z + j β μ ( ω ) H μ ( Z , ω ) = - j Γ ( ω , z ) H ν ( z , ω )             ( μ ν ) ,
C x ( z , t ) = exp [ j ( ω 0 t - β x z ) ] f [ t - ( z / v x ) ] ,
C y ( z , t ) = - j 0 z Γ ( z ) exp ( j { ω 0 t - [ β x 0 z + β y 0 × ( z - z ) ] } ) f [ t - ( z / v x ) - ( z - z / v y ) ] d z ,
η ( z ) = C y ( z , t ) 2 z , t C x ( z , t ) 2 z , t = h c z ,
h c = - + R ( u ) F ( D u ) exp ( - j Δ β u ) d u ,
F ( τ ) = f ( t + τ ) f * ( t ) t / f ( t ) f * ( t ) t .
Γ ( z ) = - ( 2 / 7 ) k ( C 1 - C 2 ) ( 0.108 - Δ ) θ d ( z ) ,
R ( u ) = η 1 2 K 2 θ ¯ d 2 exp [ - ( u / l s ) ] ,
F ( τ ) = exp ( - Δ ω τ )
F ( τ ) = exp [ - ( δ ω τ / 2 ) 2 ] .
F ( τ ) = sin ( Δ ω τ ) Δ ω τ .
G ( ω ) = { sin [ ( ω - ω 0 ) / δ ω ] / [ ( ω - ω 0 ) / δ ω ) ] } 2 , F ( τ ) = { 1 - ½ δ ω τ τ < 2 / δ ω 0 τ > 2 / δ ω
h c = 2 η 1 2 K 2 θ ¯ d 2 ( 1 l ) ( Δ β ) 2 + ( 1 l ) 2 ,
h c = 2 η 1 2 K 2 θ ¯ d 2 ( Δ β ) 2 ( 1 l s + c D L c ) ,
h c = 2 η 1 2 K 2 θ ¯ d 2 D δ ω exp { [ 1 D δ ω ( 1 l s + j Δ β ) ] 2 } × erfc [ 1 D δ ω ( 1 l s + j Δ β ) ] + c . c . ,
erfc ( x ) = x + e - t 2 d t .
erfc ( x ) ~ e - t 2 n = 0 ( - 1 ) n ( 2 n - 1 ) ! ! 2 n + 1 x 2 n + 1
h c = 2 η 1 2 K 2 θ ¯ d 2 ( Δ β ) 2 l s [ 1 + 3 2 ( D δ ω Δ β ) 2 ] .
h c = 2 η 1 2 K 2 θ ¯ d 2 ( Δ β ) 2 l s [ 1 + l s D δ ω 2 ( 1 - { exp [ - ( 2 D δ ω l s ) ] } × cos ( 2 Δ β D δ ω ) ) ] .
G T ( ω ) = n G n G ( ω - ω 0 - n ω 1 Δ ω n ) ,
G ( ω Δ ω n ) = ( Δ ω n ) 2 ω 2 + ( Δ ω n ) 2
F T ( τ ) = n G n exp ( j n ω 1 τ ) F ( τ Δ ω n ) Δ ω n / n G n Δ ω n ,
h c = η 1 2 K 2 θ ¯ d 2 n G n Δ ω n - + R ( u ) F ( D u Δ ω n ) exp [ - j ( Δ β - n ω 1 D ) u ] d u n G n Δ ω n .
P ( B n ) = ( u 2 l s ) n n ! exp [ - ( u / 2 l s ) ] .
θ d ( z + u ) θ d ( z ) z = n = 0 ( - 1 ) n θ ¯ d 2 P ( B n ) = θ ¯ d 2 exp [ - ( u / 2 l s ) ] n = 0 ( - 1 ) n ( u 2 l s ) n ! n = θ ¯ d 2 exp ( - u / l s ) .
h c = ( η 1 2 K 2 θ ¯ d 2 ) / ( D Δ ω ) arctan × [ 2 ( D Δ ω / l s ) ( 1 / l s ) 2 + ( Δ β ) 2 - ( D Δ ω ) 2 ] .
h c = ( η 1 2 K 2 θ ¯ d 2 / D Δ ω ) arctan [ ( 2 D Δ ω / l s Δ β 2 ) 1 - ( D Δ ω / Δ β ) 2 ] .
h c = 2 η 1 2 K 2 θ ¯ d 2 / [ Δ β ) 2 l s ] .

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