Abstract

Polarization dispersion in single-mode fiber with random polarization mode coupling is given a statistical treatment based on the recently proposed principal-states model. An expression for the ensemble variance of the differential delay time between the principal states of polarization is derived by using coupled-mode theory under the assumption of weak coupling. For long fiber lengths, the variance is shown to have a linear dependence on length while the probability density function for the delay time approaches a Gaussian shape.

© 1988 Optical Society of America

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References

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  1. C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
    [CrossRef]
  2. N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
    [CrossRef]
  3. D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
    [CrossRef] [PubMed]
  4. C. D. Poole, C. R. Giles, Opt. Lett. 13, 155 (1988).
    [CrossRef] [PubMed]
  5. C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).
  6. The differential delay time of previous papers was defined as a positive quantity and denoted by Δτ. The notation δτ is used here to avoid confusion.
  7. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  8. I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]
  9. S. C. Rashleigh, W. K. Burns, R. P. Moeller, R. Ulrich, Opt. Lett. 7, 40 (1982).
    [CrossRef] [PubMed]
  10. S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971). Note that lc = 1/h in this reference.
  11. S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
    [CrossRef]
  12. B. Crosignani, S. Wabnitz, P. Di Porto, Opt. Lett. 9, 371 (1984).
    [CrossRef] [PubMed]

1988 (2)

C. D. Poole, C. R. Giles, Opt. Lett. 13, 155 (1988).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

1987 (2)

N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, B. Daino, Opt. Lett. 12, 844 (1987).
[CrossRef] [PubMed]

1986 (1)

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

1984 (1)

1982 (1)

1981 (1)

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

1978 (1)

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

1971 (1)

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971). Note that lc = 1/h in this reference.

Andresciani, D.

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
[CrossRef]

Burns, W. K.

Crosignani, B.

Curti, F.

Daino, B.

Di Porto, P.

Giles, C. R.

Ikeda, M.

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Kawakami, S.

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Matera, F.

Moeller, R. P.

Personick, S. D.

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971). Note that lc = 1/h in this reference.

Poole, C. D.

C. D. Poole, C. R. Giles, Opt. Lett. 13, 155 (1988).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
[CrossRef]

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Rashleigh, S. C.

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

Ulrich, R.

Wabnitz, S.

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
[CrossRef]

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Bell Syst. Tech. J. (1)

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971). Note that lc = 1/h in this reference.

Electron. Lett. (1)

C. D. Poole, R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (2)

N. S. Bergano, C. D. Poole, R. E. Wagner, IEEE J. Lightwave Technol. LT-5, 1618 (1987).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, IEEE J. Lightwave Technol. LT-6, 1184 (1988).

IEEE J. Quantum Electron. (2)

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

S. Kawakami, M. Ikeda, IEEE J. Quantum Electron. QE-14, 608 (1978).
[CrossRef]

Opt. Lett. (4)

Other (2)

The differential delay time of previous papers was defined as a positive quantity and denoted by Δτ. The notation δτ is used here to avoid confusion.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

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Equations (18)

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E ( r , ω , z ) = T ( ω , z ) E ( r , ω , 0 ) ,
T ( ω , z ) = exp [ - α z 2 + i ψ ( ω , z ) ] × [ u 1 ( ω , z ) u 2 ( ω , z ) - u 2 * ( ω , z ) u 1 * ( ω , z ) ] ,
δ τ 2 ( z ) = 4 u 1 ( ω , z ) 2 + u 2 ( ω , z ) 2 ,
E ( r , ω , z ) z = [ - α / 2 + i β 1 i κ ( z ) i κ * ( z ) - α / 2 + i β 2 ] E ( r , ω , z ) ,
ψ ( ω , z ) z = β 1 + β 2 2 ,
a 1 ( ω , z ) z = - i κ ( z ) a 2 * ( ω , z ) exp ( - i Δ β z ) ,
a 2 ( ω , z ) z = i κ ( z ) a 1 * ( ω , z ) exp ( - i Δ β z ) ,
d δ τ 2 ( z ) d z = 4 i Δ β a 1 a 1 * + a 2 a 2 * + 2 Δ β 2 z ,
d 2 δ τ 2 ( z ) d z 2 = - 4 Δ β exp ( i Δ β z ) κ * ( z ) ( a 1 a 2 - a 1 a 2 ) + c . c . + 2 Δ β 2 ,
a m ( z ) = a m ( z 1 ) + ( - 1 ) m i a n * ( z 1 ) z 1 z κ ( x ) exp ( - i Δ β x ) d x ,
d 2 δ τ 2 ( z ) d z 2 = [ - 8 i Δ β F ( z ) ( a 1 a 1 * + a 2 a 2 * ) z 1 - 4 Δ β 2 z F ( z ) ] + c . c . + 2 Δ β 2 ,
d 2 δ τ 2 ( z ) d z 2 = - 2 h d δ τ 2 ( z ) d z + 2 Δ β 2 ,
δ τ 2 ( z ) = Δ β 2 2 h 2 [ exp ( - 2 h z ) - 1 + 2 h z ] .
lim h z 0 δ τ 2 ( z ) = Δ β 2 z 2             ( negligible mode coupling ) ,
lim h z δ τ 2 ( z ) = Δ β 2 z h             ( extensive mode coupling ) .
lim h z p out ( t ) = - [ cos 2 θ p in ( t - τ d + δ τ 2 ) + sin 2 θ p in ( t + τ d - δ τ 2 ) ] × P δ τ ( δ τ ) d δ τ ,
lim h z p out ( t ) = - p in ( t ) η ( t - t ) d t ,
lim h z P δ τ ( x ) = 1 2 π σ exp ( - x 2 2 σ 2 ) ,

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