Abstract

Intentional birefringence induces an excess loss on one of the two polarization states of a single-mode optical fiber. Yet it may be not sufficient to avoid polarization coupling completely. In this case, we have some undesired effects, such as excess attenuation of the desired polarization as well, finite value of the extinction ratio, and residual polarization dispersion. Such effects are investigated through a coupled power model, which leads to completely analytical results.

© 1985 Optical Society of America

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  1. R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
    [CrossRef]
  2. T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1148 (1982).
    [CrossRef]
  3. I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
    [CrossRef]
  4. A. W. Snyder, F. Rühl, “Single-mode, single-polarization fibers made of birefringent material,” J. Opt. Soc. Am. 73, 1165–1174 (1983).
    [CrossRef]
  5. R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
    [CrossRef]
  6. T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
    [CrossRef]
  7. M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
    [CrossRef]
  8. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  9. A. W. Snyder, F. Rühl, “Practical single-polarization anisotropic fibres,” Electron. Lett. 19, 687–688 (1983).
    [CrossRef]
  10. D. Marcuse, “Coupled-mode theory for anisotropic optical waveguides,” Bell Syst. Tech. J. 54, 985–995 (1975).
    [CrossRef]
  11. 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]
  12. D. Marcuse, “Microbending losses of single-mode, step-index and multimode, parabolic-index fibers,” Bell Syst. Tech. J. 55, 937–955 (1976).
    [CrossRef]
  13. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  14. G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibres: perturbative solution of the time-dependent power flow equation,” Opt. Quantum Electron. 15, 119–136 (1983).
    [CrossRef]
  15. G. Cancellieri, P. Fantini, U. Pesciarelli, “Effects of joints on single-mode single-polarization optical fiber links,” Appl. Opt. 24, 964–969 (1985).
    [CrossRef] [PubMed]
  16. S. Kawakami, M. Ikeda, “Transmission characteristics of a two-mode optical waveguide,” IEEE J. Quantum Electron. QE-14, 608–614 (1978).
    [CrossRef]

1985

1984

R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
[CrossRef]

1983

A. W. Snyder, F. Rühl, “Single-mode, single-polarization fibers made of birefringent material,” J. Opt. Soc. Am. 73, 1165–1174 (1983).
[CrossRef]

T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

A. W. Snyder, F. Rühl, “Practical single-polarization anisotropic fibres,” Electron. Lett. 19, 687–688 (1983).
[CrossRef]

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibres: perturbative solution of the time-dependent power flow equation,” Opt. Quantum Electron. 15, 119–136 (1983).
[CrossRef]

1982

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. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1148 (1982).
[CrossRef]

1981

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

1979

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

1978

S. Kawakami, M. Ikeda, “Transmission characteristics of a two-mode optical waveguide,” IEEE J. Quantum Electron. QE-14, 608–614 (1978).
[CrossRef]

1976

D. Marcuse, “Microbending losses of single-mode, step-index and multimode, parabolic-index fibers,” Bell Syst. Tech. J. 55, 937–955 (1976).
[CrossRef]

1975

D. Marcuse, “Coupled-mode theory for anisotropic optical waveguides,” Bell Syst. Tech. J. 54, 985–995 (1975).
[CrossRef]

Aihara, T.

T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

Bergh, R. A.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
[CrossRef]

Birch, R. D.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Cancellieri, G.

G. Cancellieri, P. Fantini, U. Pesciarelli, “Effects of joints on single-mode single-polarization optical fiber links,” Appl. Opt. 24, 964–969 (1985).
[CrossRef] [PubMed]

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibres: perturbative solution of the time-dependent power flow equation,” Opt. Quantum Electron. 15, 119–136 (1983).
[CrossRef]

Cozens, J. R.

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

Dyott, R. B.

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

Fantini, P.

G. Cancellieri, P. Fantini, U. Pesciarelli, “Effects of joints on single-mode single-polarization optical fiber links,” Appl. Opt. 24, 964–969 (1985).
[CrossRef] [PubMed]

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibres: perturbative solution of the time-dependent power flow equation,” Opt. Quantum Electron. 15, 119–136 (1983).
[CrossRef]

Ikeda, M.

S. Kawakami, M. Ikeda, “Transmission characteristics of a two-mode optical waveguide,” IEEE J. Quantum Electron. QE-14, 608–614 (1978).
[CrossRef]

Kaminow, I. P.

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

Kawakami, S.

S. Kawakami, M. Ikeda, “Transmission characteristics of a two-mode optical waveguide,” IEEE J. Quantum Electron. QE-14, 608–614 (1978).
[CrossRef]

Kikuchi, K.

T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

Lefevre, H. C.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
[CrossRef]

Love, J. D.

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

Marcuse, D.

D. Marcuse, “Microbending losses of single-mode, step-index and multimode, parabolic-index fibers,” Bell Syst. Tech. J. 55, 937–955 (1976).
[CrossRef]

D. Marcuse, “Coupled-mode theory for anisotropic optical waveguides,” Bell Syst. Tech. J. 54, 985–995 (1975).
[CrossRef]

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

Morris, D. G.

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

Okamoto, K.

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]

Okoshi, T.

T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1148 (1982).
[CrossRef]

Payne, D. N.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Pesciarelli, U.

Rühl, F.

A. W. Snyder, F. Rühl, “Practical single-polarization anisotropic fibres,” Electron. Lett. 19, 687–688 (1983).
[CrossRef]

A. W. Snyder, F. Rühl, “Single-mode, single-polarization fibers made of birefringent material,” J. Opt. Soc. Am. 73, 1165–1174 (1983).
[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]

Shaw, H. J.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
[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]

Snyder, A. W.

A. W. Snyder, F. Rühl, “Single-mode, single-polarization fibers made of birefringent material,” J. Opt. Soc. Am. 73, 1165–1174 (1983).
[CrossRef]

A. W. Snyder, F. Rühl, “Practical single-polarization anisotropic fibres,” Electron. Lett. 19, 687–688 (1983).
[CrossRef]

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

Tarbox, E. J.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Varnham, M. P.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Coupled-mode theory for anisotropic optical waveguides,” Bell Syst. Tech. J. 54, 985–995 (1975).
[CrossRef]

D. Marcuse, “Microbending losses of single-mode, step-index and multimode, parabolic-index fibers,” Bell Syst. Tech. J. 55, 937–955 (1976).
[CrossRef]

Electron. Lett.

A. W. Snyder, F. Rühl, “Practical single-polarization anisotropic fibres,” Electron. Lett. 19, 687–688 (1983).
[CrossRef]

R. B. Dyott, J. R. Cozens, D. G. Morris, “Preservation of polarization in optical-fibre waveguides with elliptical cores,” Electron. Lett. 15, 380–382 (1979).
[CrossRef]

T. Okoshi, T. Aihara, K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarization fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

IEEE J. Quantum Electron.

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

S. Kawakami, M. Ikeda, “Transmission characteristics of a two-mode optical waveguide,” IEEE J. Quantum Electron. QE-14, 608–614 (1978).
[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]

IEEE Trans. Microwave Theory Tech.

T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1148 (1982).
[CrossRef]

IEEEJ. Lightwave Technol.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, “An overview of fiber-optic gyroscopes,” IEEEJ. Lightwave Technol. LT-2, 91–107 (1984).
[CrossRef]

J. Opt. Soc. Am.

Opt. Quantum Electron.

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibres: perturbative solution of the time-dependent power flow equation,” Opt. Quantum Electron. 15, 119–136 (1983).
[CrossRef]

Other

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

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

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Figures (5)

Fig. 1
Fig. 1

Coupling coefficient hxy against the birefringence Bn with the amplitude σ of the fiber perturbation as a parameter.

Fig. 2
Fig. 2

Evolutions of γ ¯ x ( z ) and γ ¯ y ( z ) with the coupling coefficient hxy as a parameter.

Fig. 3
Fig. 3

Evolution of the extinction ratio η(2) with the coupling coefficient hxy as a parameter.

Fig. 4
Fig. 4

Behavior of the rms pulse width Δτx along z, with the coupling coefficient hxy as a parameter.

Fig. 5
Fig. 5

Variations of asymptotic extinction ratio and rms pulse width with Bn, for D = 10 mm and σ = 3.15 × 10−7, which imply hxy = 0.02 km−1 at the reference value Bn = 5 × 10−4.

Equations (28)

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B n = λ 2 π ( β x β y ) ,
V 2 π λ a n 1 x 2 Δ 2 π λ a n 1 y 2 Δ ,
τ p = 1 2 π ( d β x d ν d β y d ν ) ,
τ p = 1 c ( B n + k 0 d B n d k 0 ) ,
K x y = π ν 2 i S e x * · t ( z ) · e y d x d y ,
K x y = π ν 2 i S t x y ( z ) e x * e υ d x d y ,
h x y = | K x y | 2 = k 0 2 4 | G ( β x β y ) | 2 ,
R ( u ) = t x y ( z ) t x y ( z + u ) = σ 2 exp ( | u | D ) ,
| G ( Ω ) | 2 = 2 σ 2 D ( Ω 2 + 1 / D 2 ) .
h x y σ 2 2 D B n 2 ,
P x z = 2 α x P x + h x y ( P y P x ) , P y z = ( 2 α y + i ω τ p ) P y + h x y ( P x P y ) ,
P x ( z ) = C 1 A x 1 exp ( γ 1 z ) + C 2 A x 2 exp ( γ 2 z ) , P y ( z ) = C 1 A y 1 exp ( γ 1 z ) + C 2 A y 2 exp ( γ 2 z ) ,
C 1 A x 1 + C 2 A x 2 = P x 0 , C 1 A y 1 + C 2 A y 2 = P y 0 .
C = [ ( 2 α x + h x y ) h x y h x y ( 2 α y + h x y ) ]
A x 1 = A y 2 = h x y [ ( α y α x ) 2 + h x y 2 ] 1 / 4 2 { [ ( α y α x ) 2 + h x y 2 ] 1 / 2 ( α y α x ) } 1 / 2 , A y 1 = A x 2 = { [ ( α y α x ) 2 + h x y 2 ] 1 / 2 ( α y α x ) } 1 / 2 2 [ ( α y α x ) 2 + h x y 2 ] 1 / 4 , γ 1 = ( α x + α y + h x y ) [ ( α y α x ) 2 + h x y 2 ] 1 / 2 , γ 2 = ( α x + α y + h x y ) [ ( α y α x ) 2 + h x y 2 ] 1 / 2 .
γ j ( ω ) = γ j ( 0 ) + i ω γ j ( 1 ) + ω 2 γ j ( 2 ) , j = 1 , 2 .
P x ( ω , z ) = C 1 ( ω ) A x 1 ( 0 ) exp [ γ 1 ( ω ) z ] + C 2 ( ω ) A x 2 ( 0 ) exp [ γ 2 ( ω ) z ] , P y ( ω , z ) = C 1 ( ω ) A y 1 ( 0 ) exp [ γ 1 ( ω ) z ] + C 2 ( ω ) A y 2 ( 0 ) exp [ γ 2 ( ω ) z ] ,
C 1 ( ω ) A x 1 ( 0 ) + C 2 ( ω ) A x 2 ( 0 ) = P x 0 ( ω ) , C 1 ( ω ) A y 1 ( 0 ) + C 2 ( ω ) A y 2 ( 0 ) = P y 0 ( ω ) ,
γ 1 ( 1 ) = [ A x 2 ( 0 ) ] 2 τ p , γ 2 ( 1 ) = [ A x 1 ( 0 ) ] 2 τ p , γ 1 ( 2 ) = γ 2 ( 2 ) = [ A x 1 ( 0 ) A x 2 ( 0 ) τ p ] 2 γ 2 ( 0 ) γ 1 ( 0 ) .
C 1 = A x 1 ( 0 ) P x 0 , C 2 = A x 2 ( 0 ) P x 0 .
P x ( z ) = P x 0 { [ A x 1 ( 0 ) ] 2 exp ( γ 1 z ) + [ A x 2 ( 0 ) ] 2 exp ( γ 2 z ) } , P y ( z ) = P x 0 A x 1 ( 0 ) A x 2 ( 0 ) [ exp ( γ 1 z ) exp ( γ 2 z ) ] .
P x ( z + Δ z ) P x ( z ) = exp [ γ ¯ x ( z ) Δ z ] , P y ( z + Δ z ) P y ( z ) = exp [ γ ¯ y ( z ) Δ z ] ,
γ ¯ x ( z ) = [ A x 1 ( 0 ) ] 2 exp ( γ 1 z ) γ 1 + [ A x 2 ( 0 ) ] 2 exp ( γ 2 z ) γ 2 [ A x 1 ( 0 ) ] 2 exp ( γ 1 z ) + [ A x 2 ( 0 ) ] 2 exp ( γ 2 z ) , γ ¯ y ( z ) = exp ( γ 1 z ) γ 1 exp ( γ 2 z ) γ 2 exp ( γ 1 z ) exp ( γ 2 z ) .
Δ τ x = [ M 2 M 0 ( M 1 M 0 ) 2 ] 1 / 2 ,
M n = i n n P x ω n | ω = 0 , n = 0 , 1 , 2 .
Δ τ x ( z ) = { a 1 a 2 [ ( γ 1 ( 1 ) γ 2 ( 1 ) ) z ] 2 + 2 ( a 1 + a 2 ) ( a 1 γ 1 ( 2 ) + a 2 γ 2 ( 2 ) ) z } 1 / 2 a 1 + a 2 ,
a 1 = [ A x 1 ( 0 ) ] 2 exp ( γ 1 ( 0 ) z ) , a 2 = [ A x 2 ( 0 ) ] 2 exp ( γ 2 ( 0 ) z ) .
Δ τ x ( z ) 1 2 h x y τ p α y α x [ exp ( 2 α y z ) z 2 + z α y α x ] 1 / 2 .

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