Abstract

Exact solutions for the evolution of the state of polarization along a nonlinear single-mode birefringent fiber are given by means of the Poincaré sphere representation. This approach clearly shows the possibility of realizing a new class of devices, namely, a linear coherent amplifier–mixer and an optically activated polarization switch or a phase-sensitive optical discriminator with high fanout.

© 1986 Optical Society of America

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References

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  1. R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 7, 512 (1982).
    [CrossRef] [PubMed]
  2. J. M. Dziedzic, R. H. Stolen, A. Ashkin, Appl. Opt. 20, 1403 (1981).
    [CrossRef] [PubMed]
  3. B. Nickolaus, D. Grischkowsky, A. C. Balant, Opt. Lett. 8, 189 (1983).
    [CrossRef]
  4. K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
    [CrossRef]
  5. K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
    [CrossRef]
  6. B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1959).
  8. R. Ulrich, Opt. Lett. 1, 109 (1977).
    [CrossRef] [PubMed]
  9. G. Franceschetti, C. P. Smith, J. Opt. Soc. Am. 71, 1487 (1981).
    [CrossRef]
  10. P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  11. B. Crosignani, P. Di Porto, Opt. Acta (to be published).
  12. K. L. Sala, Phys. Rev. A 29, 1944 (1984).
    [CrossRef]
  13. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  14. H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
    [CrossRef]
  15. R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
    [CrossRef]
  16. B. Daino, G. Gregori, S. Wabnitz, presented at the International Conference on Integrated Optics and Optical Fiber Communication and European Conference on Optical Communication, October 1–4, 1985, Venice, Italy.

1985 (4)

K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
[CrossRef]

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
[CrossRef]

1984 (1)

K. L. Sala, Phys. Rev. A 29, 1944 (1984).
[CrossRef]

1983 (1)

1982 (2)

1981 (2)

1978 (1)

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

1977 (1)

1965 (1)

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Ashkin, A.

Balant, A. C.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1959).

Botineau, J.

Crosignani, B.

B. Crosignani, P. Di Porto, Opt. Acta (to be published).

Daino, B.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, presented at the International Conference on Integrated Optics and Optical Fiber Communication and European Conference on Optical Communication, October 1–4, 1985, Venice, Italy.

Di Porto, P.

B. Crosignani, P. Di Porto, Opt. Acta (to be published).

Dziedzic, J. M.

Franceschetti, G.

Gregori, G.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, presented at the International Conference on Integrated Optics and Optical Fiber Communication and European Conference on Optical Communication, October 1–4, 1985, Venice, Italy.

Grischkowsky, D.

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Kimura, Y.

K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
[CrossRef]

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

Kitayama, K.

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
[CrossRef]

Lin, C.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Nickolaus, B.

Okamoto, K.

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

Sala, K. L.

K. L. Sala, Phys. Rev. A 29, 1944 (1984).
[CrossRef]

Seikai, S.

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
[CrossRef]

Smith, C. P.

Stolen, R. H.

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Ulrich, R.

Wabnitz, S.

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

B. Daino, G. Gregori, S. Wabnitz, presented at the International Conference on Integrated Optics and Optical Fiber Communication and European Conference on Optical Communication, October 1–4, 1985, Venice, Italy.

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1959).

Appl. Opt. (1)

Appl. Phys. Lett. (3)

K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985).
[CrossRef]

K. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, Appl. Phys. Lett. 46, 623 (1985).
[CrossRef]

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

J. Appl. Phys. (1)

B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Phys. Rev. (1)

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. A (2)

K. L. Sala, Phys. Rev. A 29, 1944 (1984).
[CrossRef]

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Other (3)

B. Daino, G. Gregori, S. Wabnitz, presented at the International Conference on Integrated Optics and Optical Fiber Communication and European Conference on Optical Communication, October 1–4, 1985, Venice, Italy.

B. Crosignani, P. Di Porto, Opt. Acta (to be published).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1959).

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Figures (5)

Fig. 1
Fig. 1

Representation of the fields of velocities associated with the motion of the state of polarization on the Poincaré sphere. Upper left: linear birefringence, with angular velocity ΩL along S1. Upper right: self-induced ellipse rotation (ΩNL). Lower left and right: sum of the two effects, with resulting Ω = ΩL + ΩNL. Note the presence of a separatrix at the rear of the Poincaré sphere.

Fig. 2
Fig. 2

Trajectories of the polarization for a set of initial conditions close to the left circular polarization for a distance L = 9/Δβ.

Fig. 3
Fig. 3

Fiber output parameter S3 as a function of the input value of S1 for different fiber lengths. The numbers close to each curve give ΔβL.

Fig. 4
Fig. 4

Schematic of a linear coherent amplifier–mixer using a single-mode birefringent fiber.

Fig. 5
Fig. 5

Same as Fig. 4 but using a bulk birefringent Kerr medium.

Equations (13)

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d S / d z = V ( S ) ,
d S / d z = Ω L × S .
d S / d z = Ω NL ( S ) × S .
Ω NL = ( 0 , 0 , - 2 R S 3 / 3 ) ,
d S / d z = Ω ( S ) × S = [ Ω NL ( S ) + Ω L ] × S .
d S 1 / d z = 2 / 3 ( R S 3 S 2 ) , d S 2 / d z = - 2 / 3 ( R S 3 S 1 - Δ β S 3 ) , d S 3 / d z = Δ β S 2 .
Δ β = R ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 / 3 = R S 0 / 3.
Δ β = 4 π Z 0 n 2 P / ( 3 λ n 1 A eff ) ,
Δ S 3 ( z ) = G ( z ) Δ S 1 ( 0 ) .
G ( z ) - sinh ( Δ β z ) { tanh ( Δ β z ) / 2 + 3 Δ β z / [ 1 + cosh ( 2 Δ β z ) ] } .
Δ S 1 ( 0 ) = 2 E s E p cos [ ( ω s - ω p ) t + φ s - φ p ] .
( I v - I ¯ v ) / ( I v + I o ) = Δ I v / I t = G ( L ) Δ S 1 / ( 2 S 0 ) = G ( L ) ( E s / E p ) cos [ ( ω s - ω p ) t + φ s - φ p ] = - ( I o - I ¯ o ) / ( I v + I o ) = - Δ I o / I t ,
Δ β < 2 R S 0 / 3.

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