Abstract

We present an exact solution for the polarization evolution in a single-mode optical fiber when the self-induced, the intrinsic, and the twist-induced birefringences are taken into account and the stability characteristics of the nonlinear eigenpolarizations are studied. The relevance of the theory for the operation of nonlinear-optical signal-processing devices is discussed.

© 1986 Optical Society of America

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  1. B. Daino, G. Gregori, S. Wabnitz, J. Appl. Phys. 58, 4512 (1985).
    [Crossref]
  2. G. Gregori, S. Wabnitz, Phys. Rev. Lett. 56, 600 (1986); in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), p. 359.
    [Crossref]
  3. B. Daino, G. Gregori, S. Wabnitz, in Digest of ECOC-IOOC ’85 Meeting (Istituto Nazionale delle Comunicazioni, Genova, Italy, 1985), Vol. III, p. 93; Opt. Lett. 11, 42 (1986).
    [PubMed]
  4. S. Wabnitz, G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. (to be published).
  5. H. G. Winful, Opt. Lett. 11, 33 (1986).
    [Crossref] [PubMed]
  6. J. Yumoto, K. Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
    [Crossref] [PubMed]
  7. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [Crossref]
  8. R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 8, 189 (1983); B. Nickolaus, D. Grischkowsky, A. C. Balant, Opt. Lett. 8, 189 (1983); K. Kitayama, Y. Kimura, S. Seikai, Appl. Phys. Lett. 46, 317 (1985); H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
    [Crossref]
  9. N. J. Halas, D. Grischkowsky, Appl. Phys. Lett. 48, 823 (1986).
    [Crossref]
  10. R. Ulrich, A. Simon, Appl. Opt. 18, 2241 (1979).
    [Crossref] [PubMed]
  11. A. G. Barlow, J. J. Ramskov-Hansen, D. N. Payne, Appl. Opt. 20, 2962 (1981); A. J. Barlow, D. N. Payne, M. R. Hadley, R. J. Mansfield, Electron. Lett. 17, 725 (1981).
    [Crossref] [PubMed]
  12. M. Monerie, L. Jeunhomme, Opt. Quantum Electron. 12, 449 (1980).
    [Crossref]
  13. Linearly polarized light along the effective axes will emerge linearly polarized at the output at low powers.9
  14. B. Crosignani, P. Di Porto, J. Opt. Soc. Am. 72, 1554 (1982); Opt. Acta 32, 1251 (1985).
  15. For a description of the Poincaré sphere see M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 1; for its application to nonlinear phenomena, see Refs. 1–4.
  16. Note that the ellipse rotation vector is unaffected by the coordinate change since it is directed along S3: this property no longer holds for anisotropic third-order susceptibility.2
  17. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  18. R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, Mass., 1975).
  19. H. Schneider, H. Harms, A. Papp, H. Aulich, Appl. Opt. 17, 3035 (1978); S. R. Norman, D. N. Payne, M. J. Adams, A. M. Smith, Electron. Lett. 15, 309 (1979).
    [Crossref] [PubMed]

1986 (3)

G. Gregori, S. Wabnitz, Phys. Rev. Lett. 56, 600 (1986); in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), p. 359.
[Crossref]

H. G. Winful, Opt. Lett. 11, 33 (1986).
[Crossref] [PubMed]

N. J. Halas, D. Grischkowsky, Appl. Phys. Lett. 48, 823 (1986).
[Crossref]

1985 (2)

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

J. Yumoto, K. Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[Crossref] [PubMed]

1983 (1)

1982 (2)

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

B. Crosignani, P. Di Porto, J. Opt. Soc. Am. 72, 1554 (1982); Opt. Acta 32, 1251 (1985).

1981 (1)

1980 (1)

M. Monerie, L. Jeunhomme, Opt. Quantum Electron. 12, 449 (1980).
[Crossref]

1979 (1)

1978 (1)

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Ashkin, A.

Aulich, H.

Barlow, A. G.

Born, M.

For a description of the Poincaré sphere see M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 1; for its application to nonlinear phenomena, see Refs. 1–4.

Botineau, J.

Crosignani, B.

B. Crosignani, P. Di Porto, J. Opt. Soc. Am. 72, 1554 (1982); Opt. Acta 32, 1251 (1985).

Daino, B.

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

B. Daino, G. Gregori, S. Wabnitz, in Digest of ECOC-IOOC ’85 Meeting (Istituto Nazionale delle Comunicazioni, Genova, Italy, 1985), Vol. III, p. 93; Opt. Lett. 11, 42 (1986).
[PubMed]

Di Porto, P.

B. Crosignani, P. Di Porto, J. Opt. Soc. Am. 72, 1554 (1982); Opt. Acta 32, 1251 (1985).

Gregori, G.

G. Gregori, S. Wabnitz, Phys. Rev. Lett. 56, 600 (1986); in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), p. 359.
[Crossref]

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

B. Daino, G. Gregori, S. Wabnitz, in Digest of ECOC-IOOC ’85 Meeting (Istituto Nazionale delle Comunicazioni, Genova, Italy, 1985), Vol. III, p. 93; Opt. Lett. 11, 42 (1986).
[PubMed]

S. Wabnitz, G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. (to be published).

Grischkowsky, D.

N. J. Halas, D. Grischkowsky, Appl. Phys. Lett. 48, 823 (1986).
[Crossref]

Halas, N. J.

N. J. Halas, D. Grischkowsky, Appl. Phys. Lett. 48, 823 (1986).
[Crossref]

Harms, H.

Jensen, S. M.

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

Jeunhomme, L.

M. Monerie, L. Jeunhomme, Opt. Quantum Electron. 12, 449 (1980).
[Crossref]

Monerie, M.

M. Monerie, L. Jeunhomme, Opt. Quantum Electron. 12, 449 (1980).
[Crossref]

Otsuka, K.

J. Yumoto, K. Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[Crossref] [PubMed]

Papp, A.

Payne, D. N.

Ramskov-Hansen, J. J.

Schneider, H.

Simon, A.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Stolen, R. H.

Thom, R.

R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, Mass., 1975).

Ulrich, R.

Wabnitz, S.

G. Gregori, S. Wabnitz, Phys. Rev. Lett. 56, 600 (1986); in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), p. 359.
[Crossref]

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

B. Daino, G. Gregori, S. Wabnitz, in Digest of ECOC-IOOC ’85 Meeting (Istituto Nazionale delle Comunicazioni, Genova, Italy, 1985), Vol. III, p. 93; Opt. Lett. 11, 42 (1986).
[PubMed]

S. Wabnitz, G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. (to be published).

Winful, H. G.

Wolf, E.

For a description of the Poincaré sphere see M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 1; for its application to nonlinear phenomena, see Refs. 1–4.

Yumoto, J.

J. Yumoto, K. Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

N. J. Halas, D. Grischkowsky, Appl. Phys. Lett. 48, 823 (1986).
[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)

B. Crosignani, P. Di Porto, J. Opt. Soc. Am. 72, 1554 (1982); Opt. Acta 32, 1251 (1985).

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Monerie, L. Jeunhomme, Opt. Quantum Electron. 12, 449 (1980).
[Crossref]

Phys. Rev. Lett. (2)

J. Yumoto, K. Otsuka, Phys. Rev. Lett. 54, 1806 (1985).
[Crossref] [PubMed]

G. Gregori, S. Wabnitz, Phys. Rev. Lett. 56, 600 (1986); in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), p. 359.
[Crossref]

Other (7)

B. Daino, G. Gregori, S. Wabnitz, in Digest of ECOC-IOOC ’85 Meeting (Istituto Nazionale delle Comunicazioni, Genova, Italy, 1985), Vol. III, p. 93; Opt. Lett. 11, 42 (1986).
[PubMed]

S. Wabnitz, G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. (to be published).

Linearly polarized light along the effective axes will emerge linearly polarized at the output at low powers.9

For a description of the Poincaré sphere see M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 1; for its application to nonlinear phenomena, see Refs. 1–4.

Note that the ellipse rotation vector is unaffected by the coordinate change since it is directed along S3: this property no longer holds for anisotropic third-order susceptibility.2

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, Mass., 1975).

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Figures (4)

Fig. 1
Fig. 1

Trajectories for the Stokes vector on the rotating Poincaré sphere for t = ηβ = 0.4 and a normalized power (A) p = 1.8, (B) p = 2. Note the presence of asymmetrical bifurcated domains divided by a separatrix.

Fig. 2
Fig. 2

Bifurcation diagram showing the s3 coordinate of the critical points (with s2 = 0, s1 < 0) versus p for a, t = 0; b, t = 2 × 10−2; c, t = 1; d, t = 10. Solid (dashed) lines: stable (unstable) critical points.

Fig. 3
Fig. 3

Bifurcation power (normalized by 3|Ω′L|/2R) versus twist ratio t.

Fig. 4
Fig. 4

Normalized beat length for t = 0.4, p = 0.2 (dashed line) and p = 2 (solid line) as the input polarization state is varied on the meridian given by the plane The S2(0) = 0. longitude is 2φ = tan−1(s2/s1), and the latitude 2ψ = sin−1(s3).

Equations (8)

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d S d z = Ω × S = [ Ω L ( z ) + Ω NL ( S ) × ( S ) ] .
d S d z = Ω × S = [ Ω L + Ω NL ( S ) ] × S ,
P 2 = S 1 2 + S 2 2 + S 3 2 = S 0 2 = S 0 2 , Γ = R S 3 2 3 - Δ β S 1 - η S 3
V ( S 3 ) = R 2 S 3 4 18 - R η S 3 3 3 + 1 2 ( Δ β 2 + η 2 - 2 R T 3 ) S 3 2 + Γ η S 3 ,
E = 1 2 ( Δ β 2 P 2 - Γ 2 ) .
z = 1 2 S 30 S 3 d x [ E - V ( x ) ] 1 / 2 ,
R ( θ ) = [ cos θ sin θ 0 - sin θ cos θ 0 0 0 1 ] .
p 2 s 3 4 - 2 p t s 3 3 + ( 1 + t 2 - p 2 ) s 3 2 + 2 p t s 3 - t 2 = 0 ,

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