Abstract

We investigate second-harmonic generation beyond the scalar approximation. We show that the tensorial nature of the second-order susceptibility may lead to the onset of spatial chaos in the polarization evolution of the interacting fields. We discuss the effect of chaos on situations of interest.

© 1994 Optical Society of America

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References

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [Crossref] [PubMed]
  2. G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
    [Crossref] [PubMed]
  3. D. C. Hutchings, J. S. Aitchison, C. N. Ironside, Opt. Lett. 18, 793 (1993).
    [Crossref] [PubMed]
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
    [Crossref]
  5. S. Trillo, S. Wabnitz, R. Chisari, G. Cappellini, Opt. Lett. 17, 637 (1992).
    [Crossref] [PubMed]
  6. S. A. Akhmanov, R. V. Khoklov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972), pp. 155–165.
  7. D. J. Hagan, M. Sheik-Bahae, Z. Wang, G. I. Stegeman, E. W. Van Stryland, G. Assanto, Opt. Lett. 19, 1305 (1994).
    [Crossref] [PubMed]
  8. G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
    [Crossref]
  9. A. J. Lichtenberg, M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983), pp. 151–211, 260–285.
  10. S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
    [Crossref] [PubMed]
  11. G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
    [Crossref]
  12. C. M. Savage, D. F. Walls, Opt. Acta 30, 557 (1983).
    [Crossref]

1994 (2)

1993 (2)

1992 (2)

1987 (1)

S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
[Crossref] [PubMed]

1983 (1)

C. M. Savage, D. F. Walls, Opt. Acta 30, 557 (1983).
[Crossref]

1976 (1)

G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Aitchison, J. S.

Akhmanov, S. A.

S. A. Akhmanov, R. V. Khoklov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972), pp. 155–165.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Assanto, G.

Benettin, G.

G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Cappellini, G.

Chisari, R.

DeSalvo, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Galgani, L.

G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
[Crossref]

Hagan, D. J.

Hutchings, D. C.

Ironside, C. N.

Khoklov, R. V.

S. A. Akhmanov, R. V. Khoklov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972), pp. 155–165.

Lichtenberg, A. J.

A. J. Lichtenberg, M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983), pp. 151–211, 260–285.

Lieberman, M. A.

A. J. Lichtenberg, M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983), pp. 151–211, 260–285.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Savage, C. M.

C. M. Savage, D. F. Walls, Opt. Acta 30, 557 (1983).
[Crossref]

Sheik-Bahae, M.

Stegeman, G. I.

Strelcyn, J. M.

G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
[Crossref]

Torelli, I.

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[Crossref]

Trillo, S.

Van Stryland, E. W.

Vanherzeele, H.

Wabnitz, S.

Walls, D. F.

C. M. Savage, D. F. Walls, Opt. Acta 30, 557 (1983).
[Crossref]

Wang, Z.

Electron. Lett. (1)

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[Crossref]

Opt. Acta (1)

C. M. Savage, D. F. Walls, Opt. Acta 30, 557 (1983).
[Crossref]

Opt. Lett. (5)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 6, 1918 (1962).
[Crossref]

Phys. Rev. A (1)

G. Benettin, L. Galgani, J. M. Strelcyn, Phys. Rev. A 14, 2338 (1976).
[Crossref]

Phys. Rev. Lett. (1)

S. Wabnitz, Phys. Rev. Lett. 58, 1415 (1987).
[Crossref] [PubMed]

Other (2)

S. A. Akhmanov, R. V. Khoklov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972), pp. 155–165.

A. J. Lichtenberg, M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983), pp. 151–211, 260–285.

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Figures (3)

Fig. 1
Fig. 1

Power fractions of the SH (η, dotted curves) and the FF (η1, solid curve and η2, dashed curve) fields versus distance ζ for an angle ρ = 1 deg [i.e., η1(0) = 0.9997, η2(0) = 0.0003]. Here κ = 0, χI = 0.5, and (a) p = 0.3, (b) p = 1, (c) p = 2.

Fig. 2
Fig. 2

Maximal Lyapunov exponent λm versus distance ζ for different values of the input amplitude p. Here η1(0) = 0.99, η2(0) = 0.01, χI = 0.5, and κ = 0.

Fig. 3
Fig. 3

Generated SH power fraction versus normalized amplitude p for κ = 0, χ = 0.1, and (a) ζmax = Δk2L = 2, (b) ζmax = 20.

Equations (5)

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i d E 0 , j d z = χ j j E 2 E 0 , j * exp ( i Δ k j z ) + χ 12 E 2 E 0 , 3 j * exp ( i Δ k 1 + Δ k 2 2 z ) , i d E 2 d z = χ 11 E 0 , 1 2 exp ( i Δ k 1 z ) + χ 22 E 0 , 2 2 exp ( i Δ k 2 z ) + 2 χ 12 E 0 , 1 E 0 , 2 exp ( i Δ k 1 + Δ k 2 2 z ) ,
H j = χ j j A j 2 A 3 * 2 exp ( i Δ k j z ) + c . c . ( j = 1 , 2 ) ,
H 12 = χ 12 A 1 A 2 A 3 * exp ( i Δ k 1 + Δ k 2 2 z ) + c . c .
d η j d ζ = H ˆ θ j ; d θ j d ζ = H ˆ η j ( j = 1 , 2 ) ,
H ˆ = H ˆ ( η 1 , η 2 , θ 1 , θ 2 ) = κ η 1 η 2 + 2 p ( 1 η 1 η 2 ) 1 / 2 × ( η 1 cos θ 1 + χ I η 2 cos θ 2 + χ II η 1 η 2 cos θ 1 + θ 2 2 ) ,

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