Abstract

The propagation of intense light through a two-component nonlinear heterogeneous medium is considered by treating the medium as a composite medium. Introduction of dispersion and Kerr-type nonlinear terms leads to a nonlinear Schrödinger-type scattering equation. The effect of nonlinear scattering loss on soliton propagation is studied numerically. The propagation of two oppositely traveling waves is also discussed.

© 1987 Optical Society of America

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References

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  1. G. B. Al'tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).
  2. G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).
  3. N. C. Kothari, C. Flytzanis, Opt. Lett. 11, 806 (1986).
    [CrossRef] [PubMed]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  5. See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  6. G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).
  7. A. E. Kaplan, P. Meystre, Opt. Lett. 6, 590 (1981).
    [CrossRef] [PubMed]
  8. A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
    [CrossRef]

1986 (1)

1985 (1)

G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).

1983 (2)

G. B. Al'tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

1982 (1)

A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

1981 (1)

1980 (1)

See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Al'tshuler, G. B.

G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

G. B. Al'tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).

Ermolaev, V. S.

G. B. Al'tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

Flytzanis, C.

Gordon, J. P.

See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Inochkin, M. V.

G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Kaplan, A. E.

A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

A. E. Kaplan, P. Meystre, Opt. Lett. 6, 590 (1981).
[CrossRef] [PubMed]

Kothari, N. C.

Krylov, K. I.

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

Manenkov, A. A.

G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

Meystre, P.

A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

A. E. Kaplan, P. Meystre, Opt. Lett. 6, 590 (1981).
[CrossRef] [PubMed]

Mollenauer, L. F.

See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Stolen, R. H.

See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Opt. Commun. (1)

A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Sov. Phys. Dokl. (3)

G. B. Al'tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).

G. B. Al'tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).

G. B. Al'tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).

Other (1)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

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Figures (3)

Fig. 1
Fig. 1

Plots of |ψ|2 versus τ for α = 0.5, β = 1, η = −1, and γ0 = 0: a, N = 1 and z′ = 0, π/2; b, N = 2 and z′ = 0, π/4; c, N = 2 and z′ = π/2.

Fig. 2
Fig. 2

Plots of |ψ|2 versus τ for α = 0.5, β = 1, η = −1, and z′ = π/2. a, N = 1 and γ0 = −1; b, N = 1 and γ0 = −2; c, N = 2 and γ0 = −2. d, N = 0.5 and γ0 = −2.

Fig. 3
Fig. 3

a, Single-mirror retroreflection geometry. b, Plots of reflected intensities versus incident intensities using Eqs. (9) and (10) for η = −1, γ = 0, R = 1, and L = 3, 4, 5. c, Same as in b except using Eqs. (7) and (8).

Equations (11)

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2 E 1 c 2 2 E t 2 = 4 π c 2 2 t 2 ( P L + P NL + i P loss ) .
P L = L 1 4 π E , P NL = NL 4 π E = χ ( 3 ) | E | 2 E = 2 4 π | E | 2 E , P loss = 4 π E ,
E = A ( z , t ) exp [ i ( k 0 z ω 0 t ) ]
2 i k 0 A z k 0 k 0 2 A t 2 + 2 L k 0 2 | A | 2 A = 2 i k 0 [ α 0 2 + g ( Δ n ) 2 2 ] A .
i ( ψ z + γ 0 ψ ) + α 2 ψ τ 2 + β | ψ | 2 ψ + i 2 ( | ψ | 2 + η ) 2 ψ = 0 ,
ψ = ( | Δ n 2 Δ n L | ) 1 / 2 A , z = g ( Δ n L ) 2 z = α 1 z , γ 0 = ( α 0 2 ) / α 1 , α = ( k 0 / 2 ) / α 1 τ p 2 , β = 1 2 k 0 2 L | Δ n L Δ n 2 | / α 1 , τ = t / τ p , η = sign ( Δ n L × Δ n NL ) = ± 1 .
E = A 1 exp [ i ( k 0 z ω 0 t ) ] + A 2 exp [ i ( k 0 z + ω 0 t ) ] .
d I 1 d z = γ I 1 [ 1 + 2 η ( I 1 + 2 I 2 ) + ( I 1 2 + 5 I 1 I 2 + 3 I 2 2 ) ] I 1 ,
d I 2 d z = γ I 2 + [ 1 + 2 η ( I 2 + 2 I 1 ) + ( I 2 2 + 5 I 1 I 2 + 3 I 1 2 ) ] I 2 ,
d I 1 d z = γ I 1 ( η + I 1 + I 2 ) 2 I 1 ,
d I 2 d z = γ I 2 + ( η + I 1 + I 2 ) 2 I 2 .

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