Abstract

Theoretical results regarding the propagation of intense light through a two-component medium are presented. The light-induced scattering from such a medium can compensate for the usual linear scattering under certain conditions, thus giving rise to the so-called self-transparency effect (suppression of the scattering). The theoretical model is based on the flux theory of light scattering. It is also shown that the equation obtained through flux theory can also be derived by using the wave equation when the medium is treated as a composite (effective) medium and when the dispersion and Kerr-type nonlinear terms for such a composite medium are neglected. The complete equation without neglecting these two terms is solved numerically in order to study the effect of nonlinear scattering on soliton propagation. The problem of two oppositely traveling waves in such a composite medium without dispersion and Kerr-type terms is also discussed.

© 1988 Optical Society of America

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References

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  1. A. A. Manenkov, Sov. Phys. Dokl. 15, 155 (1970).
  2. G. B. Al’tshuler, V. S. Ermolaev, Sov. Phys. Dokl. 28, 146 (1983).
  3. G. B. Al’tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, Sov. Phys. Dokl. 28, 951 (1983).
  4. G. B. Al’tshuler, M. V. Inochkin, A. A. Manenkov, Sov. Phys. Dokl. 30, 574 (1985).
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  6. Diffused source of light is defined here as any incoherent source whose rays are not parellel (collimated) to each other. The collimated source is the one whose rays are parallel to each other; it may be a coherent source (such as a laser) or an incoherent source.
  7. G. B. Al’tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
    [CrossRef]
  8. G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).
  9. N. C. Kothari, C. Flytzanis, Opt. Lett. 11, 806 (1986).
    [CrossRef] [PubMed]
  10. A. E. Kaplan, P. Meystre, Opt. Lett. 6, 590 (1981).
    [CrossRef] [PubMed]
  11. A. E. Kaplan, P. Meystre, Opt. Commun. 40, 229 (1982).
    [CrossRef]
  12. N. C. Kothari, C. Flytzanis, Opt. Lett. 12, 492 (1987).
    [CrossRef] [PubMed]
  13. R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
    [CrossRef]
  14. See, for example, L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  15. D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983).
    [CrossRef]

1987 (1)

1986 (3)

1985 (1)

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

1983 (3)

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).

D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983).
[CrossRef]

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]

1975 (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

1970 (1)

A. A. Manenkov, Sov. Phys. Dokl. 15, 155 (1970).

Al’tshuler, G. B.

G. B. Al’tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
[CrossRef]

G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).

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).

Bischel, W. K.

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

Ermolaev, V. S.

G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).

G. B. Al’tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
[CrossRef]

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).

Fisher, R. A.

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

Flytzanis, C.

Gordon, J. P.

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

Hermansson, B.

D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983).
[CrossRef]

Inochkin, M. V.

G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).

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, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
[CrossRef]

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, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
[CrossRef]

G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).

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).

A. A. Manenkov, Sov. Phys. Dokl. 15, 155 (1970).

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]

Prokhorov, A. M.

Stolen, R. H.

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

Yevick, D.

D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983).
[CrossRef]

J. Appl. Phys. (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

J. Opt. Soc. Am. B (2)

G. B. Al’tshuler, V. S. Ermolaev, K. I. Krylov, A. A. Manenkov, A. M. Prokhorov, J. Opt. Soc. Am. B 3, 660 (1986).
[CrossRef]

G. B. Al’tshuler, V. S. Ermolaev, M. V. Inochkin, A. A. Manenkov, J. Opt. Soc. Am. B 3(13), P126 (1986).

Opt. Commun. (2)

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

D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983).
[CrossRef]

Opt. Lett. (3)

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. (4)

A. A. Manenkov, Sov. Phys. Dokl. 15, 155 (1970).

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).

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

Other (2)

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

Diffused source of light is defined here as any incoherent source whose rays are not parellel (collimated) to each other. The collimated source is the one whose rays are parallel to each other; it may be a coherent source (such as a laser) or an incoherent source.

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Figures (7)

Fig. 1
Fig. 1

A model two-component heterogeneous medium: I and II are the dielectric constants, and nI and nII are the refractive indices of the two components.

Fig. 2
Fig. 2

The scattering geometry showing the wave scattered by a single particle having dielectric constant A surrounded by a medium having dielectric constant B.

Fig. 3
Fig. 3

Schematic representations of (a) two-flux and (b) four-flux theories.

Fig. 4
Fig. 4

a, Pulse compression in a nonlinear-scattering medium: τ/τp = 0, γ = 0, η =−1, and I0 = 1. b, Square type of pulse generation: τ/τp = 0, γ = 0, η = −1, and I0 = 2. c, Effect of relaxation. The pulse shape is distorted inside the medium; however, when the distance z′ is increased, the pulse gradually regains its shape: τ/τp = 0.3, γ = 0, η =-1, and I0 = 2. d, Effect of relaxation in the presence of gain: τ/τp = 0.1, γ =−0.1, η = −1, and I0 = 1.

Fig. 5
Fig. 5

a, Single-mirror retroreflection geometry. b, Plots of reflected intensities versus incident intensities using Eqs. (3.9) and (3.10): η = −1, γ = 0, R = 1, and L = 3, 4, and 5. c, Same as b except that we use Eqs. (6.7) and (6.8). In both b and c, the boundary conditions of Eqs. (6.9) and (6.10) were used.

Fig. 6
Fig. 6

Plots of normalized pulse intensities |ψ|2 versus normalized time τ = t′/τp: α =0.5, β =1, η =−1, and γ =0. a, N = 1 and z′ = 0 and z′ = π/2; b, N = 2 and z′ = 0 and z′ = π/4; c, N = 2 and z′ = π/2.

Fig. 7
Fig. 7

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

Equations (37)

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E s ( r ) = f ( o ^ , i ^ ) e i k R R ,
f ( o ^ , i ^ ) = k 2 4 π V [ - o ^ × { o ^ × E ( r ) } ] × [ A ( r ) B - 1 ] exp ( - i k r · o ^ ) d V .
α s = 128 π 5 a 6 N 3 λ 4 | A - B A - 2 B | 2 .
d F 1 d z = - ( α a + α s ) F 1 + α s F 2 ,
d F 2 d z = ( α a + α s ) F 2 - α s F 1 .
d F c 1 d z = - ( α a + α s 1 + α s 2 ) F c 1 ,
d F c 2 d z = ( α a + α s 1 + α s 2 ) F c 2 ,
d F 1 d z = - ( α a + α s ) F 1 + α s F 2 + α s 1 F c 1 + α s 2 F c 2 ,
d F 2 d z = ( α a + α s ) F 2 - α s F 1 - α s 1 F c 2 - α s 2 F c 1 .
α s , s i = g s , s i ( Δ n ) 2 = g s , s i ( Δ n L + Δ n NL ) 2 ,
d I d z = - γ I - ( η + I ) 2 I .
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 ,
I z + 1 v I t = - α 1 [ γ + ( η + I ) 2 ] I .
τ 1 t n NL I + n NL I = n 2 I I ,
τ 2 t n NL II + n NL II + n 2 II I .
τ t Δ n NL + Δ n NL = Δ n 2 I .
I z = - γ I - ( η + I ˜ ) 2 I ,
τ t I ˜ + I ˜ = 1.
I ( 0 , t ) = I ˜ ( 0 , t ) = I 0 exp [ - ( t / τ p ) 2 ] ,
˜ = + i = L + NL + i .
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 ,
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 a 2 + α s 2 ) .
α 1 = g ( Δ n L ) 2 1 2 k 0 ( 2 / L ) Δ n L / Δ n 2 .
E = A 1 exp [ i ( k 0 z - ω 0 t ) ] + A 2 exp [ - i ( k 0 z + ω 0 t ) ] .
P NL = 2 4 π E 2 E = 2 4 π { ( A 1 2 + 2 A 2 2 ) A 1 exp [ i ( k 0 z - ω 0 t ) ] + ( A 2 2 + 2 A 1 2 ) A 2 exp [ - i ( k 0 z - ω 0 t ) ] } .
P loss a = L 4 π k 0 α a E ,
P loss s = L 4 π k 0 g ( Δ n ) 2 E = L 4 π k 0 g ( Δ n L ) 2 × ( E + 2 η | Δ n 2 Δ n L | E 2 E + | Δ n 2 Δ n L | 2 E 4 E ) .
( A 1 z + k 0 A 1 t ) = - { α a 2 + 1 2 g ( Δ n L ) 2 × [ 1 + 2 η | Δ n 2 Δ n L | ( A 1 2 + 2 A 2 2 ) + | Δ n 2 Δ n L | 2 × ( A 1 4 + 5 A 1 2 A 2 2 + 3 A 2 4 ) ] } A 1 ,
( A 2 z - k 0 A 2 t ) = { α a 2 + 1 2 g ( Δ n L ) 2 [ 1 + 2 η | Δ n 2 Δ n L | ( A 2 2 + 2 A 1 2 ) + | Δ n 2 Δ n L | 2 × ( A 2 4 + 5 A 1 2 A 2 2 + 3 A 1 4 ) ] } A 2 .
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 .
I 1 ( 0 ) = I 0
I 2 ( L ) = R I 1 ( L ) ,
i ( ψ z + γ 2 ψ ) + α 2 ψ τ 2 + β ψ 2 ψ + i 2 ( ψ 2 + η ) 2 ψ = 0 ,

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