Abstract

We investigate the reduction of Rayleigh scattering in four-wave mixing due to photo-induced spatial redistribution of atoms in atomic vapors. The Rayleigh scattering from the pump beams in optical phase conjugation is a major source of noise, which affects the fidelity of the phase-conjugated image. In the blue-shifted operation, the atoms are driven toward the low-intensity regions of the standing-wave pattern, leading to a reduction of Rayleigh scattering. We also investigate the effect of saturation on the differential scattering cross section.

© 1998 Optical Society of America

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References

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  1. R. A. Fisher, ed., Optical Phase Conjugation (Academic, San Diego, Calif., 1983).
  2. P. Yeh, “Fundamental limit of the speed of photorefractive effect and its impact on device applications and material research,” Appl. Opt. 26, 602–604 (1987).
    [CrossRef] [PubMed]
  3. D. Grischkoesky, J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
    [CrossRef]
  4. F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
    [CrossRef]
  5. C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
    [CrossRef] [PubMed]
  6. R. McGraw, D. Rogovin, “Light-scattering limitation for phase conjugation in optical Kerr media,” Appl. Phys. Lett. 54, 199–201 (1989).
    [CrossRef]
  7. R. L. Abrams, R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978).
    [CrossRef] [PubMed]
  8. R. L. Abrams, R. C. Lind, “Degenerate four-wave mixing in absorbing media: errata,” Opt. Lett. 3, 205 (1978).
    [CrossRef] [PubMed]
  9. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  10. E. A. Jackson, Equilibrium Statistical Mechanics (Prentice-Hall, Englewood Cliffs, N.J., 1968).
  11. R. Saxena, I. McMichael, P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243–253 (1990).
    [CrossRef]
  12. T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220–232 (1981).

1991 (1)

1990 (1)

R. Saxena, I. McMichael, P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243–253 (1990).
[CrossRef]

1989 (1)

R. McGraw, D. Rogovin, “Light-scattering limitation for phase conjugation in optical Kerr media,” Appl. Phys. Lett. 54, 199–201 (1989).
[CrossRef]

1987 (1)

1981 (1)

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220–232 (1981).

1978 (2)

1972 (1)

D. Grischkoesky, J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

1967 (1)

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
[CrossRef]

Abrams, R. L.

Armstrong, J. A.

D. Grischkoesky, J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

Chang, T. Y.

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220–232 (1981).

Grischkoesky, D.

D. Grischkoesky, J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

Gu, C.

Jackson, E. A.

E. A. Jackson, Equilibrium Statistical Mechanics (Prentice-Hall, Englewood Cliffs, N.J., 1968).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Lind, R. C.

McGraw, R.

R. McGraw, D. Rogovin, “Light-scattering limitation for phase conjugation in optical Kerr media,” Appl. Phys. Lett. 54, 199–201 (1989).
[CrossRef]

McMichael, I.

R. Saxena, I. McMichael, P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243–253 (1990).
[CrossRef]

Rogovin, D.

R. McGraw, D. Rogovin, “Light-scattering limitation for phase conjugation in optical Kerr media,” Appl. Phys. Lett. 54, 199–201 (1989).
[CrossRef]

Saxena, R.

R. Saxena, I. McMichael, P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243–253 (1990).
[CrossRef]

Shimizu, F.

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
[CrossRef]

Yeh, P.

Appl. Opt. (1)

Appl. Phys. B (1)

R. Saxena, I. McMichael, P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243–253 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

R. McGraw, D. Rogovin, “Light-scattering limitation for phase conjugation in optical Kerr media,” Appl. Phys. Lett. 54, 199–201 (1989).
[CrossRef]

Opt. Eng. (1)

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220–232 (1981).

Opt. Lett. (3)

Phys. Rev. A (1)

D. Grischkoesky, J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
[CrossRef]

Other (3)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

E. A. Jackson, Equilibrium Statistical Mechanics (Prentice-Hall, Englewood Cliffs, N.J., 1968).

R. A. Fisher, ed., Optical Phase Conjugation (Academic, San Diego, Calif., 1983).

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Figures (7)

Fig. 1
Fig. 1

Physical configuration.

Fig. 2
Fig. 2

Four-wave mixing in atomic vapors.

Fig. 3
Fig. 3

Spatial variation of the polarizability and the atom number density resulting from the interference pattern.

Fig. 4
Fig. 4

Reduction factor as a function of normalized frequency detuning Δ for various pump intensities I: (a) absolute temperature T=1 °K, (b) absolute temperature T=10 °K.

Fig. 5
Fig. 5

Reduction factor as a function of normalized frequency detuning Δ for various larger pump intensities I: (a) absolute temperature T=1 °K, (b) absolute temperature T=10 °K.

Fig. 6
Fig. 6

Power reflection coefficient R of phase conjugation by means of four-wave mixing as a function of pump intensity I for normalized frequency detunings Δ=10 (solid curve) and 100 (dashed curve).

Fig. 7
Fig. 7

Minimum detectable intensity per unit solid angle dIS/N=1/dΩ as a function of pump intensity I for normalized frequency detunings Δ (a) Δ=10, (b) Δ=100, with interference (solid curves) and without interference (dots).

Equations (30)

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dσdΩ=k024πd3x exp(-jq·x)e*·e0 δ02,
|e*·e0|2=12(1+cos2 θ),
n·n0=cos θ,
δ=iγδ(x-xi),
dσdΩ=k04NA(4π)2γ02|e*·e0|2F(q),
dσdΩ=dσdΩ+dσdΩ,
dσdΩ=132π2NAk04γ02F(q),
dσdΩ=cos2 θ32π2NAk04γ02F(q),
F(q)=i[exp(-jq·xi)+exp(-jq·xi)]2,
F(q)=i4 cos2 k0zi,
F(q)=4A0LN(z)cos2 k0zdz,
σ= dσdΩdΩ=16πNAk04γ02F(q).
N(z)=N0 exp-12γr|E|2kBT,
N0=NAA0L exp-12γr|E|2kBTdz
γ=0χNAγr-jγi,
χ=α0k0-j+Δ1+Δ2+|E|2/Es2,
dPRdΩ=dσdΩN(z)I(z)dV,
I(z)=I1+I2+2I1I2 cos Kz,
PR=k046πNA02|γ|2N(z)|(z)F(q)V,
f(z)=1Λ0Λf(z)dz,
η=P2/P1,
P1=NA(I1+I2) k043π02|γ|2,
P2=N0 VΛF(q)0Λ k046πNA02|γ|2×(I1+I2+2I1I2 cos Kz)×exp-γrμ00kBT(I1+I2+2I1I2 cos Kz)dz.
PPC=PsR,
R=|κ sin wL|2|w cos wL+αR sin wL|2,
w=(|κ|2-αR2)1/2,
α=α0 1+jΔ1+Δ21+2I/Is(1+4I/Is)3/2αR+jαI,
κ=-jα0 1+jΔ1+Δ22I/Is(1+4I/Is)3/2,
dIS/N=1dΩ=dPNdΩ1RA,
dPNdΩ=k0432π2NA02|γ|2N(z)I(z)F(q)V

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