Abstract

Results of experiments investigating the effects of optical pumping and atomic motion on cw degenerate four-wave mixing in atomic sodium vapor are presented. The signal strength is found to decrease as (sin θ)−2, where θ is the angle between the object and pump waves; however, the linewidth for generation is Doppler free and is independent of θ. Agreement is found with a simple model of the mixing process. Distortions of the atomic velocity distribution (produced in our experiments by optical pumping) are found to be essential for efficient cw generation. A new modulation scheme for the discrimination against background is used.

© 1980 Optical Society of America

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References

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  1. D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, AppL. Phys. Lett. 33, 41 (1978); E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978); D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978); J. P. Huignard, J. P. Herriau, P. Auborg, E. Spitz, Opt. Lett. 4, 21 (1979); C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979); R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
    [CrossRef] [PubMed]
  2. P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
    [CrossRef]
  3. P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
    [CrossRef]
  4. A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
    [CrossRef]
  5. S. M. Wandzura, Opt. Lett. 4, 208 (1979).
    [CrossRef] [PubMed]
  6. M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
    [CrossRef]
  7. R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
    [CrossRef] [PubMed]
  8. The apparent divergence of Eq. (4) as θ approaches zero is due to our replacement of the Doppler distribution with a constant (Doppler limit).
  9. The effective density, αN, which is determined by the strength of the optical pumping, was determined to be approximately the density of the 3S1/2(F = 2, mF = 2) state by measuring the transmission of a weak circularly polarized probe beam through the cell in the presence of the optical pumping fields.
  10. S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. C. Haueisen, Opt. Commun. 28, 183 (1979).
    [CrossRef]

1979 (1)

1978 (4)

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. C. Haueisen, Opt. Commun. 28, 183 (1979).
[CrossRef]

R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
[CrossRef] [PubMed]

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

1977 (3)

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, AppL. Phys. Lett. 33, 41 (1978); E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978); D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978); J. P. Huignard, J. P. Herriau, P. Auborg, E. Spitz, Opt. Lett. 4, 21 (1979); C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979); R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
[CrossRef] [PubMed]

P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
[CrossRef]

Abrams, R. L.

Bjorklund, G. C.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, AppL. Phys. Lett. 33, 41 (1978); E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978); D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978); J. P. Huignard, J. P. Herriau, P. Auborg, E. Spitz, Opt. Lett. 4, 21 (1979); C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979); R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
[CrossRef] [PubMed]

Bloom, D. M.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
[CrossRef]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, AppL. Phys. Lett. 33, 41 (1978); E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978); D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978); J. P. Huignard, J. P. Herriau, P. Auborg, E. Spitz, Opt. Lett. 4, 21 (1979); C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979); R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
[CrossRef] [PubMed]

Citron, M. L.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

Economou, N. P.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
[CrossRef]

P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
[CrossRef]

Freeman, R. R.

P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
[CrossRef]

Gabel, C. W.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

Gray, H. R.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

Hellwarth, R. W.

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. C. Haueisen, Opt. Commun. 28, 183 (1979).
[CrossRef]

Jensen, S. M.

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. C. Haueisen, Opt. Commun. 28, 183 (1979).
[CrossRef]

Liao, P. F.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
[CrossRef]

P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
[CrossRef]

Lind, R. C.

Stroud, C. R.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

Wandzura, S. M.

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

Appl. Phys. Lett. (3)

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 32, 813 (1978).
[CrossRef]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, AppL. Phys. Lett. 33, 41 (1978); E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978); D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978); J. P. Huignard, J. P. Herriau, P. Auborg, E. Spitz, Opt. Lett. 4, 21 (1979); C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979); R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
[CrossRef] [PubMed]

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. C. Haueisen, Opt. Commun. 28, 183 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, Phys. Rev. A 16, 1507 (1977). We found the presence of a small magnetic field (a few gauss) is necessary to obtain the correct two-level behavior. For example, in the absence of the field, the signal intensity is found to be approximately proportional to (sin θ)−4 instead of (sin θ)−2. We do not fully understand this change in behavior.
[CrossRef]

Phys. Rev. Lett. (1)

P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
[CrossRef]

Other (2)

The apparent divergence of Eq. (4) as θ approaches zero is due to our replacement of the Doppler distribution with a constant (Doppler limit).

The effective density, αN, which is determined by the strength of the optical pumping, was determined to be approximately the density of the 3S1/2(F = 2, mF = 2) state by measuring the transmission of a weak circularly polarized probe beam through the cell in the presence of the optical pumping fields.

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Figures (3)

Fig. 1
Fig. 1

Conjugate wave intensity versus laser frequency for 3S1/2(F = 2) → 3P3/2(F = 3) transition for θ = 22°. Solid line indicates data scan; open circles, Eq. (4); dots, model of Ref. 5. Pump intensity is 6 mW/cm2; object intensity was 3 mW/cm3. For these intensities and lower, the line shape was found to be essentially independent of intensity. At higher intensities, more-complicated line shapes are observed.3

Fig. 2
Fig. 2

Linewidth (FWHM) versus angle between pump object beams. Pump intensity is 6 mW/cm2; object intensity is 3 mW/cm2.

Fig. 3
Fig. 3

Conjugate-wave intensity versus sin θ. Theoretical plots are normalized to data point of sin θ ≃ 0.03. Pump intensity is 3.1 mW/cm2; object intensity is 4.8 mW/cm2.

Equations (4)

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( d d t + Γ 2 ) ρ 22 ( v ) = μ 2 [ ˜ ρ ˜ 12 ( v ) + ˜ * ρ ˜ 21 ( v ) ] , ( d d t + Γ 12 ) ρ ˜ 12 ( v ) = μ ˜ 2 [ 1 - 2 ρ 22 ( v ) ] ,
ρ 12 ( x , v ) = μ 3 E 1 E 2 E 0 * 4 3 × - ( Γ 12 - i Ω ) [ ( Γ 12 - i Ω ) 2 + ( k 1 · v ) 2 ] [ ( Γ 12 - i k 0 · v ) 2 + Ω 2 ] ,
ρ 12 = N ( v ) ρ 12 ( v ) d 3 v .
R = | E I E 0 | 2 = ( 4 μ 4 π 4 α N E 1 E 2 L 3 λ ( k u ) 2 sin θ ) 2 × ( Γ 0 Γ 12 + Γ 0 ) 2 1 ( Γ 12 + Γ 0 ) 2 + 4 Ω 2 ,

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