Abstract

Third-order susceptibilities are calculated for a Doppler-broadened two-level system. The dependence of four-wave mixing on the angle θ between the pump and signal fields is studied, and the reflection coefficient is shown to have a narrow field of view that is inversely proportional to the ratio of the Doppler width to the homogeneous linewidth. For the collinear geometry, θ = 0°, the frequency dependence of the nondegenerate case is analyzed and shown capable of yielding a real-time narrow-bandwidth optical filter whose bandwidth is limited by the homogeneous linewidth.

© 1981 Optical Society of America

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  1. D. M. Bloom, P. F. Liao, and N. P. Economou, "Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor," Opt. Lett. 2, 58 (1978).
  2. P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813 (1978).
  3. R. A. Fischer and B. J. Feldman, "On-resonant phase-conjugate reflection and amplification at 10.6 µm in inverted CO2," Opt. Lett. 4, 140 (1979).
  4. R. C. Lind et al., "Phase conjugation at 10.6 µm by resonantly enhanced degenerate four-wave mixing," Appl. Phys. Lett. 34, 457 (1979).
  5. A. Tomita, "Phase conjugation using gain saturation of a Nd:YAG laser," Appl. Phys. Lett. 34, 463 (1979).
  6. R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94 (1978).
  7. J. Nilsen and A. Yariv, "Nearly degenerate four-wave mixing applied to optical filters," Appl. Opt. 18, 143 (1979).
  8. S. M. Wandzura, "Effects of atomic motion on wavefront conjugation by resonantly enhanced degenerate four-wave mixing," Opt. Lett. 4, 208 (1979).
  9. A. Yariv and D. M. Pepper, "Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing," Opt. Lett. 1, 16 (1977).
  10. A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 149–155, 418–421, 553–558.
  11. A. Elci and D. Rogovin, "Phase conjugation in an inhomogeneously broadened medium," Opt. Lett.5, 255 (1980). Elci and Rogovin account for the effects of Doppler motion by starting with X(3) calculated for a stationary atom. They replace ω with a Doppler-shifted frequency, ω - kv in X(3), and integrate X(3) over the velocity profile. Their method is basically incorrect because it does not allow for the fact that the two pump waves and the signal wave are each Doppler shifted by a different amount, depending on their propagation direction relative to the velocity v of a given atom.
  12. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), pp. 931, 932.

1980 (1)

1979 (5)

1978 (3)

1977 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), pp. 931, 932.

Abrams, R. L.

Bloom, D. M.

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813 (1978).

D. M. Bloom, P. F. Liao, and N. P. Economou, "Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor," Opt. Lett. 2, 58 (1978).

Economou, N. P.

D. M. Bloom, P. F. Liao, and N. P. Economou, "Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor," Opt. Lett. 2, 58 (1978).

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813 (1978).

Elci, A.

Feldman, B. J.

Fischer, R. A.

Liao, P. F.

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813 (1978).

D. M. Bloom, P. F. Liao, and N. P. Economou, "Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor," Opt. Lett. 2, 58 (1978).

Lind, R. C.

R. C. Lind et al., "Phase conjugation at 10.6 µm by resonantly enhanced degenerate four-wave mixing," Appl. Phys. Lett. 34, 457 (1979).

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94 (1978).

Nilsen, J.

Pepper, D. M.

Rogovin, D.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), pp. 931, 932.

Tomita, A.

A. Tomita, "Phase conjugation using gain saturation of a Nd:YAG laser," Appl. Phys. Lett. 34, 463 (1979).

Wandzura, S. M.

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813 (1978).

R. C. Lind et al., "Phase conjugation at 10.6 µm by resonantly enhanced degenerate four-wave mixing," Appl. Phys. Lett. 34, 457 (1979).

A. Tomita, "Phase conjugation using gain saturation of a Nd:YAG laser," Appl. Phys. Lett. 34, 463 (1979).

Opt. Lett. (6)

Other (2)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), pp. 931, 932.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 149–155, 418–421, 553–558.

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