Abstract

Degenerate four-wave mixing in a two-level absorbing (or amplifying) system is treated, leading to a quantitative description of amplified reflection, oscillation, and phase conjugation.

© 1978 Optical Society of America

Full Article  |  PDF Article

Corrections

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media: errata," Opt. Lett. 3, 205-205 (1978)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-3-5-205

References

  • View by:
  • |
  • |
  • |

  1. V. Wang, C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” 1977 IEEE/ OSA Conference on Laser Engineering and Applications, Washington, D.C., June 1977, paper 17.6, andOpt. Lett. 2, 4–6 (1978).
    [PubMed]
  2. A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
    [CrossRef]
  3. B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).
  4. B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).
  5. R. W. Hellwarth, “Generation of time-reversed wavefronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
    [CrossRef]
  6. C. V. Heer, P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977).
    [CrossRef]
  7. A. Yariv, D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
    [CrossRef] [PubMed]
  8. D. M. Bloom, G. E. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977).
    [CrossRef]
  9. S. L. Jensen, R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” Appl. Phys. Lett. 32, 166–167 (1978).
    [CrossRef]
  10. D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
    [CrossRef]
  11. A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 149–158.
  12. W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).

1978 (2)

S. L. Jensen, R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” Appl. Phys. Lett. 32, 166–167 (1978).
[CrossRef]

D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
[CrossRef]

1977 (5)

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

R. W. Hellwarth, “Generation of time-reversed wavefronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
[CrossRef]

C. V. Heer, P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977).
[CrossRef]

A. Yariv, D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
[CrossRef] [PubMed]

D. M. Bloom, G. E. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977).
[CrossRef]

1976 (1)

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

1972 (1)

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

1964 (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).

Bjorklund, G. E.

D. M. Bloom, G. E. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977).
[CrossRef]

Bloom, D. M.

D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
[CrossRef]

D. M. Bloom, G. E. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977).
[CrossRef]

Economu, N. P.

D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
[CrossRef]

Fagullov, F. S.

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

Giuliano, C. R.

V. Wang, C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” 1977 IEEE/ OSA Conference on Laser Engineering and Applications, Washington, D.C., June 1977, paper 17.6, andOpt. Lett. 2, 4–6 (1978).
[PubMed]

Heer, C. V.

C. V. Heer, P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977).
[CrossRef]

Hellwarth, R. W.

S. L. Jensen, R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” Appl. Phys. Lett. 32, 166–167 (1978).
[CrossRef]

R. W. Hellwarth, “Generation of time-reversed wavefronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
[CrossRef]

Jensen, S. L.

S. L. Jensen, R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” Appl. Phys. Lett. 32, 166–167 (1978).
[CrossRef]

Lamb, W. E.

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).

Liao, P. F.

D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
[CrossRef]

McManamon, P. F.

C. V. Heer, P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977).
[CrossRef]

Mel'nikov, N. A.

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

Pepper, D. M.

Pilipetskii, N. F.

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

Popovickev, V. I.

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

Ragul'skii, V. V.

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

Wang, V.

V. Wang, C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” 1977 IEEE/ OSA Conference on Laser Engineering and Applications, Washington, D.C., June 1977, paper 17.6, andOpt. Lett. 2, 4–6 (1978).
[PubMed]

Yariv, A.

A. Yariv, D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
[CrossRef] [PubMed]

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 149–158.

Zel'dovich, B. Y.

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

Appl. Phys. Lett. (3)

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

D. M. Bloom, G. E. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977).
[CrossRef]

S. L. Jensen, R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” Appl. Phys. Lett. 32, 166–167 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

JETP Lett. (2)

B. Y. Zel'dovich, N. A. Mel'nikov, N. F. Pilipetskii, V. V. Ragul'skii, “Observation of wave-front inversion in stimulated Raman scattering of light,” JETP Lett. 25, 36–39 (1977).

B. Y. Zel'dovich, V. I. Popovickev, V. V. Ragul'skii, F. S. Fagullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel'Shtam–Brillouin scattering,” JETP Lett. 15, 109–112 (1972).

Opt. Commun. (1)

C. V. Heer, P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977).
[CrossRef]

Opt. Lett. (2)

A. Yariv, D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977).
[CrossRef] [PubMed]

D. M. Bloom, P. F. Liao, N. P. Economu, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” Opt. Lett. 2, 158–160 (1978).
[CrossRef]

Phys. Rev. A (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).

Other (2)

V. Wang, C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” 1977 IEEE/ OSA Conference on Laser Engineering and Applications, Washington, D.C., June 1977, paper 17.6, andOpt. Lett. 2, 4–6 (1978).
[PubMed]

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 149–158.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Geometry for degenerate four-wave mixing. A1 and A2 are taken as nondepleted pump waves.

Fig. 2
Fig. 2

Calculated reflectivity versus normalized pump intensity for line-center operation and various values of small-signal field absorption.

Fig. 3
Fig. 3

Calculated reflectivity versus pump intensity (normalized to the line-center saturation intensity) for fixed small-signal absorption, βL, and varying detuning, δ.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E i ( r , t ) = 1 2 A i ( r i ) exp [ i ( ω t k i × r ) ] + c . c . ,
k 1 + k 2 = 0 , k 3 + k 4 = 0 .
2 E = μ 0 0 2 E t 2 + μ 0 2 P t 2 ,
P = 0 χ ( E ) E ,
χ ( E ) = 2 α 0 k ( i + δ ) ( 1 + δ 2 + | E / E s | 2 ) ,
E = E 0 + Δ E ,
P = 0 χ 0 E 0 + 0 χ 0 Δ E 0 χ 0 ( E 0 Δ E * + E 0 * Δ E ) E 0 | E s | 2 ( 1 + δ 2 + | E 0 / E s | 2 ) ,
d A 3 d z = + α A 3 + i κ * A 4 * , d A 4 * d z = α * A 4 * + i κ A 3 .
α = α 0 ( 1 i δ ) ( 1 + δ 2 ) ( 1 + δ 2 + | A 1 | 2 + | A 2 | 2 A s 2 ) 2 α R i α I .
κ * = 2 i α 0 1 i δ ( 1 + δ 2 + | A 1 | 2 + | A 2 | 2 A s 2 ) 2 × A 1 A 2 A s 2 = 2 i α R 1 i δ 1 + δ 2 × A 1 A 2 A s 2 ,
A 3 ( z ) = A 3 ( L ) exp [ i α I ( z L ) ] ( w cos w z + α R sin w z ) + i κ * A 4 * ( 0 ) exp ( i α I z ) sin w ( z L ) w cos w L + α R sin w L , A 4 * ( z ) = i κ A 3 ( L ) exp ( i α I z ) sin w z + A 4 * ( 0 ) exp ( i α I z ) [ w cos w ( z L ) α R sin w ( z L ) ] w cos w L + α R sin w L ,
R = | A 3 ( 0 ) A 4 ( 0 ) | 2 = | κ sin w L | 2 | w cos w L + α R sin w L | 2 ,
T = | A 4 ( L ) A 4 ( 0 ) | 2 = | w | 2 | w cos w L + α R sin w L | 2 .
tan w L = w α R ,
tanh w L = w / α R .
w = α 0 ( 1 + δ 2 ) = 4 ( 1 + δ 2 ) ( I / I s ) 2 1 [ 1 + 2 ( I / I s ) ] 2 ,
w = α 0 1 + δ 2 × δ 4 = 1 4 β δ ,

Metrics