Abstract

The theory of degenerate four-wave mixing using two-photon transitions is formulated. Two kinds of mechanisms compete in generating conjugate waves leading to two phenomena that do not occur in two-level media: (1) a double-peaked reflection spectrum and (2) coupled-mode oscillation in absorbing media. In addition, because of the dynamic Stark-shifted line center, the reflection coefficient approaches a constant value at large intensities, unlike the two-level coefficient, which bleaches to zero.

© 1980 Optical Society of America

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References

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  1. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]
  2. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  3. R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978);Opt. Lett. 3, 205 (1978).
    [CrossRef] [PubMed]
  4. E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978);R. A. Fisher, B. J. Feldman, Opt. Lett 7, 140 (1979).
    [CrossRef] [PubMed]
  5. A. Tomita, Appl. Phys. Lett. 34, 7 (1979).
    [CrossRef]
  6. D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett, 31, 592 (1978).
    [CrossRef]
  7. P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978).
    [CrossRef] [PubMed]
  8. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 158 (1978);Appl. Phys. Lett. 32, 12 (1978).
    [CrossRef]
  9. T. Fu, M. Sargent, Opt. Lett. 4, 366 (1979).
    [CrossRef] [PubMed]
  10. P. F. Liao, N. P. Economou, R. R. Freeman, Phys. Rev. Lett. 39, 1473 (1977).
    [CrossRef]
  11. D. G. Steel, J. F. Lam, Phys. Rev. Lett. 43, 1588 (1979).
    [CrossRef]
  12. L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
    [CrossRef]
  13. M. Sargent, Phys. Rep. 43, 223 (1978).
    [CrossRef]
  14. The two-level Doppler-broadened case is discussed by S. M. Wandzura, Opt. Lett. 4, 208 (1979).
    [CrossRef] [PubMed]

1979 (4)

1978 (6)

1977 (4)

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

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

Abrams, R. L.

Bergmann, E. E.

Bigio, I. J.

Bjorklund, G. C.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett, 31, 592 (1978).
[CrossRef]

Bloom, D. M.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett, 31, 592 (1978).
[CrossRef]

P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978).
[CrossRef] [PubMed]

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 158 (1978);Appl. Phys. Lett. 32, 12 (1978).
[CrossRef]

Economou, N. P.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 158 (1978);Appl. Phys. Lett. 32, 12 (1978).
[CrossRef]

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

Eidson, W. W.

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

Eteson, P. C.

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

Feldman, B. J.

Fisher, R. A.

Freeman, R. R.

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

Fu, T.

Furcinitti, P.

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

Hellwarth, R. W.

Lam, J. F.

D. G. Steel, J. F. Lam, Phys. Rev. Lett. 43, 1588 (1979).
[CrossRef]

Liao, P. F.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 158 (1978);Appl. Phys. Lett. 32, 12 (1978).
[CrossRef]

P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978).
[CrossRef] [PubMed]

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

Lind, R. C.

Narducci, L M.

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

Pepper, D. M.

Sargent, M.

Steel, D. G.

D. G. Steel, J. F. Lam, Phys. Rev. Lett. 43, 1588 (1979).
[CrossRef]

Tomita, A.

A. Tomita, Appl. Phys. Lett. 34, 7 (1979).
[CrossRef]

Wandzura, S. M.

Yariv, A.

Appl. Phys. Lett (1)

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett, 31, 592 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

A. Tomita, Appl. Phys. Lett. 34, 7 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (7)

Phys. Rep. (1)

M. Sargent, Phys. Rep. 43, 223 (1978).
[CrossRef]

Phys. Rev. A (1)

L M. Narducci, W. W. Eidson, P. Furcinitti, P. C. Eteson, Phys. Rev. A 16, 1665 (1977).
[CrossRef]

Phys. Rev. Lett. (2)

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

D. G. Steel, J. F. Lam, Phys. Rev. Lett. 43, 1588 (1979).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Four-wave mixing configuration. A4 and A3 are the nonsaturating signal and conjugate waves, respectively.

Fig. 2
Fig. 2

Energy-level diagram for an active atom.

Fig. 3
Fig. 3

Reflectivity R versus frequency detuning, normalized to T2. T2 = T1, I2 = 1.0.

Fig. 4
Fig. 4

Reflectivity R versus pump intensity I2 in an absorbing medium, α0L = 1.0, and T1 = T2. Notice that coupled-mode oscillation occurs for ωsT1 = 4.

Equations (10)

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E ( r , t ) = 1 2 ( r ) e i ν t + c . c .
( r ) = n = 1 4 A n exp ( i K n r ) ,
C ˙ a = i 4 k a a | | 2 C a + i 4 k a b e i ( ω 2 ν ) t 2 C b , C ˙ b = i 4 k b b | | 2 C b + i 4 k a b e i ( ω 2 ν ) t * 2 C a ,
k α α = 2 j | P j α | 2 ω j α ω j α 2 ν 2 , α = a or b , k a b = 1 j P j a P j b ω j b ν .
P ( r ) = N 2 ( k a a + k b b ) + N k a b T 1 T 2 ω s 1 + I 2 + N k a b T 1 T 2 D * 1 + I 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 .
R = | κ sinh w L | 2 | w cosh w L + α R sinh w L | 2 ,
α R 2 = α 0 2 T 2 T 1 ( 1 + I l 2 ) 5 / 2 × [ 4 + 5 I l 2 + I l 4 + I l 4 + I l 2 4 ( 1 + I l 2 ) 1 / 2 ] ,
| κ | 2 = α 0 2 T 2 T 1 I l 2 / 2 ( 1 + I l 2 ) 5 / 2 [ ( ω s 2 T 1 2 + 1 ) ( I l 2 + 1 ) + ( ω s 2 T 1 2 1 ) 3 I l 2 1 ( 1 + I l 2 ) 1 / 2 + ω s T 1 δ I l 3 3 I l 2 ( 1 + I l 2 ) 1 / 2 ] .
I l = 4 I 2 [ 1 + ( ω + ω s I 2 2 ν ) 2 T 2 2 ] 1 / 2 .

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