Abstract

A number of new optical effects that result from degenerate four-wave mixing in transparent optical media are proposed and analyzed. The applications are relevant to time-reversed (phase-conjugated) propagation as well as to a new mode of parametric oscillation.

© 1977 Optical Society of America

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Errata

T J Karr, "Power and stability of phase-conjugate lasers," J. Opt. Soc. Am. 73, 600-609 (1983)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-73-5-600

References

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  1. P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  2. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  3. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  4. J. J. Wynne, G. D. Boyd, Appl. Phys. Lett. 12, 191 (1968).
    [CrossRef]
  5. S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
    [CrossRef]
  6. B. Zeldovich, Phys. JETP Lett. 15, 109 (1972).
  7. A. Yariv, Appl. Phys. Lett. 28, 88 (1976); also, Opt. Commun. (to be published).
    [CrossRef]
  8. R. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]

1977

1976

A. Yariv, Appl. Phys. Lett. 28, 88 (1976); also, Opt. Commun. (to be published).
[CrossRef]

1972

B. Zeldovich, Phys. JETP Lett. 15, 109 (1972).

1968

J. J. Wynne, G. D. Boyd, Appl. Phys. Lett. 12, 191 (1968).
[CrossRef]

1966

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

1965

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Boyd, G. D.

J. J. Wynne, G. D. Boyd, Appl. Phys. Lett. 12, 191 (1968).
[CrossRef]

Harris, S. E.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Hellwarth, R.

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Wynne, J. J.

J. J. Wynne, G. D. Boyd, Appl. Phys. Lett. 12, 191 (1968).
[CrossRef]

Yariv, A.

A. Yariv, Appl. Phys. Lett. 28, 88 (1976); also, Opt. Commun. (to be published).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Zeldovich, B.

B. Zeldovich, Phys. JETP Lett. 15, 109 (1972).

Appl. Phys. Lett.

J. J. Wynne, G. D. Boyd, Appl. Phys. Lett. 12, 191 (1968).
[CrossRef]

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

A. Yariv, Appl. Phys. Lett. 28, 88 (1976); also, Opt. Commun. (to be published).
[CrossRef]

J. Opt. Soc. Am.

Phys. JETP Lett.

B. Zeldovich, Phys. JETP Lett. 15, 109 (1972).

Phys. Rev.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Other

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Four-wave mixing geometry (assuming nondepleting pump waves).

Fig. 2
Fig. 2

Intensity distributions of the input power (P4) and the conjugate field power (P3) as a function of |x|z near oscillation condition (|x|L = π/2).

Fig. 3
Fig. 3

Four-wave mixing utilizing external mirror of reflectivity R3, which provides preferred direction for oscillation.

Equations (19)

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E i ( r , t ) = 1 2 A i ( r i ) e i ( ω t - k i · r ) + c . c .
k 1 + k 2 = 0 ,             k 3 + k 4 = 0.
P ( NL ) ( ω 4 = ω 1 + ω 2 - ω 3 ) = 1 2 χ A 1 A 2 A 3 * exp { i [ ω 4 t - ( k 1 + k 2 - k 3 ) · r ] } , P ( NL ) ( ω 3 = ω 1 + ω 2 - ω 4 ) = P ( NL ) ( ω = ω + ω - ω ) = 1 2 χ A 1 A 2 A 4 * exp { i [ ω 3 t - ( k 1 + k 2 - k 4 ) · r ] } .
× × E + c 2 2 E t 2 = - 4 π c 2 2 t 2 P ( NL ) ,
d A 3 d z = i 2 π ω c n χ A 1 A 2 A 4 * exp { - i ( k 1 + k 2 - k 3 - k 4 ) · r } = i x * A 4 * , d A 4 * dz = i x A 3 ,
| d 2 A i d z 2 | | k i d A i d z |
x * = 2 π ω c n χ A 1 A 2 .
A 3 ( z ) = cos x z cos x L A 3 ( L ) + i x * x sin x ( z - L ) cos x L A 4 * ( 0 ) , A 4 * ( z ) = i x x * sin x z cos x L A 3 ( L ) + cos x ( z - L ) cos x L A 4 * ( 0 ) .
A 3 ( 0 ) = - i ( x * x tan x L ) A 4 * ( 0 ) ,
A 4 * ( L ) = A 4 * ( 0 ) cos x L .
A 3 ( 0 ) > A 4 ( 0 ) ,
x L = π / 2 , A 3 ( 0 ) A 4 * ( 0 ) = ,             A 4 * ( L ) A 4 * ( 0 ) = ,
A 4 ( x , y , z ) = A 4 ( k , z ) e i k · r d 2 k = A 4 ( - k , z ) e - i k · r d 2 k ,
A 3 ( x , y , z ) = A 3 ( k , z ) e i k · r d 2 k .
z A 3 ( k , z ) = - i λ k 2 4 π A 3 ( k , z ) + i x * A 4 * ( - k , z ) , z A 4 * ( - k , z ) = - i λ k 2 4 π A 4 * ( - k , z ) + i x A 3 ( k , z ) ,
A 3 ( k , z ) = i e - i λ 2 z / 4 π ( x * x ) A 4 ( - k , 0 ) cos x L sin x ( z - L ) , A 4 * ( - k , z ) = e - i λ 2 z / 4 π A 4 * ( - k , 0 ) cos x ( z - L ) cos x L .
A 3 ( k , 0 ) = - i ( x * x tan x L ) A 4 * ( - k , 0 ) ,
A 3 ( x , y , z < 0 ) = - i [ ( x * x tan x L ) ] A 4 * ( x , y , z < 0 ) ,
x L = tan - 1 ( 1 / r ) ,

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