Abstract

It is shown that pump waves A and B at angle φ in a nonlinear medium generate gain for a signal wave C at the half-angle between the pump waves.

© 1981 Optical Society of America

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References

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  1. C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979).
    [CrossRef] [PubMed]
  2. C. V. Heer, in Proceedings of the International Conference on Lasers '79 (STS Press, McLean, Va., 1980), p. 506.
  3. N. C. Griffen, C. V. Heer, Appl. Phys. Lett. 33, 865 (1978).
    [CrossRef]
  4. T. Fu, M. Sargent, Opt. Lett. 4, 366 (1979).
    [CrossRef] [PubMed]
  5. For reviews see A. Yariv, in Physics of Quantum Electronics (Addison-Wesley, Reading, Mass., 1978), Vol. 6, Chap. 6;IEEE J. Quantum Electron. QE-14, 650 (1978);B. Ya Zel'dovich, N. F. Pilipetskii, V. V. Reful'skii, V. V. Shkunov, Kvantovaya Electron. (Moscow) 5, 1800 (1979)[Sov. J. Quantum Electron. 8, 8 (1978)];R. W. Hellwarth, IEEE J. Quantum Electron. QE-15, 101 (1979)
    [CrossRef]
  6. N. C. Griffen, Ph.D. dissertation, Ohio State University, Columbus, Ohio, 1979 (unpublished).
  7. N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
    [CrossRef]
  8. D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
    [CrossRef]
  9. E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978).
    [CrossRef] [PubMed]
  10. R. K. Jain, M. B. Klein, R. C. Lind, Opt. Lett. 4, 328 (1979).
    [CrossRef] [PubMed]
  11. T. Baer, I. C. Abella, Phys. Rev. A 16, 2093 (1977).
    [CrossRef]
  12. D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
    [CrossRef]
  13. R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
    [CrossRef]
  14. R. A. Fisher, B. J. Feldman, Opt. Lett. 4, 140 (1979).
    [CrossRef] [PubMed]

1981 (1)

N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
[CrossRef]

1979 (5)

1978 (3)

D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
[CrossRef]

E. E. Bergmann, I. J. Bigio, B. J. Feldman, R. A. Fisher, Opt. Lett. 3, 82 (1978).
[CrossRef] [PubMed]

N. C. Griffen, C. V. Heer, Appl. Phys. Lett. 33, 865 (1978).
[CrossRef]

1977 (2)

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

T. Baer, I. C. Abella, Phys. Rev. A 16, 2093 (1977).
[CrossRef]

Abella, I. C.

T. Baer, I. C. Abella, Phys. Rev. A 16, 2093 (1977).
[CrossRef]

Abrams, R. L.

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

Baer, T.

T. Baer, I. C. Abella, Phys. Rev. A 16, 2093 (1977).
[CrossRef]

Bennett, R. J.

D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
[CrossRef]

Bergmann, E. E.

Bigio, I. J.

Bjorklund, G. C.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

Bloom, D. M.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

Feldman, B. J.

Fisher, R. A.

Fu, T.

Giuliano, C. R.

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

Griffen, N. C.

C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979).
[CrossRef] [PubMed]

N. C. Griffen, C. V. Heer, Appl. Phys. Lett. 33, 865 (1978).
[CrossRef]

N. C. Griffen, Ph.D. dissertation, Ohio State University, Columbus, Ohio, 1979 (unpublished).

Grischkowsky, D.

D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
[CrossRef]

Heer, C. V.

C. V. Heer, N. C. Griffen, Opt. Lett. 4, 239 (1979).
[CrossRef] [PubMed]

N. C. Griffen, C. V. Heer, Appl. Phys. Lett. 33, 865 (1978).
[CrossRef]

C. V. Heer, in Proceedings of the International Conference on Lasers '79 (STS Press, McLean, Va., 1980), p. 506.

Inaba, H.

N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
[CrossRef]

Jain, R. K.

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

R. K. Jain, M. B. Klein, R. C. Lind, Opt. Lett. 4, 328 (1979).
[CrossRef] [PubMed]

Klein, M. B.

R. K. Jain, M. B. Klein, R. C. Lind, Opt. Lett. 4, 328 (1979).
[CrossRef] [PubMed]

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

Lind, R. C.

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

R. K. Jain, M. B. Klein, R. C. Lind, Opt. Lett. 4, 328 (1979).
[CrossRef] [PubMed]

Ohkawara, K.

N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
[CrossRef]

Sargent, M.

Shiren, N. S.

D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
[CrossRef]

Steel, D. G.

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

Tan-no, N.

N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
[CrossRef]

Yariv, A.

For reviews see A. Yariv, in Physics of Quantum Electronics (Addison-Wesley, Reading, Mass., 1978), Vol. 6, Chap. 6;IEEE J. Quantum Electron. QE-14, 650 (1978);B. Ya Zel'dovich, N. F. Pilipetskii, V. V. Reful'skii, V. V. Shkunov, Kvantovaya Electron. (Moscow) 5, 1800 (1979)[Sov. J. Quantum Electron. 8, 8 (1978)];R. W. Hellwarth, IEEE J. Quantum Electron. QE-15, 101 (1979)
[CrossRef]

Appl. Phys. Lett. (4)

N. C. Griffen, C. V. Heer, Appl. Phys. Lett. 33, 865 (1978).
[CrossRef]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

D. Grischkowsky, N. S. Shiren, R. J. Bennett, Appl. Phys. Lett. 33, 805 (1978).
[CrossRef]

R. C. Lind, D. G. Steel, M. B. Klein, R. L. Abrams, C. R. Giuliano, R. K. Jain, Appl. Phys. Lett. 34, 457 (1979).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

T. Baer, I. C. Abella, Phys. Rev. A 16, 2093 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

N. Tan-no, K. Ohkawara, H. Inaba, Phys. Rev. Lett. 46, 1282 (1981).
[CrossRef]

Other (3)

C. V. Heer, in Proceedings of the International Conference on Lasers '79 (STS Press, McLean, Va., 1980), p. 506.

For reviews see A. Yariv, in Physics of Quantum Electronics (Addison-Wesley, Reading, Mass., 1978), Vol. 6, Chap. 6;IEEE J. Quantum Electron. QE-14, 650 (1978);B. Ya Zel'dovich, N. F. Pilipetskii, V. V. Reful'skii, V. V. Shkunov, Kvantovaya Electron. (Moscow) 5, 1800 (1979)[Sov. J. Quantum Electron. 8, 8 (1978)];R. W. Hellwarth, IEEE J. Quantum Electron. QE-15, 101 (1979)
[CrossRef]

N. C. Griffen, Ph.D. dissertation, Ohio State University, Columbus, Ohio, 1979 (unpublished).

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Figures (1)

Fig. 1
Fig. 1

Two pump waves A and B at angle φ in an optically nonlinear medium generate gain for a signal wave C at the half-angle. Other waves (a, b, c, d, etc.) or waves at angles ±m (φ/2) also are generated. C can be generated by spontaneous emission; b and a are the phase conjugates of C formed with A and B, respectively.

Equations (19)

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P ( r , t ) = z ̂ N 1 / 4 M 2 ( Δ + i / T 2 ) E Δ 2 + ( 1 / T 2 ) 2 + M 2 | E | 2 ( T 1 / T 2 ) × e i ω t + c . c .
E = A e i ψ 1 + B e i ψ 2 + C e i ψ 3 .
F = M 2 ( T 1 / T 2 ) [ Δ 2 + 1 / T 2 2 + M 2 ( A A * + B B * ) ( T 1 / T 2 ) ] 1
α = 1 / 4 N ( Δ + i / T 2 ) ( T 2 + T 1 ) F ( π / λ 0 ) ,
P z = α ( λ 0 / π ) E ( 1 F { A B * exp [ i ( ψ 1 ψ 2 ) ] + B C * exp [ i ( ψ 2 ψ 3 ) ] + C A * exp [ i ( ψ 3 ψ 1 ) ] + c . c } + higher-order terms ) e i ω t + c . c .
A B C * exp [ i ( ψ 1 + ψ 2 ψ 3 ) ]
2 ψ 3 = ψ 1 + ψ 2
φ 1 = [ ( φ / 2 ) z 1 / 2 ( φ / 2 ) 2 y ] k
ξ = C e i φ 3
2 u = k ( φ / 2 ) 2 .
d ξ d y = i α [ ξ F ( A A * + B B * ) ξ 2 FAB ξ * e i 2 u y ] .
ξ = ( U + i V ) e m y e iuy e i δ / 2 ,
m ± = α ( 1 2 F A 2 ) ± [ α 2 ( 1 2 F A 2 ) 2 ( 1 4 F A 2 ) ( α 2 + α 2 α u ) + α u u 2 ] 1 / 2 .
[ ξ + ( 0 ) e m + y + ξ ( 0 ) e m y ] exp [ i ( K y ω t ) ] + c . c . ,
m ± ± ( α α * u 2 ) 1 / 2 .
E [ x 1 sin x t i Δ x 2 ( 1 cos x t ) ] ,
α 1 . 6 ( P mT / I p ) Δ ,
I p 4 × 10 13 Δ 2 ,
α 4 × 10 12 P mT / Δ .

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