Abstract

We present a plane-wave theory of nondegenerate oscillation in the linear passive (self-pumped) phase-conjugate mirror (PPCM). The circumstances under which the plane-wave theory permits spontaneous nondegenerate oscillation in this and other PPCM’s are discussed.

© 1986 Optical Society of America

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References

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  1. K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (1984).
  2. B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
    [CrossRef]
  3. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
    [CrossRef]
  4. J. Feinberg, Opt. Lett. 7, 486 (1982). In previous publications, we have called this the two-interaction-region PPCM. The appropriateness of this name is now in doubt, so for the moment we will adopt its colloquial name, in honor of the cat that assisted in its initial demonstration.
    [CrossRef] [PubMed]
  5. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  6. M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1983) (unpublished).
  7. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
    [CrossRef]
  8. K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
    [CrossRef] [PubMed]
  9. M. Ewbank, P. Yeh, Opt. Lett. 10, 496 (1985).
    [CrossRef] [PubMed]
  10. I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
  11. T. Y. Chang, R. W. Hellwarth, Opt. Lett. 10, 408 (1985).
    [CrossRef] [PubMed]

1985 (4)

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

T. Y. Chang, R. W. Hellwarth, Opt. Lett. 10, 408 (1985).
[CrossRef] [PubMed]

M. Ewbank, P. Yeh, Opt. Lett. 10, 496 (1985).
[CrossRef] [PubMed]

1984 (2)

K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (1984).

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

1982 (2)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Chang, T. Y.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1983) (unpublished).

Ewbank, M.

Feinberg, J.

Fischer, B.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Hellwarth, R. W.

Khoshnevisan, M.

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (1984).

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

McMichael, I.

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Sternklar, S.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Yeh, P.

M. Ewbank, P. Yeh, Opt. Lett. 10, 496 (1985).
[CrossRef] [PubMed]

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Appl. Phys. Lett. (2)

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12, (1984).
[CrossRef]

J. Opt. Soc. Am. A (1)

K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (1984).

Opt. Lett. (3)

Phys. Rev. Lett. (1)

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Other (2)

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1983) (unpublished).

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Figures (2)

Fig. 1
Fig. 1

The linear passive PCM.

Fig. 2
Fig. 2

Phase-conjugate reflectivity R (dashes) and oscillation-beam frequency detuning δ versus optical path length kL modulo 2π in empty oscillation cavity. Only the path-length range 0 to π is shown: the results show natural symmetry about the origin. In each case, the undetuned coupling constant γl0 = −3 and M2 = 0.98. The detuning δ is normalized by the constant quantity I4(0)/(I0τ). M1 varies as follows: (a) 1.00, (b) 0.125, (c) 0.025, (d) 0.01. Note the change of scale in δ for (b), (c), and (d).

Equations (18)

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d A 1 / d z = - γ g A 4 ,
d A 2 * / d z = - γ g A 3 * ,
d A 3 / d z = - γ g A 2 ,
d A 4 * / d z = - γ g A 1 * ,
ψ ( l ) - ψ ( 0 ) + 2 k L = 2 π m ,
γ = ω r eff n 0 3 E q ( E 0 + i E d ) 4 c cos ϑ [ E 0 - δ τ ( E d + E μ ) ] + i [ E d + E q + δ τ E 0 ] ,
δ = ω 1 - ω 4 = ω 3 - ω 2 ,
d log A 1 d z = - γ I 4 ( 1 + f ) ,
d log A 2 * d z = - γ I 3 ( 1 + 1 / f ) ,
f = A 2 * A 3 / A 1 A 4 * .
d ψ / d z = - Im [ γ I 4 ( 1 + I 34 + f + I 34 / f ) ] ,
M 1 M 2 = | T ( 0 ) + Q Δ T ( 0 ) + Q + ( 1 + Δ ) T ( 0 ) / M 2 | 2 ,
I 12 ( z ) I 1 ( z ) I 2 ( z ) = 1 M 2 | T ( z ) + Q [ Δ T ( z ) + Q + ( 1 + Δ ) T ( z ) / M 2 ] | 2 ,
I 34 ( z ) = ( 1 + Δ ) 2 T ( z ) 2 M 2 Δ T ( z ) + Q 2 ,
I 4 ( z ) = 1 - Δ - I 12 ( z ) ( 1 + Δ ) 2 [ 1 - I 12 ( z ) I 34 ( z ) ] ,
f = - ( Δ + 1 ) T ( z ) T ( z ) + Q { 1 + ( Δ + 1 ) T ( z ) M 2 [ Δ T ( z ) + Q ] } .
T ( 0 ) + Q = 0 ,
c A 4 ( 0 ) A 2 ( l ) = A 1 ( l ) A 4 ( 0 ) = t 14 = A 3 ( 0 ) A 2 ( l ) = t 32 ,

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