Abstract

The propagation of electromagnetic radiation in phase-conjugate oscillators is considered. These oscillators consist of conventional resonators containing a nonlinear medium that is pumped by a pair of counterpropagating beams. Both linear and ring oscillators are treated.

© 1985 Optical Society of America

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References

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  1. J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
    [CrossRef]
  2. P. A. Belanger, A. Hardy, A. E. Seigman, Appl. Opt. 19, 602 (1980).
    [CrossRef]
  3. J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
    [CrossRef]
  4. J. F. Lam, W. P. Brown, Opt. Lett. 5, 61 (1980).
    [CrossRef] [PubMed]
  5. P. A. Belanger, Opt. Eng. 21, 266 (1982), and references therein.
    [CrossRef]
  6. P. Yeh, J. Tracy, “Phase-conjugate ring gyro,” Rockwell International Science Center patent disclosure No. 81SC38 (unpublished, 1981).
  7. P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).
  8. J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  9. See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 165.
  10. P. Yeh, A. Yariv, C. Hong, J. Opt. Soc. Am. 67, 423 (1977).
    [CrossRef]
  11. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  12. X is an operator that is defined as XF= F*, where F is an arbitrary complex number.
  13. See, for example, P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford U. Press, New York, 1967), p. 21.
  14. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 219.
  15. J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
    [CrossRef]
  16. J. P. Huignard, A. Marrakchi, Opt. Lett. 6, 622 (1981).
    [CrossRef] [PubMed]
  17. P. Yeh, Opt. Commun. 45, 323 (1983).
    [CrossRef]
  18. Y. H. Ja, Opt. Quantum Electron. 14, 547 (1982).
    [CrossRef]
  19. P. Yeh, J. Opt. Soc. Am. 73, 1268 (1983).
    [CrossRef]

1983 (2)

1982 (4)

Y. H. Ja, Opt. Quantum Electron. 14, 547 (1982).
[CrossRef]

P. A. Belanger, Opt. Eng. 21, 266 (1982), and references therein.
[CrossRef]

P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

1981 (2)

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

J. P. Huignard, A. Marrakchi, Opt. Lett. 6, 622 (1981).
[CrossRef] [PubMed]

1980 (2)

1979 (2)

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
[CrossRef]

1977 (1)

AuYeung, J.

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Bel’dyugin, J. M.

J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
[CrossRef]

Belanger, P. A.

P. A. Belanger, Opt. Eng. 21, 266 (1982), and references therein.
[CrossRef]

P. A. Belanger, A. Hardy, A. E. Seigman, Appl. Opt. 19, 602 (1980).
[CrossRef]

Brown, W. P.

Cronin-Colomb, M.

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Dirac, P. A. M.

See, for example, P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford U. Press, New York, 1967), p. 21.

Fakete, D.

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Fisher, B.

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Galushkin, M. G.

J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
[CrossRef]

Hardy, A.

Hong, C.

Huignard, J. P.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

J. P. Huignard, A. Marrakchi, Opt. Lett. 6, 622 (1981).
[CrossRef] [PubMed]

Ja, Y. H.

Y. H. Ja, Opt. Quantum Electron. 14, 547 (1982).
[CrossRef]

Khoshnevisan, M.

P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).

Lam, J. F.

Marrakchi, A.

J. P. Huignard, A. Marrakchi, Opt. Lett. 6, 622 (1981).
[CrossRef] [PubMed]

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Pepper, D. M.

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Seigman, A. E.

Tracy, J.

P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).

P. Yeh, J. Tracy, “Phase-conjugate ring gyro,” Rockwell International Science Center patent disclosure No. 81SC38 (unpublished, 1981).

White, J. O.

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Yariv, A.

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

P. Yeh, A. Yariv, C. Hong, J. Opt. Soc. Am. 67, 423 (1977).
[CrossRef]

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 165.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 219.

Yeh, P.

P. Yeh, Opt. Commun. 45, 323 (1983).
[CrossRef]

P. Yeh, J. Opt. Soc. Am. 73, 1268 (1983).
[CrossRef]

P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).

P. Yeh, A. Yariv, C. Hong, J. Opt. Soc. Am. 67, 423 (1977).
[CrossRef]

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 165.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 219.

P. Yeh, J. Tracy, “Phase-conjugate ring gyro,” Rockwell International Science Center patent disclosure No. 81SC38 (unpublished, 1981).

Zemskov, E. M.

J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. O. White, M. Cronin-Colomb, B. Fisher, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. AuYeung, D. Fakete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

P. Yeh, Opt. Commun. 45, 323 (1983).
[CrossRef]

Opt. Eng. (1)

P. A. Belanger, Opt. Eng. 21, 266 (1982), and references therein.
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

Y. H. Ja, Opt. Quantum Electron. 14, 547 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. Yeh, J. Tracy, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1982).

Sov. J. Quantum Electron. (1)

J. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, Sov. J. Quantum Electron. 9, 20 (1979).
[CrossRef]

Other (6)

P. Yeh, J. Tracy, “Phase-conjugate ring gyro,” Rockwell International Science Center patent disclosure No. 81SC38 (unpublished, 1981).

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 165.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

X is an operator that is defined as XF= F*, where F is an arbitrary complex number.

See, for example, P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford U. Press, New York, 1967), p. 21.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 219.

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Figures (4)

Fig. 1
Fig. 1

Schematic drawing of a linear phase-conjugate oscillator.

Fig. 2
Fig. 2

Threshold phase-conjugate gain as a function of cavity length ϕ of a linear oscillator, with R = 0.9.

Fig. 3
Fig. 3

Schematic drawing of a ring phase-conjugate oscillator.

Fig. 4
Fig. 4

Threshold phase-conjugate gain as a function of cavity length ϕ of a ring oscillator with R = 0.9.

Equations (30)

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E = { { A exp [ i k ( z + s 1 ) ] + B exp [ i k ( z + s 1 ) ] } exp ( i ω t ) , z < - s 1 , [ A 1 ( z ) exp ( - i k z ) + A 2 ( z ) exp ( i k z ) ] exp ( i ω t ) , 0 < z < l , { C exp [ - i k ( z - l - s 2 ) ] + D exp [ i k ( z - l - s 2 ) ] } exp ( i ω t ) , l + s 2 < z ,
[ C D ] = M 2 [ A 1 ( l ) A 2 ( l ) ] ,
[ A 1 ( 0 ) A 2 ( 0 ) ] = M 1 [ A B ] ,
M 2 = F 2 P ( ϕ 2 ) ,
M 1 = P ( ϕ 1 ) F 1 ,
F 2 = 1 t 2 [ 1 - r 2 - r 2 1 ] ,             F 1 = 1 t 1 [ 1 - r 1 - r 1 1 ] ,
P ( ϕ ) = [ e - i ϕ 0 0 e i ϕ ] ,
[ A 1 ( l ) A 2 ( l ) ] = P ( ϕ 3 ) K [ A 1 ( 0 ) A 2 ( 0 ) ] ,
K = [ c - i σ X i σ X c ] ,
[ C D ] = F 2 P ( ϕ 2 ) P ( ϕ 3 ) K P ( ϕ 1 ) F 1 [ A B ] .
P ( ϕ 1 ) P ( ϕ 2 ) = P ( ϕ 1 + ϕ 2 ) ,
[ C D ] = F 2 P ( ϕ ) K F 1 [ A B ] ,
C = 1 t 1 * t 1 t 2 { e - i ϕ [ c t 1 * ( A - r 1 B ) - i σ t 1 ( B - r 1 A ) * ] - r 2 e i ϕ [ c t 1 * ( B - r 1 A ) + i σ t 1 ( A - r 1 B ) * ] } , D = 1 t 1 * t 1 t 2 { e i ϕ [ c t 1 * ( B - r 1 A ) + i σ t 1 ( A - r 1 B ) * ] - r 2 e i ϕ [ c t 1 * ( A - r 1 B ) - i σ t 1 ( B - r 1 A ) * ] } .
C = 1 t 1 * t 1 t 2 { e - i ϕ [ - c t 1 * r 1 B - i σ t 1 B * ] - r 2 e i ϕ [ c t 1 * B - i σ t 1 r 1 * B * ] } ,
0 = 1 t 1 * t 1 t 1 { e - i ϕ [ c t 1 * B - i σ t 1 r 1 * B * ] - r 2 e - i ϕ [ - c t 1 * r 1 B - i σ t 1 B * ] } ,
B = B * i σ t 1 ( r 1 * - r 2 e - 2 i ϕ ) c t 1 * ( 1 + r 1 r 2 e - 2 i ϕ ) ,
C = - B c t 2 e - i ϕ ( 1 + r 1 * r 1 ) t 1 ( r 1 * - r 1 e - 2 i ϕ ) .
| σ ( r 1 * - r 2 e - 2 i ϕ ) c ( 1 + r 1 r 2 e - 2 i ϕ ) | = 1.
ρ = - i κ * κ tan κ l ,
ρ = | 1 + r 1 r 2 e - 2 i ϕ r 1 * - r 2 e - 2 i ϕ | .
ρ r = 1.
ρ 2 = 1 + R - 2 R cos 2 ϕ 1 + R + 2 R cos 2 ϕ .
ρ = 1 - R 1 + R T 4 .
A 1 ( 0 ) = r A 1 ( l ) exp ( - i ϕ 1 ) , A 2 ( l ) = r A 2 ( 0 ) exp ( - i ϕ 1 ) ,
1 r exp ( i ϕ ) A 1 ( 0 ) = c A 1 ( 0 ) - i σ A 2 * ( 0 ) , r exp ( - i ϕ ) A 2 ( 0 ) = c A 2 ( 0 ) + i σ A 1 * ( 0 ) ,
r exp ( - 2 i ϕ ) - c ( 1 + r 2 ) exp ( - i ϕ ) + r * = 0.
c = cos κ l = 2 R cos ϕ 1 + R .
ρ 2 = ( 1 - R ) 2 + 4 R sin 2 ϕ 4 R cos 2 ϕ .
ρ 2 = ( 1 - R ) 2 / 4 R .
ρ = T / 2 ,

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