Abstract

A theory of phase conjugation in asymmetric materials that allow a phase shift between the grating and the light-interference pattern is developed. We find that when this phase is nonzero, maximum phase-conjugate reflectivity occurs for unequal pump intensities. The conditions for self-oscillation are studied.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  2. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
    [CrossRef] [PubMed]
  3. D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
    [CrossRef]
  4. A. Yariv, Opt. Commun. 25, 23 (1978).
    [CrossRef]
  5. J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
    [CrossRef] [PubMed]
  6. J. P. Huignard, J. P. Herriau, G. Rivet, P. Günter, Opt. Lett. 5, 102 (1980).
    [CrossRef] [PubMed]
  7. For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
    [CrossRef]
  8. A. Yariv, IEEE J. Quantum Electron. QE-13, 943 (1977).
    [CrossRef]
  9. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  10. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  11. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  12. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

1980 (3)

1979 (2)

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

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

1978 (3)

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
[CrossRef] [PubMed]

1977 (2)

A. Yariv, IEEE J. Quantum Electron. QE-13, 943 (1977).
[CrossRef]

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

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Bloom, D. M.

Economou, N. P.

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
[CrossRef] [PubMed]

Fekete, D.

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

Günter, P.

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
[CrossRef] [PubMed]

Herriau, J. P.

Huignard, J. P.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kukhtarev, N. V.

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

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Liao, P. F.

Markov, V. B.

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

Odulov, S. G.

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

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Pepper, D. M.

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

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

Rivet, G.

Soskin, M. S.

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

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

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Vinetskii, V. L.

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

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

Yariv, A.

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-13, 943 (1977).
[CrossRef]

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

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Appl. Phys. Lett. (1)

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

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)

A. Yariv, IEEE J. Quantum Electron. QE-13, 943 (1977).
[CrossRef]

J. Appl. Phys. (1)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Opt. Commun. (1)

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

Opt. Lett. (4)

Usp. Fiz. Nauk (1)

For a review, see V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Other (1)

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Scheme of the four beams involved in phase conjugation.

Fig. 2
Fig. 2

Phase-conjugate reflectivity as a function of pump-intensity ratio for ϕ = π/2 and different coupling strengths al.

Fig. 3
Fig. 3

Phase-conjugate reflectivity for coupling strength al = 3.627 and, peaking from left to right, ϕ = 0, π/6, π/3, and π/2. Oscillation here occurs for ϕ = π/6 and r = 6.13.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

E j = A j ( r ) exp [ i ( k j r ω t ) ] + c . c .
n = n 0 + n I e i ϕ I 2 ( A 1 * A 4 + A 2 A 3 * ) I 0 exp ( i k I r ) + c . c . + n II e i ϕ II 2 ( A 1 A 3 * + A 2 * A 4 ) I 0 exp ( i k II r ) + c . c . + n III e i ϕ III 2 ( A 1 A 2 * ) I 0 exp ( i k III r ) + c . c . + n IV e i ϕ IV 2 ( A 3 * A 4 ) I 0 exp ( i k IV r ) + c . c . ,
I 0 = j = 1 4 | A j | 2 ,
n I = r eff n 0 3 E p [ ( E 0 2 + E d 2 ) E 0 2 + ( E d + E p ) 2 ] 1 / 2 ,
tan ϕ I = E d ( E d + E p ) + E 0 2 E 0 E p ,
2 c ω cos α 1 d A 1 d z = i n I e i ϕ I I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 i n II e i ϕ II I 0 ( A 1 A 3 * + A 2 * A 4 ) A 3 i n III e i ϕ III I 0 ( A 1 A 2 * ) A 2 ,
2 c ω cos α 1 d A 2 d z = i n I e i ϕ I I 0 ( A 1 * A 4 + A 2 A 3 * ) A 3 + i n II e i ϕ II I 0 ( A 1 * A 3 + A 2 A 4 * ) A 4 + i n III e i ϕ III I 0 ( A 1 * A 2 ) A 1 ,
2 c ω cos α 2 d A 3 d z = i n I e i ϕ I I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 + i n II e i ϕ II I 0 ( A 1 * A 3 + A 2 A 4 * ) A 1 + i n IV e i ϕ IV I 0 ( A 3 A 4 * ) A 4 ,
2 c ω cos α 2 d A 4 d z = i n I e i ϕ I I 0 ( A 1 * A 4 + A 2 A 3 * ) A 1 i n II e i ϕ II I 0 ( A 1 A 3 * + A 2 * A 4 ) A 2 i n IV e i ϕ IV I 0 ( A 3 * A 4 ) A 3 .
2 c ω cos α 2 d A 3 d z = i n I e i ϕ I I 0 [ | A 2 | 2 A 3 + ( A 1 A 2 ) A 4 * ] ,
2 c ω cos α 2 d A 4 * d z = i n I e i ϕ I I 0 [ | A 1 | 2 A 4 * + ( A 1 A 2 ) * A 3 ] .
A 3 ( z ) = A 4 * ( 0 ) A 1 / A 2 * r 1 e γ l + 1 ( e γ ( z l ) 1 ) ,
A 4 * ( z ) = A 4 * ( 0 ) 1 r 1 e γ l + 1 ( r 1 e γ ( z l ) + 1 ) ,
r = A 2 A 2 * A 1 A 1 * I 2 I 1 ,
γ = i ω n I e i ϕ I 2 c cos α 2 i a e i ϕ ,
R = | A 3 ( 0 ) A 4 * ( 0 ) | 2 = | sinh ( γ l 2 ) cosh ( γ l 2 + ln r 2 ) | 2 ,
T = | A 4 ( l ) A 4 * ( 0 ) | 2 = | e γ l / 2 cosh ( ln r 2 ) cosh ( γ l 2 + ln r 2 ) | 2 ,
R max = | sinh ( i a l 2 e i ϕ ) cos ( a l 2 cos ϕ ) | 2 .
a l cos ϕ = π , r = exp ( a l sin ϕ ) .

Metrics