Abstract

The photorefractive transmission grating ring self-pumped phase-conjugate mirror is shown to be formally equivalent to a double phase-conjugate mirror with internal losses and equal-intensity input beams. These mirrors are also equivalent to a self-pumped phase conjugator consisting of a photorefractive crystal with one face highly reflecting. This result shows that all transmission grating self-pumped phase-conjugate mirrors, with the exception of the linear self-pumped phase conjugator, are topologically equivalent to a double phase-conjugate mirror. No similar equivalence can be shown for the reflection grating ring phase conjugator.

© 1990 Optical Society of America

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References

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  1. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. 20, 12 (1984).
    [CrossRef]
  2. S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987).
    [CrossRef] [PubMed]
  3. M. D. Ewbank, Opt. Lett. 13, 47 (1988).
    [CrossRef] [PubMed]
  4. A. M. C. Smout, R. W. Eason, Opt. Lett. 12, 498 (1987).
    [CrossRef] [PubMed]
  5. A. A. Zozulya, V. P. Silin, V. T. Tikhonchuk, Sov. Phys. JETP 65, 443 (1987).
  6. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  7. A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP Lett. 49, 553 (1989).
  8. R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
    [CrossRef]

1989 (2)

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP Lett. 49, 553 (1989).

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

1988 (1)

1987 (3)

1984 (1)

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

1982 (1)

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Cronin-Golomb, M.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

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

Eason, R. W.

Ewbank, M. D.

Feinberg, J.

Fischer, B.

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987).
[CrossRef] [PubMed]

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

Glass, A. M.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP Lett. 49, 553 (1989).

Olson, D. H.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Silin, V. P.

A. A. Zozulya, V. P. Silin, V. T. Tikhonchuk, Sov. Phys. JETP 65, 443 (1987).

Smout, A. M. C.

Sternklar, S.

Tikhonchuk, V. T.

A. A. Zozulya, V. P. Silin, V. T. Tikhonchuk, Sov. Phys. JETP 65, 443 (1987).

Weiss, S.

White, J. O.

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

Yariv, A.

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

Zozulya, A. A.

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP Lett. 49, 553 (1989).

A. A. Zozulya, V. P. Silin, V. T. Tikhonchuk, Sov. Phys. JETP 65, 443 (1987).

Appl. Phys. Lett. (1)

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Opt. Lett. (4)

Sov. Phys. JETP (1)

A. A. Zozulya, V. P. Silin, V. T. Tikhonchuk, Sov. Phys. JETP 65, 443 (1987).

Sov. Phys. JETP Lett. (1)

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP Lett. 49, 553 (1989).

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Figures (5)

Fig. 1
Fig. 1

Topological manipulations to demonstrate equivalence of the interconnected ring mirror to the DPCM. (a) Interconnected ring mirror, (b) topological equivalent, (c) interaction regions rotated by π/2, (d) left-hand interaction region and beams rotated by π about the horizontal axis, (e) left-hand interaction region rotated by π about the vertical axis, (f) interaction regions placed together to form a DPCM.

Fig. 2
Fig. 2

(a) Bird-wing self-pumped phase conjugator, (b) mutually incoherent beam coupler.

Fig. 3
Fig. 3

(a) Ring self-pumped phase conjugator, (b) the cat mirror.

Fig. 4
Fig. 4

Topological manipulations to demonstrate validity of transformation of Fig. 1(e). (a) Original interaction region and beams with c axis as shown, (b) the entire system rotated by π about the vertical axis, (c) the beams and z relabeled have the same coupled-wave equations as the original system.

Fig. 5
Fig. 5

Low-threshold self-pumped phase conjugator single crystal with mirrored face. The curved lines indicate the directions in which the amplified scattering (fanning) travels to seed the conjugator.

Equations (2)

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d A 1 d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 , d A 2 * d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 3 * , d A 3 d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 , d A 4 * d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 1 * ,
γ l = log ( 2 + 1 / M ) ,

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