Abstract

Most photorefractive crystals that are suitable for self-pumped four-wave-mixing phase-conjugation and mutual-conjugation geometries are characterized by significant levels of fanning. In some cases this may mean that the nonlinearity in these crystals is already too large to be good, and a decrease in the value of the nonlinear coupling coefficient may result in an improvement in the performance of these geometries. We illustrate this point, using the geometry of a self-pumped ring mirror as an example.

© 1993 Optical Society of America

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References

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  1. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  2. B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
    [CrossRef]
  3. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
    [CrossRef]
  4. S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
    [CrossRef]
  5. N. V. Bogodaev, V. V. Eliseev, L. I. Ivleva, A. S. Korshunov, S. S. Orlov, N. M. Polozkov, and A. A. Zozulya, “Double phase-conjugate mirror: experimental investigation and comparison with theory,” J. Opt. Soc. Am. B 9, 1493–1498 (1992).
    [CrossRef]
  6. A. A. Zozulya and A. V. Mamaev, “Theoretical and experimental investigation of a photorefractive semilinear mirror,” Kvantovaya Elektron. (Moscow) 17, 1335 (1990).
  7. V. T. Tikhonchuk, M. G. Zhanuzakov, and A. A. Zozulya, “Stationary states of two coupled double phase-conjugate mirrors,” Opt. Lett. 16, 288 (1991).
    [CrossRef] [PubMed]
  8. J. Feinberg, “Self-pumped continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  9. S. W. James and R. W. Eason, “Extraordinary polarized light does not always yield the highest reflectivity from self-pumped BaTiO3,” in Photorefractive Materials, Effects and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 416–419.

1992 (1)

1991 (1)

1990 (1)

A. A. Zozulya and A. V. Mamaev, “Theoretical and experimental investigation of a photorefractive semilinear mirror,” Kvantovaya Elektron. (Moscow) 17, 1335 (1990).

1989 (1)

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
[CrossRef]

1984 (2)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

1983 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

1982 (1)

Bogodaev, N. V.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

Eason, R. W.

S. W. James and R. W. Eason, “Extraordinary polarized light does not always yield the highest reflectivity from self-pumped BaTiO3,” in Photorefractive Materials, Effects and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 416–419.

Eliseev, V. V.

Feinberg, J.

Fischer, B.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Ivleva, L. I.

James, S. W.

S. W. James and R. W. Eason, “Extraordinary polarized light does not always yield the highest reflectivity from self-pumped BaTiO3,” in Photorefractive Materials, Effects and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 416–419.

Korshunov, A. S.

Kwong, S. K.

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya and A. V. Mamaev, “Theoretical and experimental investigation of a photorefractive semilinear mirror,” Kvantovaya Elektron. (Moscow) 17, 1335 (1990).

Orlov, S. S.

Polozkov, N. M.

Sternklar, S.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
[CrossRef]

Tikhonchuk, V. T.

Weiss, S.

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

Zhanuzakov, M. G.

Zozulya, A. A.

Appl. Phys. Lett. (2)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “A passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumped phase conjugate mirror,” Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

B. Fischer, S. Sternklar, and S. Weiss, “Photorefractive oscillators,” IEEE J. Quantum Electron. 25, 550 (1989).
[CrossRef]

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

Kvantovaya Elektron. (Moscow) (1)

A. A. Zozulya and A. V. Mamaev, “Theoretical and experimental investigation of a photorefractive semilinear mirror,” Kvantovaya Elektron. (Moscow) 17, 1335 (1990).

Opt. Lett. (2)

Other (1)

S. W. James and R. W. Eason, “Extraordinary polarized light does not always yield the highest reflectivity from self-pumped BaTiO3,” in Photorefractive Materials, Effects and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 416–419.

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Figures (5)

Fig. 1
Fig. 1

Geometry of a parametric ring oscillator: Aj and Bj (j = 1–4) are the amplitudes of two mutually uncorrelated sets of beams; beams Aj represent the conjugate configuration, whereas beams Bj are fanning beams; M’s, mirrors.

Fig. 2
Fig. 2

Theoretical dependence of the stationary nonlinear reflectivity R of a parametric ring oscillator on the value of nonlinear coupling coefficient γl. For both figures γ = 6.6 cm−1, α = 0.76 cm−1, T = 0.4, and f = 6 × 10−3. (a) = 10−7, (b) = 10−5.

Fig. 3
Fig. 3

Experimental dependence of nonlinear reflectivity of a ring oscillator R = Pc/Pin on the power of an erase beam Per.

Fig. 4
Fig. 4

Experimental dependence of nonlinear reflectivity of a ring oscillator R = Pc/Pin on the input pumping beam polarization angle ϕ.

Fig. 5
Fig. 5

Theoretical dependence of nonlinear reflectivity of a ring oscillator R on the input pumping beam polarization angle ϕ. The parameters are γl = 3.85, αl = 0.46, T = 0.4, = 10−5, and f = 6 × 10−3.

Equations (13)

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( / x ) A 1 = - ( α / 2 ) A 1 + ν A 4 + ν f 2 B 4 , ( / x ) A 2 * = ( α / 2 ) A 2 * + ν A 3 * + ν f 2 B 3 * , ( / x ) A 3 = ( α / 2 ) A 3 - ν A 2 - ν f 4 B 2 , ( / x ) A 4 * = - ( α / 2 ) A 4 * - ν A 1 * - ν f 4 B 1 * , ( / x ) B 1 = - ( α / 2 ) B 1 + ν s B 4 + ν f 4 A 4 , ( / x ) B 2 * = ( α / 2 ) B 2 * + ν s B 3 * + ν f 4 A 3 * , ( / x ) B 3 = ( α / 2 ) B 3 - ν s B 2 - ν f 2 A 2 , ( / x ) B 4 * = - ( α / 2 ) B 4 * - ν s B 1 * - ν f 2 A 1 * .
( τ / t + 1 ) ν = ( γ / I T ) A 1 A 4 * + A 2 * A 3 ) , ( τ / t + 1 ) ν s = γ s / I T ) ( B 1 B 4 * + B 2 * B 3 ) , ( τ / t + 1 ) ν f 2 = ( γ f 2 / I T ) ( A 1 B 4 * + A 2 * B 3 ) , ( τ / t + 1 ) ν f 4 = ( γ f 4 / I T ) ( B 1 A 4 * + B 2 * A 3 ) .
I T = j = 1 4 ( A j 2 + B j 2 )
ν ( x , t = 0 ) = ν s ( x , t = 0 ) = ν f 2 ( x , t = 0 ) = ν f 4 ( x , t = 0 ) = 0 ,
A 2 ( x = l , t ) = A 2 ( 0 ) ,             B 2 ( x = l , t ) = 0 ,
A 3 ( x = l , t ) = A 2 ( x = l , t ) ,             B 3 ( x = l , t ) = f A 2 ( x = l , t ) ,
A 1 ( x = 0 , t ) = T A 3 ( x = 0 , t ) ,             A 4 ( x = 0 , t ) = T A 2 ( x = 0 , t ) ,
B 1 ( x = 0 , t ) = T B 3 ( x = 0 , t ) ,             B 4 ( x = 0 , t ) = T B 2 ( x = 0 , t ) .
B 1 ( x = 0 , t ) = f A 4 ( x = 0 , t ) ,             B 4 ( x = 0 , t ) = 0.
T f A 2 ( x = 0 , t = ) / A 2 ( x = 0 , t = 0 ) 2
R = T exp ( - 2 α l ) .
I T = j = 1 4 ( A j 2 + B j 2 ) + I er ,
I er ( x ) = A 2 ( 0 ) 2 ( sin 2 ϕ ) × { exp [ - α ( l - x ) ] + T exp ( - α l - α x ) } .

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