Abstract

We solve the undepleted-pumps photorefractive four-wave mixing equations for the case of orthogonally polarized pump beams. Advantages over the parallel-polarized-pumps case include the potential for reflectivity enhancement and easy isolation of the conjugator from the source. The phase-conjugate reflectivities for both the parallel and orthogonally polarized pump beam cases were measured with a BaTiO3 crystal, and the results support our theoretical predictions.

© 1988 Optical Society of America

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  1. B. Fischer, J. O. White, M. Cronin-Golomb, A. Yariv, Opt. Lett. 11, 239 (1986).
    [CrossRef] [PubMed]
  2. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  3. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  4. S. I. Stepanov, M. D. Petrov, Opt. Commun. 53, 64 (1985).
    [CrossRef]
  5. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).
  6. M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1983).
  7. G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).
  8. 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]
  9. S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
    [CrossRef]
  10. N. V. Kukhtarev, B. V. Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]

1987 (1)

G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).

1986 (1)

1985 (2)

S. I. Stepanov, M. D. Petrov, Opt. Commun. 53, 64 (1985).
[CrossRef]

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

1984 (1)

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

1981 (1)

1979 (2)

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

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]

1964 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

Cronin-Golomb, M.

B. Fischer, J. O. White, M. Cronin-Golomb, A. Yariv, Opt. Lett. 11, 239 (1986).
[CrossRef] [PubMed]

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

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

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

Fischer, B.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

Kukhtarev, N. V.

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

Markov, B. V.

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

Odulov, S. G.

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]

Papen, G. C.

G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).

Petrov, M. D.

S. I. Stepanov, M. D. Petrov, Opt. Commun. 53, 64 (1985).
[CrossRef]

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

Saleh, B. E. A.

G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).

Soskin, M. S.

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

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

S. I. Stepanov, M. D. Petrov, Opt. Commun. 53, 64 (1985).
[CrossRef]

Tataronis, J. A.

G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).

Vinetskii, V. L.

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

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]

White, J. O.

Yariv, A.

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

Ferroelectrics (1)

N. V. Kukhtarev, B. V. Markov, 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)

G. C. Papen, J. A. Tataronis, B. E. A. Saleh, J. Opt. Soc. Am. A 4 (13), p. 13 (1987).

Opt. Commun. (2)

S. I. Stepanov, M. D. Petrov, Opt. Commun. 53, 64 (1985).
[CrossRef]

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

Opt. Lett. (2)

Usp. Fiz. Nauk (1)

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)

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

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Figures (4)

Fig. 1
Fig. 1

Four-wave mixing geometry. Beams 1 and 2 are pumping beams. Beam 4 is the signal beam, and beam 3 is the phase-conjugate beam.

Fig. 2
Fig. 2

Theoretical plots of log reflectivity R versus log pumping ratio r with ϕb = π/2 and aextl = 3.05. Curve a: m = 1, ϕbϕf = π; curve b: m = 18, ϕb = ϕf; curve c: m = 1, ϕb = ϕf.

Fig. 3
Fig. 3

Experiment arrangement for the measurement of 4WM phase-conjugate reflectivities with parallel and orthogonal pumps. S’s, He–Ne lasers; P’s, polarizers; BS’s, beam splitters; M’s, reflection mirrors; D’s, photodetectors; W, half-wave plate; I1 and I2, pumping beams; I4, signal beam.

Fig. 4
Fig. 4

Experimental data of phase-conjugate reflectivities versus pumping ratio for BaTiO3. Triangles, cross pumps; crosses, parallel pumps. Solid lines are theoretical plots with ϕb = ϕf = π/2 and aextl = 3.05.

Equations (22)

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E j = A j ( r ) e j exp [ i ( k j · r ωt ) ] + c . c . ,
d A 1 d z = γ f I 0 ( A 1 A 4 * e 1 · e 4 + A 2 * A 3 e 2 · e 3 ) A 4 ,
d A 2 * d z = γ b I 0 ( A 1 A 4 * e 1 · e 4 + A 2 * A 3 e 2 · e 3 ) A 3 * ,
d A 3 d z = γ b I 0 ( A 1 A 4 * e 1 · e 4 + A 2 * A 3 e 2 · e 3 ) A 2 ,
d A 4 * d z = γ f I 0 ( A 1 A 4 * e 1 · e 4 + A 2 * A 3 e 2 · e 3 ) A 1 * ,
I 0 = j = 1 4 I j ,
d A 3 d z = a 33 A 3 + a 34 A 4 * ,
d A 4 * d z = a 44 A 4 * + a 43 A 3 ,
A 3 ( z ) = a 34 A 4 * ( 0 ) × exp [ ( z l ) λ 2 ] exp [ ( z l ) λ 1 ] ( a 33 λ 2 ) exp ( λ 2 l ) ( a 33 λ 1 ) exp ( λ 1 l ) ,
A 4 ( z ) * = A 4 * ( 0 ) × ( a 33 λ 2 ) exp [ ( z l ) λ 2 ] ( a 33 λ 1 ) exp [ ( z l ) λ 1 ] ( a 33 λ 2 ) exp ( λ 2 l ) ( a 33 λ 1 ) exp ( λ 1 l ) ,
λ 1 = 1 2 { ( a 33 + a 44 ) + [ ( a 33 a 44 ) 2 + 4 a 43 a 34 ] 2 } ,
λ 2 = 1 2 { ( a 33 + a 44 ) + [ ( a 33 a 44 ) 2 + 4 a 43 a 34 ] 2 } .
R = | A 3 ( 0 ) / A 4 * ( 0 ) | 2 = m [ cosh ( η 1 l ) cos ( η 2 l ) ] cosh [ η 1 l ln ( mr ) ] + cos ( ϕ b ϕ f + η 2 l ) ,
η 1 = ( a b I 2 sin ϕ b + a f I 1 sin ϕ f ) / I 0 ,
η 2 = ( a b I 2 cos ϕ b + a f I 1 cos ϕ f ) / I 0 ,
r = A 2 A 2 * / A 1 A 1 * I 2 / I 1 .
R = cosh ( al sin ϕ ) cos ( al cos ϕ ) cosh ( al sin ϕ ln r ) + cos ( al cos ϕ ) .
R = cosh ( alQ sin ϕ ) cos ( alQ cos ϕ ) cosh ( alQ sin ϕ + ln r ) cos ( alQ cos ϕ ) ( r 1 ) ,
R = 1 cos 2 ϕ + [ sin ϕ 2 / ( al ) ] 2 ( r = 1 ) ,
r + 1 r 1 ln r = al ( r 1 ) ,
al = 2 ( r = 1 ) .
R = m cosh ( a ext lT sin ϕ ) cos ( a ext lT cos ϕ ) cosh [ a ext lT sin ϕ ln ( mr ) ] + cos ( a ext lT cos ϕ ) ,

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