Abstract

We present a theory of the frequency-detuning properties of various oscillators formed by four-wave mixing in photorefractive crystals. It is shown that the detuning originates from the self-induced grating dynamics in the mixing crystal, governed by phase conditions of the optical paths and several other parameters, such as external and internal electric fields in the mixing crystal.

© 1986 Optical Society of America

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  1. W. B. Whitten, J. M. Ramsey, Opt. Lett. 9, 44 (1984).
    [Crossref] [PubMed]
  2. F. J. Jahoda, R. G. Weber, J. Feinberg, Opt. Lett. 9, 362 (1984); J. Feinberg, G. D. Bacher, Opt. Lett. 9, 420 (1984).
    [Crossref] [PubMed]
  3. M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
    [Crossref] [PubMed]
  4. B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
    [Crossref]
  5. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE, J. Quantum Electron. QE-20, 12 (1984).
    [Crossref]
  6. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [Crossref]
  7. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [Crossref] [PubMed]
  8. H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
    [Crossref] [PubMed]
  9. After this Letter was completed and submitted, other relevant work was published, among them a paper by K. R. MacDonald, J. Feinberg [Phys. Rev. Lett. 55, 821 (1985)] with an approach similar to that of Ref.8. Other papers, by A. Yariv, S. K. Kwong [Opt. Lett. 10, 359 (1985); Appl. Phys. Lett. 47, 460 (1985)] and M. D. Ewbank, P. Yeh [Opt. Lett. 10, 496 (1985)], describe mainly oscillators by two-wave mixing.
    [Crossref] [PubMed]
  10. S. Sternklar, S. Weiss, B. Fischer, Appl. Opt. 24, 3121 (1985).
    [Crossref] [PubMed]
  11. V. M. Fridkin, Appl. Phys. 13, 357 (1977).
    [Crossref]
  12. J. Lam, Appl. Phys. Lett. 46, 909 (1985).
    [Crossref]
  13. A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
    [Crossref]
  14. Recent experimental findings confirm the results of the present theory: S. Sternklar, S. Weiss, B. Fischer, Opt. Lett. 11, 165 (1986).
    [Crossref] [PubMed]

1986 (1)

1985 (6)

J. Lam, Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[Crossref] [PubMed]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[Crossref]

H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
[Crossref] [PubMed]

After this Letter was completed and submitted, other relevant work was published, among them a paper by K. R. MacDonald, J. Feinberg [Phys. Rev. Lett. 55, 821 (1985)] with an approach similar to that of Ref.8. Other papers, by A. Yariv, S. K. Kwong [Opt. Lett. 10, 359 (1985); Appl. Phys. Lett. 47, 460 (1985)] and M. D. Ewbank, P. Yeh [Opt. Lett. 10, 496 (1985)], describe mainly oscillators by two-wave mixing.
[Crossref] [PubMed]

S. Sternklar, S. Weiss, B. Fischer, Appl. Opt. 24, 3121 (1985).
[Crossref] [PubMed]

1984 (3)

1982 (1)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

1981 (1)

1977 (1)

V. M. Fridkin, Appl. Phys. 13, 357 (1977).
[Crossref]

1974 (1)

A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
[Crossref]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[Crossref] [PubMed]

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

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

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

Feinberg, J.

After this Letter was completed and submitted, other relevant work was published, among them a paper by K. R. MacDonald, J. Feinberg [Phys. Rev. Lett. 55, 821 (1985)] with an approach similar to that of Ref.8. Other papers, by A. Yariv, S. K. Kwong [Opt. Lett. 10, 359 (1985); Appl. Phys. Lett. 47, 460 (1985)] and M. D. Ewbank, P. Yeh [Opt. Lett. 10, 496 (1985)], describe mainly oscillators by two-wave mixing.
[Crossref] [PubMed]

F. J. Jahoda, R. G. Weber, J. Feinberg, Opt. Lett. 9, 362 (1984); J. Feinberg, G. D. Bacher, Opt. Lett. 9, 420 (1984).
[Crossref] [PubMed]

Fischer, B.

Fridkin, V. M.

V. M. Fridkin, Appl. Phys. 13, 357 (1977).
[Crossref]

Glass, A. M.

A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
[Crossref]

Huignard, J. P.

Jahoda, F. J.

Kwong, S. K.

Lam, J.

J. Lam, Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

MacDonald, K. R.

After this Letter was completed and submitted, other relevant work was published, among them a paper by K. R. MacDonald, J. Feinberg [Phys. Rev. Lett. 55, 821 (1985)] with an approach similar to that of Ref.8. Other papers, by A. Yariv, S. K. Kwong [Opt. Lett. 10, 359 (1985); Appl. Phys. Lett. 47, 460 (1985)] and M. D. Ewbank, P. Yeh [Opt. Lett. 10, 496 (1985)], describe mainly oscillators by two-wave mixing.
[Crossref] [PubMed]

Negran, T. J.

A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
[Crossref]

Rajbenbach, H.

Ramsey, J. M.

Sternklar, S.

Von der Linde, D.

A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
[Crossref]

Weber, R. G.

Weiss, S.

White, J. O.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[Crossref] [PubMed]

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

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

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

Whitten, W. B.

Yariv, A.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[Crossref] [PubMed]

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

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

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

Appl. Opt. (1)

Appl. Phys. (1)

V. M. Fridkin, Appl. Phys. 13, 357 (1977).
[Crossref]

Appl. Phys. Lett. (4)

J. Lam, Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

A different photovoltaic current dependence, J̄ ∝ Iĉ, where I is the light intensity [A. M. Glass, D. Von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974)], gives similar conclusions.
[Crossref]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[Crossref]

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

Opt. Lett. (6)

Phys. Rev. Lett. (1)

After this Letter was completed and submitted, other relevant work was published, among them a paper by K. R. MacDonald, J. Feinberg [Phys. Rev. Lett. 55, 821 (1985)] with an approach similar to that of Ref.8. Other papers, by A. Yariv, S. K. Kwong [Opt. Lett. 10, 359 (1985); Appl. Phys. Lett. 47, 460 (1985)] and M. D. Ewbank, P. Yeh [Opt. Lett. 10, 496 (1985)], describe mainly oscillators by two-wave mixing.
[Crossref] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

The oscillators with photorefractive crystals C and C′ described in this Letter. (a) Semilinear and linear (dashed lines) PPCM’s. (b) Ring PPCM. (c) 2IR PPCM. Usually the two regions C and C′ are in one crystal of which the faces are the mirrors. (d) Unidirectional and double-directional (dashed arrows) ring oscillators.

Equations (20)

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γ ( δ ) = γ 0 / [ 1 + i ( τ δ ) ] ,
R = | sinh [ γ ( δ ) l 2 ] / cosh [ γ ( δ ) l 2 + ln r 2 ] | 2 ,
γ 0 l [ 1 1 + i ( τ δ ) ] + ln r = i q π ,
m 1 = T + Q m 2 [ ( Δ + B ) T + Q ] ,
r 1 = - ( Δ + 1 ) T m 2 [ ( Δ T + Q ) ] ,
m = A 1 ( 0 ) / A 3 ( 0 ) ,             m ˜ = A 4 ( 0 ) / A 2 ( 0 ) .
( T + Q ) ( Δ T + Q ) [ ( Δ + B ) T + Q ] ( Δ + 1 ) T = - M e i ϑ .
( τ δ ) α ϑ ,
T + Q = 0.
A 1 ( l ) / A 4 ( 0 ) = A 3 ( 0 ) / A 2 ( l ) .
γ ( E 0 , δ ) = γ 0 f ( E 0 ) 1 + i ( τ δ ) ,
f ( E 0 ) = a E p ( E 0 + i E d ) E 0 + i ( E d + E p )
( τ δ ) = - E p E 0 E 0 2 + E d ( E d + E p ) - ( E p E d ( E d + E p ) ) E 0 = - β E 0
( τ δ ) α ϑ - β E 0
α = [ M / ( M + 1 ) ] sinh ( γ 0 l ) / ( γ 0 l ) ,             β = E p E d ( E d + E p ) .
τ 1 ( δ 1 + δ 2 ) = α ϑ - β ( E 0 ) 1 ,             τ 2 ( δ 1 - δ 2 ) = - β ( E 0 ) 2 ,
J ¯ p v = v n p c ^ ,
γ = γ 0 f / [ 1 + i ( τ δ ) ] ,
f = a E p ( E 0 + E p v + i E d ) E 0 + i ( E d + E p ) ,
- β E 0 - β E 0 - ( 1 / E d ) E p v .

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