Abstract

It is predicted that when a dc electric field is present or when a probe beam contains temporal frequencies different from that of the pump waves a beam reflected from a photorefractive phase-conjugate mirror will experience lateral and focal shifts. These shifts are a consequence of angular dependence of the phase of the reflectivity and are similar to the Goos–Hänchen effect. The phenomenon becomes more pronounced near resonance.

© 1989 Optical Society of America

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References

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  1. J. P. Huignard, J. P. Herriau, G. Rivet, Opt. Lett. 5, 102 (1980).
    [CrossRef] [PubMed]
  2. J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
    [CrossRef] [PubMed]
  3. T. Wilson, D. K. Saldin, L. Solymar, Opt. Quantum Electron. 13, 411 (1981).
    [CrossRef]
  4. For a review see A. Puri, J. L. Birman, J. Opt. Soc. Am. A 3, 543 (1986).
    [CrossRef]
  5. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  6. K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
    [CrossRef] [PubMed]
  7. B. Fischer, Opt. Lett. 11, 236 (1986).
    [CrossRef] [PubMed]
  8. G. C. Valley, J. Opt. Soc. Am. B 4, 14 (1986).
    [CrossRef]

1986 (3)

1985 (1)

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

1981 (2)

T. Wilson, D. K. Saldin, L. Solymar, Opt. Quantum Electron. 13, 411 (1981).
[CrossRef]

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

1980 (2)

Birman, J. L.

Cronin-Golomb, M.

Feinberg, J.

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

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

Fischer, B.

Hellwarth, R. W.

Herriau, J. P.

Huignard, J. P.

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Puri, A.

Rivet, G.

Saldin, D. K.

T. Wilson, D. K. Saldin, L. Solymar, Opt. Quantum Electron. 13, 411 (1981).
[CrossRef]

Solymar, L.

T. Wilson, D. K. Saldin, L. Solymar, Opt. Quantum Electron. 13, 411 (1981).
[CrossRef]

Valley, G. C.

White, J. O.

Wilson, T.

T. Wilson, D. K. Saldin, L. Solymar, Opt. Quantum Electron. 13, 411 (1981).
[CrossRef]

Yariv, A.

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Figures (4)

Fig. 1
Fig. 1

Geometry of the problem. A probe beam of angular extent Δα is incident upon a phase-conjugate mirror. The central ray of the beam forms an angle αc with respect to the c axis. The pump beam forms an angle β.

Fig. 2
Fig. 2

Calculated lateral shift of a phase-conjugate beam in BaTiO3 versus the detuning frequency, Ω/2π, between the probe and the pump beams. There is no applied field, the total intensity is 1 W/cm2, r = eπ, and the central grating wave vector is oriented along the c axis. The solid curve is for an angle of 2.55° between the central probe ray and the pump beam and an interaction length l (at αc) of 1 cm. The dotted curve is for an angle of 5.1° and l = 5 mm. For both geometries ∣γl ≈ 3 at αc. The other parameters (from Ref. 8) are ordinary refractive index of 2.505; extraordinary refractive index of 2.434; electro-optic coefficients r13 = 24 pm/V, r33 = 80 pm/V, r42 = 1640 pm/V; dielectric constants 11 = 3700, 33 = 150; total trap density of 4 × 1018 cm−3; acceptor trap density of 6 × 1016 cm−3; absorption coefficient of 2 cm−1; mobility anisotropy μ33/μ11 = 0.1; and mobility lifetime product μ33τR = 10−10 cm2/V.

Fig. 3
Fig. 3

Calculated focal shift of a phase-conjugate beam versus the detuning frequency with the same conditions as in Fig. 2.

Fig. 4
Fig. 4

Calculated lateral shift of a phase-conjugate beam versus the detuning frequency with the conditions as in Fig. 2, except that only the anisotropic effects (electro-optic coefficient, static permittivity, and mobility) and the angular dependence of the effective interaction length are included. The grating wave number is fixed to the value at αc. The weak dependence on the antisotropic effects and interaction length imply that the nonlocal response is the dominant contribution to the lateral shift.

Equations (10)

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ρ = 2 r ( r 1 ) + ( r + 1 ) coth ( γ l / 2 ) ,
γ ( Ω ) = γ 0 1 + i Ω τ ,
ϕ ( α c + Δ α ) = ϕ ( α c ) + Δ α ϕ α | α = α c + 1 2 Δ α 2 2 ϕ α 2 | α = α c + .
ϕ ( Δ α ) ϕ 0 + a k x + b k x 2 2 k ,
a = 1 k ϕ α | α = α c , b = 1 k 2 ϕ α 2 | α = α c ,
ρ = | ρ | exp [ i ( ϕ 0 + a k x + b k x 2 2 k ) ] .
A p * ( x , z = 0 ) = a ˜ p ( k x ) exp [ i ( k x x ) ] d k x 2 π ,
A c ( x , z = 0 ) = ρ 0 a ˜ p ( k x ) × exp { i [ k x ( a + x ) + b k x 2 2 k ] } d k x 2 π ,
A c ( x , z = 0 ) = ρ 0 exp ( ibk ) a ˜ p ( k x ) × exp { i [ k x ( a + x ) b k z ] } d k x 2 π .
A c ( x , z = 0 ) = ρ 0 exp ( ibk ) A p * ( x + a , b ) .

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