Abstract

We show that a constant component of the holographic current may emerge in photorefractive crystals even in the absence of an applied electric field if the recording pattern is oscillating in a definite law. We derive conditions on the oscillations for the effect to appear. For instance, a fringe pattern with an intensity I ~ 1 + m cos[kx + Δcos ωt + δ cos(2ωt + φ)] is fitted (here x is a linear coordinate, t is time, and m, k, ω, and φ are constants). In this case the dc component is j0 ~ −sin φ. One can detect the relative phases of the harmonics by this means.

© 1993 Optical Society of America

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  1. N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  2. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  3. A. Krumins, P. Günter, Phys. Status Solidi A 63, K111 (1981).
    [CrossRef]
  4. A. Krumins, P. Günter, Appl. Phys. 19, 153 (1979).
    [CrossRef]
  5. G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 30, 534 (1988).
  6. G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 28, 1559 (1986).
  7. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
    [CrossRef]
  8. I. A. Sokolov, S. I. Stepanov, Electron. Lett. 26, 1275 (1990).
    [CrossRef]
  9. V. V. Bryksin, S. N. Dorogovtsev, Pis’ma Zh. Eksp. Teor. Fiz. 57, 439 (1993).

1993

V. V. Bryksin, S. N. Dorogovtsev, Pis’ma Zh. Eksp. Teor. Fiz. 57, 439 (1993).

1990

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

I. A. Sokolov, S. I. Stepanov, Electron. Lett. 26, 1275 (1990).
[CrossRef]

1988

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 30, 534 (1988).

1986

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 28, 1559 (1986).

1981

A. Krumins, P. Günter, Phys. Status Solidi A 63, K111 (1981).
[CrossRef]

1979

A. Krumins, P. Günter, Appl. Phys. 19, 153 (1979).
[CrossRef]

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

1976

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Bryksin, V. V.

V. V. Bryksin, S. N. Dorogovtsev, Pis’ma Zh. Eksp. Teor. Fiz. 57, 439 (1993).

Dorogovtsev, S. N.

V. V. Bryksin, S. N. Dorogovtsev, Pis’ma Zh. Eksp. Teor. Fiz. 57, 439 (1993).

Günter, P.

A. Krumins, P. Günter, Phys. Status Solidi A 63, K111 (1981).
[CrossRef]

A. Krumins, P. Günter, Appl. Phys. 19, 153 (1979).
[CrossRef]

Krumins, A.

A. Krumins, P. Günter, Phys. Status Solidi A 63, K111 (1981).
[CrossRef]

A. Krumins, P. Günter, Appl. Phys. 19, 153 (1979).
[CrossRef]

Kukhtarev, N. V.

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

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Markov, V. B.

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

Odulov, S. G.

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

Petrov, M. P.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Sokolov, I. A.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

I. A. Sokolov, S. I. Stepanov, Electron. Lett. 26, 1275 (1990).
[CrossRef]

Soskin, M. S.

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

Stepanov, S. I.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

I. A. Sokolov, S. I. Stepanov, Electron. Lett. 26, 1275 (1990).
[CrossRef]

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 30, 534 (1988).

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 28, 1559 (1986).

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 30, 534 (1988).

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 28, 1559 (1986).

Vinetskii, V. L.

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

Appl. Phys.

A. Krumins, P. Günter, Appl. Phys. 19, 153 (1979).
[CrossRef]

Electron. Lett.

I. A. Sokolov, S. I. Stepanov, Electron. Lett. 26, 1275 (1990).
[CrossRef]

Ferroelectrics

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

J. Appl. Phys.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Phys. Status Solidi A

A. Krumins, P. Günter, Phys. Status Solidi A 63, K111 (1981).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz.

V. V. Bryksin, S. N. Dorogovtsev, Pis’ma Zh. Eksp. Teor. Fiz. 57, 439 (1993).

Sov. Phys. Solid State

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 30, 534 (1988).

G. S. Trofimov, S. I. Stepanov, Sov. Phys. Solid State 28, 1559 (1986).

Sov. Tech. Phys. Lett.

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

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Figures (1)

Fig. 1
Fig. 1

Dependence of j0 on α = ωτM(1 + k2Ld2) for fringe pattern oscillation by Eq. (13), with τ0τM and ωτ0 ≪ 1.

Equations (16)

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W = W 0 [ 1 + m F ( x , t ) ] , F ( x , t ) = cos ( k x + Δ cos ω t ) ,
ρ t = j e x , n + t = g [ 1 + m F ( x , t ) ] , n t = n τ 0 , E x = 4 π ρ , j e = e μ ( n E + k B T e n x ) , ρ = e ( n + n n ) ,
ω τ 0 N τ = 1 + m F ( ξ , τ ) N ω τ M ( k L d ) 2 2 ξ τ , ω τ M τ + N + N ξ = J ( τ ) ,
0 2 π d ξ ( ξ ) = 0 .
G p , q = 1 ( 2 π ) 2 0 2 π d ξ d τ G ( ξ , τ ) exp [ ( p ξ + q τ ) ] ,
( 1 + i ω τ 0 q ) N p , q = δ p , 0 δ q , 0 + m F p , q + ω τ M ( k L d ) 2 p q p , q , i ω τ M q p , q + p q N p p , q q p , q + i p N p , q = J q δ p , 0 ,
J 0 = N p , q p , q .
N p , q ( 0 ) = δ p , 0 δ q , 0 , p , q = 0 , J q ( 0 ) = 0 .
N p , q ( 1 ) = i p ( 1 + i ω τ M q ) p , q ( 1 ) , p , q ( 1 ) = p F p , q B p , q ,
B p , q = ω τ M ( k L d ) 2 q p 2 i ( 1 + i ω τ 0 q ) ( 1 + i ω τ M q ) .
J 0 = p , q = 1 2 ω τ M m p q ( | F p , q | 2 | F p , q | 2 ) ω 2 q 2 [ τ M ( 1 + k 2 L d 2 p 2 ) 2 + τ 0 ] 2 + ( 1 ω 2 τ 0 τ M q 2 ) 2 .
| F p , q | | F p , q | = | F p , q | .
F ( ξ , τ ) = cos [ ξ + f ( τ ) ] , f = Δ cos τ + δ cos ( 2 τ + φ ) .
j 0 = I sin φ ( 1 + β 2 γ + 5 γ 2 α 2 ) [ ( 1 γ α 2 ) 2 + ( 1 + β ) 2 α 2 ] [ ( 1 4 γ α 2 ) 2 + 4 ( 1 + β ) 2 α 2 ] ,
α = ω τ M ( 1 + k 2 L d 2 ) , β = τ 0 / τ M ( 1 + k 2 L d 2 ) , γ = β / ( 1 + k 2 L d 2 ) , I = 3 E d m 2 Δ 2 δ / 4 π τ M ( 1 + k 2 L d 2 ) .
j 0 = I sin φ α 3 ( 1 + α 2 ) ( 1 + 4 α 2 ) .

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