Abstract

We analyze the circumstances under which a real-time hologram written with amplitude-modulated beams behaves as a linear mixer. We calculate nonlinear correction terms that can be used to analyze the linearity of a variety of photorefractive time-integrative devices.

© 1994 Optical Society of America

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References

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  1. A. B. Carlson, Communication Systems, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 201.
  2. M. L. Mead, Lock-in Amplifiers, Principles and Applications (Pergamon, London, 1983).
  3. A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
    [CrossRef]
  4. J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Lett. 16, 1442 (1991).
    [CrossRef] [PubMed]
  5. J. Khoury, V. Ryan, M. Cronin-Golomb, C. L. Woods, J. Opt. Soc. Am. B 10, 72 (1993).
    [CrossRef]
  6. G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
    [CrossRef]
  7. G. H. de Montchenault, J. P. Huignard, J. Appl. Phys. 63, 624 (1988).
    [CrossRef]
  8. F. M. Davidson, L. Boutsikaris, Opt. Eng. 29, 369 (1990).
    [CrossRef]
  9. J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Commun. 85, 5 (1991).
    [CrossRef]
  10. J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).
  11. J. H. Hong, P. Yeh, Opt. Lett. 16, 1343 (1991).
    [CrossRef] [PubMed]
  12. F. Ito, K. I. Kitayama, Opt. Lett. 17, 1152 (1992).
    [CrossRef] [PubMed]
  13. H. Lee, D. Psaltis, Opt. Lett. 12, 456 (1987).
    [CrossRef]
  14. H. Rohleder, P. M. Peterson, A. Marrakchi, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 528.
  15. G. Zhou, D. Z. Anderson, Opt. Lett. 18, 167 (1993).
    [CrossRef] [PubMed]

1993 (2)

1992 (1)

1991 (3)

1990 (1)

F. M. Davidson, L. Boutsikaris, Opt. Eng. 29, 369 (1990).
[CrossRef]

1988 (1)

G. H. de Montchenault, J. P. Huignard, J. Appl. Phys. 63, 624 (1988).
[CrossRef]

1987 (2)

G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
[CrossRef]

H. Lee, D. Psaltis, Opt. Lett. 12, 456 (1987).
[CrossRef]

1980 (1)

A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
[CrossRef]

Anderson, D. Z.

Boutsikaris, L.

F. M. Davidson, L. Boutsikaris, Opt. Eng. 29, 369 (1990).
[CrossRef]

Carlson, A. B.

A. B. Carlson, Communication Systems, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 201.

Cronin-Golomb, M.

Davidson, F. M.

F. M. Davidson, L. Boutsikaris, Opt. Eng. 29, 369 (1990).
[CrossRef]

de Montchenault, G. H.

G. H. de Montchenault, J. P. Huignard, J. Appl. Phys. 63, 624 (1988).
[CrossRef]

G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
[CrossRef]

Hemmer, P.

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

Herriau, J. P.

A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
[CrossRef]

Hong, J. H.

Huignard, J. P.

G. H. de Montchenault, J. P. Huignard, J. Appl. Phys. 63, 624 (1988).
[CrossRef]

G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
[CrossRef]

Ito, F.

Kane, J. S.

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

Khoury, J.

J. Khoury, V. Ryan, M. Cronin-Golomb, C. L. Woods, J. Opt. Soc. Am. B 10, 72 (1993).
[CrossRef]

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Lett. 16, 1442 (1991).
[CrossRef] [PubMed]

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Commun. 85, 5 (1991).
[CrossRef]

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

Kierstead, J.

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

Kitayama, K. I.

Lee, H.

Loiseaux, B.

G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
[CrossRef]

Marrakchi, A.

A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
[CrossRef]

H. Rohleder, P. M. Peterson, A. Marrakchi, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 528.

Mead, M. L.

M. L. Mead, Lock-in Amplifiers, Principles and Applications (Pergamon, London, 1983).

Peterson, P. M.

H. Rohleder, P. M. Peterson, A. Marrakchi, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 528.

Psaltis, D.

Rohleder, H.

H. Rohleder, P. M. Peterson, A. Marrakchi, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 528.

Ryan, V.

Woods, C.

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Commun. 85, 5 (1991).
[CrossRef]

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Lett. 16, 1442 (1991).
[CrossRef] [PubMed]

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

Woods, C. L.

Yeh, P.

Zhou, G.

Appl. Phys. Lett. (1)

G. H. de Montchenault, B. Loiseaux, J. P. Huignard, Appl. Phys. Lett. 50, 1794 (1987).
[CrossRef]

J. Appl. Phys. (1)

G. H. de Montchenault, J. P. Huignard, J. Appl. Phys. 63, 624 (1988).
[CrossRef]

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

Opt. Commun. (2)

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, Opt. Commun. 85, 5 (1991).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, Opt. Commun. 34, 15 (1980).Our Eq. (8) of Ref. 5 can be applied to this device.
[CrossRef]

Opt. Eng. (1)

F. M. Davidson, L. Boutsikaris, Opt. Eng. 29, 369 (1990).
[CrossRef]

Opt. Lett. (5)

Other (4)

A. B. Carlson, Communication Systems, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 201.

M. L. Mead, Lock-in Amplifiers, Principles and Applications (Pergamon, London, 1983).

J. Khoury, J. Kierstead, J. S. Kane, C. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. (to be published).

H. Rohleder, P. M. Peterson, A. Marrakchi, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 528.

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Equations (25)

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E SC t + E SC τ = G τ A 1 ( t ) A 4 * ( t ) I ( t ) ,
E SCL ( t ) = exp ( - t / τ 0 ) G A 1 ( t ) A 4 ( t ) τ 0 I 0 exp ( t / τ 0 ) d t + E SCL ( 0 ) exp ( - t / τ 0 ) .
τ = τ 0 / [ 1 + v ( t ) ] ,
E SCN ( t ) = exp [ - t / τ 0 - Δ ( t ) ] × { G A 1 ( t ) A 4 ( t ) τ I exp [ t / τ 0 + Δ ( t ) ] d t + E SCN ( 0 ) } ,
Δ ( t ) = 0 t v ( t ) / τ 0 d t .
I = I 0 [ 1 + v ( t ) ] .
E SCN = exp [ - Δ ( t ) ] ( E SCL + E Δ ) ,
E Δ ( t ) = exp ( - t / τ 0 ) G A 1 ( t ) A 4 ( t ) τ 0 I 0 × exp ( t / τ 0 ) { exp [ Δ ( t ) ] - 1 } d t .
E SCN ( t ) E SCL - Δ ( t ) E SCL + E Δ 1 ,
E Δ 1 ( t ) = exp ( - t / τ 0 ) G A 1 ( t ) A 4 ( t ) Δ ( t ) τ 0 I 0 exp ( t / τ 0 ) d t .
A 1 ( t ) = A 1 sin ( ω 1 t + ψ 1 ) , A 4 ( t ) = A 4 sin ( ω 4 t + ψ 4 ) .
E SCL = G A 1 A 4 2 I 0 τ 0 cos [ ( ω 1 - ω 4 ) t + ( ψ 1 - ψ 4 ) + α ] [ ( 1 / τ 0 ) 2 + ( ω 1 - ω 4 ) 2 ] 1 / 2 ,
α = tan 1 ( ω 1 - ω 4 ) τ 0 ,
I 0 = A 3 2 + ( 1 / 2 ) A 1 2 + ( 1 / 2 ) A 4 2 ,
v ( t ) = A 1 2 I 0 [ sin 2 ( ω 1 t + ψ 1 ) - 1 / 2 ] + A 4 2 I 0 [ sin 2 ( ω 4 t + ψ 4 - 1 / 2 ) ] .
Δ ( t ) = - 1 4 τ 0 × [ C ω 1 sin ( 2 ω 1 t + 2 ψ 1 ) + D ω 4 sin ( 2 ω 4 t + 2 ψ 4 ) ] ,
C = A 1 2 I 0 ,             D = A 4 2 I 0 ,
E Δ 1 = C / ω 1 + D / ω 4 8 τ 0 G A 1 A 4 2 I 0 τ 0 × sin [ ( ω 1 - ω 4 ) t + ( ψ 1 - ψ 4 ) + α ] [ ( 1 / τ 0 ) 2 + ( ω 1 - ω 4 ) 2 ] 1 / 2 ,
A 1 ( t ) = A 1 exp [ - i β sin ( ω 1 t + ψ 1 ) ] , A 4 ( t ) = A 4 sin ( ω 4 t + ψ 4 ) ,
E SCL = G A 1 A 4 J 1 ( β ) I 0 τ 0 cos [ ( ω 1 - ω 4 ) t + ( ψ 1 - ψ 4 ) + α ] [ ( ω 4 ) - ( ω 1 ) 2 + ( 1 τ ) 2 ] 1 / 2 ,
Δ ( t ) = - D sin ( 2 ω 4 t + 2 ψ 4 ) 4 ω 4 τ 0 ,
E Δ 1 = - B A 1 A 4 4 ω 4 τ 0 G I 0 τ 0 × { J 3 ( β ) sin [ 3 ( ω 4 - ω 1 ) + 3 ( ψ 4 - ψ 1 ) + α 3 ] [ 3 ( ω 4 - ω 1 ) 2 + ( 1 τ 0 ) 2 ] 1 / 2 - J 1 ( β ) sin [ ( ω 4 - ω 1 ) t + ( ψ 4 - ψ 1 ) + α 1 [ ( ω 4 - ω 1 ) 2 + ( 1 τ 0 ) 2 ] 1 / 2 } ,
α 3 = - tan - 1 3 ( ω 4 - ω 1 ) τ 0 ,
α 1 = - tan - 1 ( ω 4 - ω 1 ) τ 0 ,
B = A 4 2 I 0 .

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