Abstract

The problem of cross talk in image-bearing wavelength-multiplexed holograms was raised recently [A. Yariv, in Digest of Conference on Nonlinear Optics (Optical Society of America, Washington, D.C., 1992), postdeadline paper E-2]. In the limit of a large aperture (lens, crystal) it is shown that the cross talk is independent of the information content. The reduction of the hologram volume is shown to introduce interpixel as well as interpage cross talk.

© 1993 Optical Society of America

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References

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  1. G. Rakuljic, A. Yariv, V. Leyva, in Digest of Conference on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1991), paper MD-3.
  2. G. Rakuljic, V. Leyva, A. Yariv, Opt. Lett. 17, 1471 (1992).
    [CrossRef] [PubMed]
  3. V. Leyva, G. Rakuljic, A. Yariv, in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper FU-7.
  4. This material was first presented by the author in Digest of Conference on Nonlinear Optics (Optical Society of America, Washington, D.C., 1992), postdeadline paper E-2.

1992 (1)

Leyva, V.

G. Rakuljic, V. Leyva, A. Yariv, Opt. Lett. 17, 1471 (1992).
[CrossRef] [PubMed]

V. Leyva, G. Rakuljic, A. Yariv, in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper FU-7.

G. Rakuljic, A. Yariv, V. Leyva, in Digest of Conference on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1991), paper MD-3.

Rakuljic, G.

G. Rakuljic, V. Leyva, A. Yariv, Opt. Lett. 17, 1471 (1992).
[CrossRef] [PubMed]

V. Leyva, G. Rakuljic, A. Yariv, in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper FU-7.

G. Rakuljic, A. Yariv, V. Leyva, in Digest of Conference on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1991), paper MD-3.

Yariv, A.

G. Rakuljic, V. Leyva, A. Yariv, Opt. Lett. 17, 1471 (1992).
[CrossRef] [PubMed]

G. Rakuljic, A. Yariv, V. Leyva, in Digest of Conference on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1991), paper MD-3.

V. Leyva, G. Rakuljic, A. Yariv, in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper FU-7.

Opt. Lett. (1)

Other (3)

G. Rakuljic, A. Yariv, V. Leyva, in Digest of Conference on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1991), paper MD-3.

V. Leyva, G. Rakuljic, A. Yariv, in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper FU-7.

This material was first presented by the author in Digest of Conference on Nonlinear Optics (Optical Society of America, Washington, D.C., 1992), postdeadline paper E-2.

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Figures (2)

Fig. 1
Fig. 1

Geometry used to record a single page () at λ. The depth of focus of the lens is much larger than the crystal length.

Fig. 2
Fig. 2

Plot in one dimension of the spatial frequency (k) dependence of the three field amplitudes of the recorded (and reconstructed) pages (, + 1, and s) in the focal plane in the limit of negligible transverse aperturing (i.e., large lens, large crystal cross-sectional area).

Equations (18)

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E ( s ) = m = 1 N 2 - A m ( s ) ( k ) exp [ - i k · r - i k z ( s ) z ] d 2 k , k z ( s ) = k s 2 - ( k ) 2 ,             k s = ω s c n s ,
A m ( s ) ( k ) = A mo ( s ) Π ( - k x - m x S k s f δ k s / f ) × ( - k y - m y S k s f δ k s / f ) ,
( x ) = { 1 x 1 / 2 0 otherwise .
Δ n ( r ) = s = 1 h m = 1 N 2 E R * ( s ) κ A m ( s ) ( k ) × exp { - i k · r - i [ k z ( s ) + k s ] z } d 2 k + c . c . ,
E d ( ) = t a t ( ) ( k ) exp [ - i k · r - i k z ( ) z ] d 2 k ,
a t ( k ) = const . A t ( ) ( k )
2 E + ω 2 μ 0 [ n 2 + n Δ n ( r ) ] E = 0 ,
E = E read exp ( i k z ) + t a t ( ) ( k ) exp [ - i k · r - i k z ( ) z ] d 2 k .
2 i t k t z ( ) [ d d z a t ( ) ( k ) ] exp [ - i k · r - i k z ( ) z ] d 2 k = s h m β A m ( s ) ( k ) × exp { - i [ ( k z ( s ) + k s - k ) z + k · r ] } d 2 k , k z ( s ) = k s 2 - k 2 ,
t 2 i k t z ( ) d d z a t ( ) ( k ) exp ( - i k 2 - k 2 z ) = s m β A m ( s ) ( k ) exp [ - i ( k s 2 - k 2 - k + k s ) z ] ,
- exp [ i ( k - k ) · r ] d 2 r = 4 π 2 δ ( k x - k x ) δ ( k y - k y ) .
t 2 i k t z ( ) d d z a t ( ) ( k ) exp ( - i k 2 - k 2 z ) = s β A u ( s ) ( k ) exp [ - i ( k s 2 - k 2 - k + k s ) z ] .
2 i k u z ( ) d d z a u ( ) ( k ) = β A u ( ) ( k ) ,
a u ( ) ( k ) = g A u ( ) ( k ) z             ( g is a constant ) .
2 i k u z ( ) d d z a u ( ) ( k ) = β { A u ( ) ( k ) + s exp [ - i 2 ( k s - k ) ( 1 + k 2 4 k k s ) z ] A u ( s ) ( k ) } ,
a u ( ) [ k ] = g A u ( ) ( k ) z + s h g z sin ( k s - k ) ( 1 + k 2 4 k k s ) z ( k s - k ) z A u ( s ) ( k ) ,
A m ( s ) ( k ) = A mo ( s ) ( 2 π δ D λ f ) 2 sinc [ ( - k y - m y S k s f ) D 2 ] × sinc [ ( - k x - m x S k s f ) D 2 ] .
a u ( ) ( k ) ( 2 π δ D λ f ) 2 g z A u ( ) ( k ) + m u ( 2 π δ D λ f ) 2 g z A mo ( ) × sinc [ ( - k x - m x S k s f ) D 2 ] sinc [ ( - k y - m y S k s f ) D 2 ] + s m ( 2 π δ D λ f ) 2 g z A mo ( s ) sinc [ ( - k x - m x S k s f ) D 2 ] × sinc [ ( - k y - m y S k s f ) D 2 ] × sinc [ ( k x - k ) ( 1 + k 2 4 k k s ) z ] ,

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