Abstract

The first Born approximation is applied to calculate the angular selectivity for different positions on the reconstructed image as a function of the object beam’s optical axis angle θob and reference beam angle θrw for a holographic data storage system that records the Fourier transform holograms in a medium with an infinite plane-wave reference beam. Results are compared with those calculated by the coupled-wave theory.

© 2008 Optical Society of America

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References

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  1. C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.
  2. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Gu, C.

C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.

Hong, J.

C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Yeh, P.

C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.

Yi, X.

C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Other (1)

C. Gu, P. Yeh, X. Yi, and J. Hong, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer, 2000), p. 64.

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Figures (6)

Fig. 1
Fig. 1

Holographic data storage system with an object and a reference beam incident to the medium with oblique angles.

Fig. 2
Fig. 2

Sensitivity curves for x 1 = 5 , 0, and 5 mm ; θ o b = 30 ° ; θ r w = 0 ° ; and Δ θ = θ r r θ r w .

Fig. 3
Fig. 3

CCD image for θ r r = 0.028 ° with θ o b = 30 ° and θ r w = 0 ° .

Fig. 4
Fig. 4

First null values obtained from the Born approximation for x 1 = 5 , 0, and 5 mm and θ o b = 30 ° (CCD plane).

Fig. 5
Fig. 5

First null values obtained from the Born approximation for x 1 = 0 mm ; θ o b = 20 ° , 30 ° , and 40 ° ; and compared with the results from coupled-wave theory.

Fig. 6
Fig. 6

First null values obtained from the Born approximation for x 1 = 0 mm , θ o b = 30 ° , and from a coupled-wave theory for θ o b = 30 ° and different Δ n values.

Equations (10)

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U 1 ( x 1 , y 1 ) E r r ( r ) Δ ε ( r ) exp ( i k d r ) d 3 r ,
Δ ε ( r ) E r w * ( r ) S ( r ) ,
S ( r ) = c 1 d x 0 d y 0 U 0 ( x 0 , y 0 ) exp [ i ( λ f ) 1 2 π y 0 y ] × exp [ i ( λ f ) 1 2 π x 0 ( z sin θ o b + x cos θ o b ) ] × exp [ i ( 2 λ f 2 ) 1 2 π ( 2 f 2 x 0 2 y 0 2 ) ( z cos θ o b x sin θ o b ) ] ,
E r w ( r ) = exp [ i λ 1 2 π ( x sin θ r w + z cos θ r w ) ] ,
E r r ( r ) = exp [ i λ 1 2 π ( x sin θ r r + z cos θ r r ) ] ,
exp ( i k d r ) = exp { i λ 1 2 π [ f 1 x 1 cos θ o b ( 2 f 2 ) 1 ( 2 f 2 x 1 2 y 1 2 ) sin θ o b ] x } × exp ( i λ 1 2 π y 1 y ) × exp { i λ 1 2 π [ f 1 x 1 sin θ o b + ( 2 f 2 ) 1 ( 2 f 2 x 1 2 y 1 2 ) cos θ o b ] z } ,
I 1 ( x 1 , y 1 ) U 1 2 ( x 1 , y 1 ) U 0 2 ( x , y 1 ) sinc 2 { λ 1 T [ f 1 ( x + x 1 ) sin θ o b + ( 2 f 2 ) 1 ( x 2 x 1 2 ) cos θ o b + cos θ r w cos θ r r ] } ,
x = [ ( x 1 + f cot θ o b ) 2 + 2 f 2 sin 1 θ o b ( sin θ r w sin θ r r ) ] 1 2 + f cot θ o b .
I 1 ( x 1 , y 1 ) U 0 2 ( x , y 1 ) sinc 2 { λ 1 T Δ θ × [ f cos θ r w ( x 1 + f cot θ o b ) 1 ( 1 f 1 x 1 cot θ o b ) + sin θ r w ] } .
Δ θ null = λ cos θ o b [ T sin ( θ r w + θ o b ) ] 1 ,

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