Abstract

One of the difficulties encountered during the many years of research on holographic information storage was the lack of an easy theoretical way to assess proposed paradigms. I exploit the fact that for bit-oriented holographic storage, Gaussian beams are usually involved. For this case I show that the reconstructed wave can be represented as a superposition of simple Gaussian beams, regardless of the exact recording condition, and a virtual source for this wave can be determined. This theoretical result is used to explore several holographic storage architectures, in particular thick volume holograms and layered volume holograms. Simulation results demonstrate the power of the method, show good correspondence with earlier experimental studies, and provide clues for further developments.

© 2006 Optical Society of America

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References

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  1. R. R. McLeod, A. J. Daiber, M. E. McDonald, T. L. Robertson, T. Slagle, S. L. Sochava, and L. Hesselink, "Microholographic multilayer optical disk data storage," Appl. Opt. 44, 3197-3207 (2005).
    [CrossRef] [PubMed]
  2. G. Maire, G. Pauliat, and G. Roosen, "The holographi Lippmann disk: data storage performance modeling," presented at the International Conference on Holography, Optical Recording, and Processing of Information, Varna, Bulgaria, 21-25 May 2005.
  3. L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, 1981).
  4. R. R. A. Syms, Practical Volume Holography (Clarendon, 1990).
  5. J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).
  6. J. Shamir and K. Wagner, "Generalized Bragg effect in volume holography," Appl. Opt. 41, 6773-6785 (2002).
    [CrossRef] [PubMed]
  7. J. Shamir, "Holograms of volumes and volume holograms," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed., Vol. PM124 of SPIE Press Monographs (SPIE Press, 2004), Chap. 14, pp. 239-260.
  8. J. Shamir, "Analysis of volume holographic storage allowing large-angle illumination," J. Opt. Soc. Am. B 22, 975-986 (2005).
    [CrossRef]
  9. J. Shamir, "Volume holographic recording of narrow-band information," in Holography 2005, Y.Denisyuk, V.Sainov, and E.Stoykova, eds., Proc. SPIE 6252,244-254 (2005).
  10. J. Shamir, "Volume holographic information storage and beam structuring," Asian J. Phys. (to be published).
  11. M. Nazarathy and J. Shamir, "First-order optics--a canonical operator representation: lossless systems," J. Opt. Soc. Am. 72, 356-364 (1982).
    [CrossRef]
  12. J. Shamir, Optical Systems and Processes (SPIE Press, 1999).
    [CrossRef]

2005 (2)

2002 (1)

1982 (1)

Cook, D. J.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, 1981).

Daiber, A. J.

Hesselink, L.

Maire, G.

G. Maire, G. Pauliat, and G. Roosen, "The holographi Lippmann disk: data storage performance modeling," presented at the International Conference on Holography, Optical Recording, and Processing of Information, Varna, Bulgaria, 21-25 May 2005.

McDonald, M. E.

McLeod, R. R.

Nazarathy, M.

Pauliat, G.

G. Maire, G. Pauliat, and G. Roosen, "The holographi Lippmann disk: data storage performance modeling," presented at the International Conference on Holography, Optical Recording, and Processing of Information, Varna, Bulgaria, 21-25 May 2005.

Robertson, T. L.

Roosen, G.

G. Maire, G. Pauliat, and G. Roosen, "The holographi Lippmann disk: data storage performance modeling," presented at the International Conference on Holography, Optical Recording, and Processing of Information, Varna, Bulgaria, 21-25 May 2005.

Shamir, J.

J. Shamir, "Analysis of volume holographic storage allowing large-angle illumination," J. Opt. Soc. Am. B 22, 975-986 (2005).
[CrossRef]

J. Shamir and K. Wagner, "Generalized Bragg effect in volume holography," Appl. Opt. 41, 6773-6785 (2002).
[CrossRef] [PubMed]

M. Nazarathy and J. Shamir, "First-order optics--a canonical operator representation: lossless systems," J. Opt. Soc. Am. 72, 356-364 (1982).
[CrossRef]

J. Shamir, Optical Systems and Processes (SPIE Press, 1999).
[CrossRef]

J. Shamir, "Volume holographic recording of narrow-band information," in Holography 2005, Y.Denisyuk, V.Sainov, and E.Stoykova, eds., Proc. SPIE 6252,244-254 (2005).

J. Shamir, "Volume holographic information storage and beam structuring," Asian J. Phys. (to be published).

J. Shamir, "Holograms of volumes and volume holograms," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed., Vol. PM124 of SPIE Press Monographs (SPIE Press, 2004), Chap. 14, pp. 239-260.

J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).

Slagle, T.

Sochava, S. L.

Solymar, L.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, 1981).

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography (Clarendon, 1990).

Wagner, K.

J. Shamir and K. Wagner, "Generalized Bragg effect in volume holography," Appl. Opt. 41, 6773-6785 (2002).
[CrossRef] [PubMed]

J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).

Appl. Opt. (2)

Asian J. Phys. (1)

J. Shamir, "Volume holographic information storage and beam structuring," Asian J. Phys. (to be published).

J. Opt. Soc. Am. (1)

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

Other (7)

J. Shamir, "Volume holographic recording of narrow-band information," in Holography 2005, Y.Denisyuk, V.Sainov, and E.Stoykova, eds., Proc. SPIE 6252,244-254 (2005).

J. Shamir, "Holograms of volumes and volume holograms," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed., Vol. PM124 of SPIE Press Monographs (SPIE Press, 2004), Chap. 14, pp. 239-260.

G. Maire, G. Pauliat, and G. Roosen, "The holographi Lippmann disk: data storage performance modeling," presented at the International Conference on Holography, Optical Recording, and Processing of Information, Varna, Bulgaria, 21-25 May 2005.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, 1981).

R. R. A. Syms, Practical Volume Holography (Clarendon, 1990).

J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).

J. Shamir, Optical Systems and Processes (SPIE Press, 1999).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Recording in a plane-parallel slab of thickness d. The recording waves are u 1 and u 2 and the reconstruction is implemented by illumination with wave u r . The reconstructed wave is represented by u 3.

Fig. 2
Fig. 2

Intensity distribution over the surface of the RM (x, y plane) for the reconstructed field of a confocal hologram recorded in a 10 μm RM. Marked spatial coordinates are in micrometers while the intensities are in arbitrary units that are different for (a) the linear recording and (b) the quadratic recording.

Fig. 3
Fig. 3

Intensity distributions of the propagating waves (x, z plane) corresponding to those of Fig. 2. In (a) and (b) the beam waists are at z = 0, while in (c) and (d) they are at z = 5 μm.

Fig. 4
Fig. 4

Intensity distributions in the virtual source region of the propagating waves corresponding to those of Fig. 3 with beam waists at z = 0 but with the reconstruction beam shifted by (a) and (b) 0.3 μm and (c) and (d) 0.5 μm.

Fig. 5
Fig. 5

As in Figs. 2–4 but with the reconstructing beam waist at z = 5 μm.

Fig. 6
Fig. 6

As in Figs. 2–4 but with the recording waists at z = 60 μm in a d = 125 μm thick RM. (a) and (b) Reconstruction with the correct reconstruction beam (z r = 60; s = 0); (c) and (d) 1 μm lateral shift (z r = 60; s = 0.3 μm); (e) and (f) 5 μm focal shift (z r = 65; s = 0).

Fig. 7
Fig. 7

Same parameters as in Fig. 6 but (a) and (b) with a wavelength shift of 5%. Intensity cross section over the exit (x, y) plane (z = 125 μm) with reconstruction at (c) and (d) the original wavelength and (e) and (f) with a wavelength shift of 1%.

Equations (41)

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I ( z ) = | u 1 ( z ) + u 2 ( z ) | 2 = | u 1 ( z ) | 2 + | u 2 ( z ) | 2 + u 1 ( z ) u 2 * ( z ) + u 1 * ( z ) u 2 ( z ) .
T l ( z ) I ( z ) ; T q u ( z ) I 2 ( z ) .
d u l ( z ) = u r ( z ) u 1 * ( z ) u 2 ( z ) d z ,
I 2 ( z ) = [ | u 1 ( z ) | 2 + | u 2 ( z ) | 2 ] 2 + [ u 1 ( z ) u 2 * ( z ) + u 1 * ( z ) u 2 ( z ) ] 2 + 2 [ | u 1 ( z ) | 2 + | u 2 ( z ) | 2 ] × [ u 1 ( z ) u 2 * ( z ) + u 1 * ( z ) u 2 ( z ) ] ,
d u q ( z ) = u r ( z ) [ | u 1 ( z ) | 2 + | u 2 ( z ) | 2 ] u 1 * ( z ) u 2 ( z ) d z ,
u ( x , y , z ) = 1 O ν u ( x , y , 0 ) ˜ [ z ] u ( x , y , 0 ) .
˜ [ z ] = 1 O ν
O ν exp [ j k z 1 λ 2 ( ν x     2 + ν y     2 ) ] .
x ^ ν x + y ^ ν y ν x y
2 π ν x y = k x y .
k z = 2 π ν z = ± k 2 k x 2 k y 2 = ± k 1 λ 2 ( ν x 2 + ν y 2 ) ,
λ 2 ( ν z 2 + ν x 2 + ν y 2 ) = 1 λ ν z = 1 λ 2 ν x y 2 ; λ 2 ν x y 2 1
u 3 ( L ) = 0 d ˜ r [ L z ] d u l ( z ) + α 0 d ˜ r [ L z ] d u q ( z ) + .
u ( x , y , z ) = Ψ ( z ) Q [ 1 q ( z ) ] ,
Q [ a ] exp [ j k a 2 ( x 2 + y 2 ) ] ,
1 q ( z ) 1 R ( z ) + j λ π w 2 ( z ) .
˜ [ z ] [ z ] = exp ( j k z ) 1 Q [ λ 2 z ] exp ( j k z ) ¯ [ z ] .
¯ [ b ] Q [ 1 q ] = q b + q Q [ 1 b + q ] .
u ( x , y , z ) = q 0 q ( z ) exp [ j k ( z z 0 ) ] Q [ 1 q ( z ) ] ,
q 0 = π w 0     2 j λ ; q ( z ) = q 0 + z z 0 .
d u g , l ( z ) = exp [ j k r ( z z r , 0 ) ] q r , 0 q r ( z ) Q [ 1 q r ( z ) ] ×   exp [ j k ( z z 1 , 0 ) ] q 1 , 0 q 1 * ( z ) Q [ 1 q 1 * ( z ) ] ×   exp [ j k ( z z 2 , 0 ) ] q 2 , 0 q 2 ( z ) Q [ 1 q 2 ( z ) ] d z ,
q r ( z ) = q r , 0 z + z r , 0 , q 1 ( z ) = q 1 , 0 z + z 1 , 0 ,
q 2 ( z ) = q 2 , 0 + z z 2 , 0 .
d u g , l ( x , y , z ) = exp [ j ( 2 k k r ) z ] A Q r [ 1 q ] d z ,
1 q = 1 q r ( z ) + k k r q 1 * ( z ) + k k r q 2 ( z ) ,
A = q r , 0 q r ( z ) × q 1 , 0 q 1 * ( z ) × q 2 , 0 q 2 ( z ) .
u g , l ( x , y , L ) = 0 d exp [ j k r ( L z ) ] ¯ r [ L z ] × exp [ j ( 2 k k r ) z ] A Q r [ 1 q ] d z ,
u g , l ( x , y , L ) = exp ( j k r L ) 0 d exp [ j 2 ( k k r ) z ] × A Q r [ 1 q + L z ] d z ,
A = A q q + L z .
| u i | 2 = u i u i * = | q i , 0 q i ( z ) | 2 Q [ 1 q i ( z ) ] Q [ 1 q i * ( z ) ] = | q i , 0 q i ( z ) | 2 Q [ 1 q i ( z ) 1 q i * ( z ) ] ,
u g , q ( x , y , L ) = exp ( j k r L ) 0 d exp [ j 2 ( k k r ) z ] × { A 1 Q r [ 1 q 1 + L z ] + A 2 Q r [ 1 q 2 + L z ] } d z ,
A i = | q i , 0 q i ( z ) | 2 A q i q i + L z ;
1 q i = k k r q i ( z ) k k r q i * ( z ) + 1 q ,
u g , l , s ( x , y , L ) = 0 d exp [ j 2 ( k k r ) z ] A E × S [ s q r ( z ) ( z L ) ] Q r [ 1 q + L z ] d z ,
E = exp [ j k r 2 q r ( z ) | s | 2 ( 1 L z q r ( z ) ) ] ×  exp [ j k r q r ( z ) ( s x x + s y y ) ] .
u g , q , s ( x , y , L ) = exp ( j k r L ) 0 d exp [ j 2 ( k k r ) z ] E × S [ s q r ( z ) ( z L ) ] { A 1 Q r [ 1 q 1 + L z ] + A 2 Q r [ 1 q 2 + L z ] } d z .
S [ s ] f ( x , y ) = f ( x s x , y s y ) .
S [ s ] Q [ 1 q ] = Q s [ 1 q ] G [ s q ] Q [ 1 q ] ,
G [ s ] = exp [ j k ( x s x + y s y ) ] .
d u g , l , s ( z ) ( x , y , z ) = exp [ j ( 2 k k r ) z ] × A Q s [ 1 q r ( z ) ] G [ s q r ( z ) ] Q [ 1 q ] d z ,
¯ [ d ] G [ m ] = Q m [ d ] G [ m ] S [ m d ] ¯ [ d ] .

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