Abstract

The erasure, which occurs during readout of holograms in photochromic or photorefractive media, imposes limitations on the amount of information which can be stored. It is shown that storage of several holograms by varying the angle of incidence of the reference beam is particularly unfavorable. It is much more advantageous to use a large number of bits per page or to store the holograms in separate parts of the sample. If erasure is prevented by some kind of physical or chemical fixing or biasing process, the storage capacity is limited by the bit rate required during readout. This limitation may also be severe, in some cases reducing the storage capacity to several orders of magnitude below the diffraction-limited value.

© 1979 Optical Society of America

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References

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  1. P. J. van Heerden, Appl. Opt. 2, 393 (1963).
    [CrossRef]
  2. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  3. R. G. Zech, Ph.D. Thesis, U. Michigan, 1974; University Microfilms order 74-25-369.
  4. W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).
  5. S. D. Personick, Bell Syst. Tech. J. 52, 843 (1973).
  6. W. J. Tomlinson, Appl. Opt. 14, 2456 (1975).
    [CrossRef] [PubMed]
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  8. R. A. Baugh, Ph.D. Thesis, Stanford U., 1969; University Microfilms order 70-10-422.
  9. S. K. Case, J. Opt. Soc. Am. 65, 724 (1975).
    [CrossRef]
  10. K. Blotekjaer, J. Appl. Phys. 48, 2495 (1977).
    [CrossRef]
  11. A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
    [CrossRef]
  12. J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540 (1971).
    [CrossRef]
  13. D. L. Staebler, W. Phillips, Appl. Opt. 13, 788 (1974).
    [CrossRef] [PubMed]
  14. W. J. Tomlinson, E. A. Chandross, R. L. Fork, C. A. Pryde, A. A. Lamola, Appl. Opt. 11, 533 (1972).
    [CrossRef] [PubMed]

1977

K. Blotekjaer, J. Appl. Phys. 48, 2495 (1977).
[CrossRef]

1975

1974

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
[CrossRef]

D. L. Staebler, W. Phillips, Appl. Opt. 13, 788 (1974).
[CrossRef] [PubMed]

1973

S. D. Personick, Bell Syst. Tech. J. 52, 843 (1973).

1972

1971

J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540 (1971).
[CrossRef]

1969

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

1963

Amodei, J. J.

J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540 (1971).
[CrossRef]

Baugh, R. A.

R. A. Baugh, Ph.D. Thesis, Stanford U., 1969; University Microfilms order 70-10-422.

Blotekjaer, K.

K. Blotekjaer, J. Appl. Phys. 48, 2495 (1977).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Case, S. K.

Chandross, E. A.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Fork, R. L.

Glass, A. M.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
[CrossRef]

Kogelnik, H.

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

Lamola, A. A.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Negran, T. J.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
[CrossRef]

Personick, S. D.

S. D. Personick, Bell Syst. Tech. J. 52, 843 (1973).

Phillips, W.

Pratt, W. K.

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

Pryde, C. A.

Staebler, D. L.

D. L. Staebler, W. Phillips, Appl. Opt. 13, 788 (1974).
[CrossRef] [PubMed]

J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540 (1971).
[CrossRef]

Tomlinson, W. J.

van Heerden, P. J.

von der Linde, D.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
[CrossRef]

Zech, R. G.

R. G. Zech, Ph.D. Thesis, U. Michigan, 1974; University Microfilms order 74-25-369.

Appl. Opt.

Appl. Phys. Lett.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 75, 233 (1974).
[CrossRef]

J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540 (1971).
[CrossRef]

Bell Syst. Tech. J.

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

S. D. Personick, Bell Syst. Tech. J. 52, 843 (1973).

J. Appl. Phys.

K. Blotekjaer, J. Appl. Phys. 48, 2495 (1977).
[CrossRef]

J. Opt. Soc. Am.

Other

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

R. G. Zech, Ph.D. Thesis, U. Michigan, 1974; University Microfilms order 74-25-369.

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

R. A. Baugh, Ph.D. Thesis, Stanford U., 1969; University Microfilms order 70-10-422.

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Figures (1)

Fig. 1
Fig. 1

The general dependence of storage capacity on the readout bit rate.

Tables (6)

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Table I Number of Photons μ Required for a Given Error Rate pe

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Table II Maximum Degree of Angular Multiplexing for Given Bit Rate r and Readout Power Pr for a Photochromic Material with ρ = 0 and ρ = 100 a

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Table III Maximum Degree of Angular Multiplexing for Given Bit Rate r and Readout Power Pr for Lithium Niobate

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Table IV Thickness of a LiNbO3 Sample Having the Same Storage Capacity as a Photochromic Material with Given ρ

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Table V Maximum Storage Capacity and Bit Rate for the Photodimer Acridizinium for Two Different Wavelengths and Various Values of the Product NsNb

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Table VI Maximum Storage Capacity of Lithium Niobate for Two Different Sample Thicknesses and Various Values of the Product NsNb

Equations (90)

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τ r = ( h c μ ) / ( η b P r λ ) ,
s = ( q 2 2 μ 2 R L ) / ( 32 k T n τ r ) ,
R L τ r / ( 2 π C ) ,
μ = ( 64 π k T n C s ) 1 / 2 / ( q ) .
p e = 1 2 ( 1 - erf s ) exp ( - s / 2 ) ( 2 π s ) 1 / 2 ,
s = - 2 ln [ ( 2 π s ) 1 / 2 p e ] 2 ln ( 1 / p e ) ,
μ = [ 128 π k T n C ln ( 1 / p e ) ] 1 / 2 / ( q ) .
r max = N b τ r = P r λ η b N b h c μ .
η = exp ( - L ) [ sin 2 ( ρ δ L 4 ) + sinh 2 ( δ L 4 ) ] .
L = 2 α 0 d cos θ = D ln 10 ,
δ = α 1 / α 0 ,
ρ = ( 2 π n 1 ) / ( λ α 1 )
η b p = 1 N 1 p exp ( - L ) { sin 2 [ ρ ( N 1 p ) 1 / 2 δ b L 4 ] + sinh 2 [ ( N 1 p ) 1 / 2 δ b L 4 ] } ,
η b = ( 1 + ρ 2 ) exp ( - L ) ( δ b L 4 ) 2 .
( 1 + ρ 2 ) ( δ b L 4 ) 2 1 N b .
N b η b exp ( - L ) ,
α = α i exp ( - T ) ,
E p = R exp ( - j ρ p · x ) + S i = 1 N b s i p exp ( - j σ i · x ) ,
T p = E p E p * = T R + T S N 1 p + 2 ( T R T S ) 1 / 2 i = 1 N b s i p cos ( K i p · x + ϕ i p ) + 2 T S i = 1 N b j = 1 i - 1 s i p s j p cos ( K i j · x + ϕ i j ) ,
K i p = σ i - ρ p ,
K i j = σ i - σ j ,
T R = R 2 ,
T S = S 2 ,
T = N a T R + N 1 T S + 2 ( T R T S ) 1 / 2 p = 1 N a i = 1 N b s i p cos ( K i p · x + ϕ i p ) + 2 T S i = 1 N b j = 1 i - 1 ( p = 1 N a s i p s i p ) cos ( K i j · x + ϕ i j ) ,
0 N 1 N a N b .
T = N a ( T R + N b T S ) + 2 ( T R T S ) 1 / 2 p = 1 N a i = 1 N b cos ( K i p · x + ϕ i p ) + 2 N a T S i = 1 N b j = 1 i - 1 cos ( K i j · x + ϕ i j ) .
T a v = N a ( T R + N b T S ) .
T b = 2 ( T R T S ) 1 / 2 .
T max = N a [ ( T R ) 1 / 2 + N b ( T S ) 1 / 2 ] 2 .
T rms = ( N a N b T s ) 1 / 2 [ 2 T R + N a ( N b - 1 ) T S ] 1 / 2 .
α α i exp ( T a v ) [ 1 - ( T - T a v ) ] .
δ b = T b = 2 ( T R T S ) 1 / 2 ,
L = L i exp ( - T a v ) = L i exp [ - N a ( T R + N b T S ) ] ,
η b = ( 1 + ρ 2 ) L i 2 4 T R T S exp [ - 2 N a ( T R + N b T S ) ] × exp { - L i exp [ - N a ( T R + N b T S ) ] } .
T R = ( T a v ) / ( 2 N a ) ,
T S = ( T a v ) / ( 2 N a N b ) ,
T a v [ 1 - L i 2 exp ( - T a v ) ] = 1.
T R = 1 / ( 2 N a ) ,
T S = 1 / ( 2 N a N b ) ,
δ b , max = 1 / [ N a ( N b ) 1 / 2 ] ,
η b , max = ( 1 + ρ 2 ) L i 2 16 N a 2 N b exp ( - 2 ) exp [ - L i exp ( - 1 ) ] = 0.0085 ( 1 + ρ 2 ) L i 2 N a 2 N b exp ( - 0.37 L i ) .
0.0085 ( 1 + ρ 2 ) L i 2 N a 2 ,
T max = 1 2 [ 1 + ( N b ) 1 / 2 ] 2 N b 2 ,
T rms = 1 2 ( 1 + 2 N a - 1 N b ) 1 / 2 1 2 .
η b , max 0.0085 ( 1 + ρ 2 ) L i 2 N a 2 N b .
r max = 0.0085 P r λ h c ( 1 + ρ 2 ) L i 2 μ N a 2 ,
N a , max = 0.090 [ P r λ h c ( 1 + ρ 2 ) L i 2 μ r ] 1 / 2 .
ρ δ b L = 2 π n 1 λ α 1 α 1 α 0 2 α 0 d cos θ = 4 π n b d λ cos θ ,
η b = [ ( π n b d ) / ( λ cos θ ) ] 2 ,
n b = Δ n T b T a v [ 1 - exp ( - T a v ) ] .
n b , p = Δ n T b , p T a v , p [ 1 - exp ( - T a v , p ) ] exp ( i = p + 1 N a T a v , i ) .
1 - exp ( - T a v , p ) = exp ( T a v , p + 1 ) - 1.
exp ( - T a v , p ) = 1 - [ 1 / ( p + χ ) ] ,
[ 1 - exp ( - T a v , p ) ] exp ( - i = p + 1 N a T a v , i ) = 1 N a + χ ,
n b = Δ n ( T R T S ) 1 / 2 N a ( T R + N b T S ) ,
n b , max = ( Δ n ) / [ 2 N a ( N b ) 1 / 2 ] .
η b , max = ( π Δ n d 2 λ cos θ ) 2 1 N a 2 N b .
( π Δ n d ) / ( 2 λ cos θ ) N a .
η b , max 1 / ( N b )
r max = ( π Δ n d 2 λ cos θ ) 2 P r λ h c 1 μ N a 2 ,
N a , max = π Δ n d 2 λ cos θ ( P r λ h c 1 μ r ) 1 / 2 ,
η b = η b o exp ( - 2 T r ) ,
T r = t / τ e .
μ = P r λ h c η b o exp [ - 2 ( M - 1 ) τ r / τ e ] 0 τ t exp ( - 2 t / τ e ) d t .
τ r exp ( - 2 M τ e ) = ( h c μ ) / ( μ b o P r λ ) ,
M = τ e 2 τ r ln τ r η b o P r λ h c μ ,
τ r = ( e h c μ ) / ( P r λ η b o ) ,
M max = ( τ e P r λ η b o ) / ( 2 e h c μ ) .
r N b τ r = P r λ η b o N b e h c μ ,
M = τ e r 2 N b ln P r λ η b o N b h c μ r .
d n d t = - n τ e = - ϕ σ n P r A / N s λ h c ,
τ e = ( A h c ) / ( ϕ σ P r λ N s ) .
M max = 0.0016 A ( 1 + ρ 2 ) L i 2 ϕ σ 1 μ N a 2 N s N b .
N a , max = 0.12 [ A ( 1 + ρ 2 ) L i 2 ϕ σ μ N s N b ] 1 / 3 ,
N max = N a , max N s N b = 0.12 [ A ( 1 + ρ 2 ) L i 2 ( N s N b ) 2 ϕ σ μ ] 1 / 3 .
r 0 = 0.23 P r λ h c [ 1 + ρ 2 μ ( ϕ σ L i N s N b A ) 2 ] 1 / 3 .
N a , max = 0.12 [ λ 2 ( 1 + ρ 2 ) L i 2 ϕ σ μ ] 1 / 3
N max = 0.12 A [ ( 1 + ρ 2 ) L i 2 ϕ σ μ λ 4 ] 1 / 3 .
r 0 = 0.23 P r λ h c [ ( 1 + ρ 2 ) ( ϕ σ L i ) 2 μ λ 4 ] 1 / 3 .
τ e = e / σ e ,
σ e = q μ e n e = q μ e ϕ α P r A / N s λ h c τ l ,
τ e = ( e A h c N s ) / ( q μ e ϕ α P r λ τ l ) .
M max = 0.45 ( Δ n d λ cos θ ) 2 e A q μ e ϕ α τ l 1 μ N a 2 N s N b ,
N a , max = 0.77 [ ( Δ n d λ cos θ ) 2 e A q μ e ϕ α τ l μ N s N b ] 1 / 3 ,
N max = 0.77 [ ( Δ n d λ cos θ ) 2 e A ( N s N b ) 2 q μ e ϕ α τ l μ ] 1 / 3 .
r 0 = 1.5 P r λ h c [ 1 μ ( Δ n d q μ c ϕ α τ l N s N b λ cos θ e A ) 2 ] 1 / 3 .
N a , max = 0.77 [ ( Δ n d λ cos θ ) 2 e λ 2 q μ e ϕ α τ l μ ] 1 / 3 ,
N max = 0.77 A [ ( Δ n d λ cos θ ) 2 e q μ e ϕ α τ l μ λ 4 ] 1 / 3 .
r 0 = 1.5 P r λ h c [ 1 μ λ 4 ( Δ n d q μ e ϕ α τ l λ cos θ e ) 2 ] 1 / 3 .
q μ e ϕ α τ l 5 × 10 - 33 Asm / V .

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