Abstract

For holographic data storage, it is necessary to adjust the wavelength and direction of the reading beam if the reading and recording temperature do not match. An analytical solution for this adjustment is derived using first-order approximations in a two-dimensional model. The optimum wavelength is a linear function of the temperature difference between recording and reading, and is independent of the direction of the reference beam. However, the optimum direction of incidence is not only a linear function of the temperature difference, but also depends on the direction of the reference beam. The retrieved image, which is produced by a diffracted beam, shrinks or expands slightly according to the temperature difference.

© 2008 Optical Society of America

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References

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  1. L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
    [CrossRef]
  2. M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
    [CrossRef]
  3. T. Tanaka, K. Sako, R. Kasegawa, M. Toishi, and K. Watanabe, “Tunable blue laser compensates for thermal expansion of the medium in holographic data storage,” Appl. Opt. 46, 6263-6272 (2007).
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

1998 (1)

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Bair, H.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Boyd, C.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Dhar, L.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Kasegawa, R.

Sako, K.

Schilling, M.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Schonoes, M. G.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Sugiki, M.

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

Tanaka, T.

T. Tanaka, K. Sako, R. Kasegawa, M. Toishi, and K. Watanabe, “Tunable blue laser compensates for thermal expansion of the medium in holographic data storage,” Appl. Opt. 46, 6263-6272 (2007).
[CrossRef] [PubMed]

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

Toishi, M.

T. Tanaka, K. Sako, R. Kasegawa, M. Toishi, and K. Watanabe, “Tunable blue laser compensates for thermal expansion of the medium in holographic data storage,” Appl. Opt. 46, 6263-6272 (2007).
[CrossRef] [PubMed]

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

Watanabe, K.

T. Tanaka, K. Sako, R. Kasegawa, M. Toishi, and K. Watanabe, “Tunable blue laser compensates for thermal expansion of the medium in holographic data storage,” Appl. Opt. 46, 6263-6272 (2007).
[CrossRef] [PubMed]

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

Wysocki, T. L.

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Dhar, M. G. Schonoes, T. L. Wysocki, H. Bair, M. Schilling, and C. Boyd, “Temperature-induced changes in photopolymer volume holograms,” Appl. Phys. Lett. 73, 1337-1339 (1998).
[CrossRef]

Jpn. J. Appl. Phys. Part 1 (1)

M. Toishi, T. Tanaka, M. Sugiki, and K. Watanabe, “Improvement in temperature tolerance of holographic data storage using wavelength tunable laser,” Jpn. J. Appl. Phys. Part 1 45, 1297-1304 (2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Two beam optics: (a) recording, and (b) reading. Small Greek letters stand for the directions in the air, while large Greek letters stand for the directions in the photopolymer.

Fig. 2
Fig. 2

Recorded grating. When the temperature changes from T 0 to T 1 , the direction and interval of the grating change from (a) to (b). Λ 0 and Λ 1 are the grating intervals, and l 0 and l 0 ( 1 + G x ) are the grating intervals in the x direction.

Fig. 3
Fig. 3

Correction of reading beam direction versus signal beam direction. The parameter is Δ λ / λ 0 , where Δ λ is the difference between the reading and recording wavelengths, and λ 0 is the recording wavelength. The reading beam direction before correction is 0.3398 rad in the medium. The other conditions for the calculation are listed in Tables 1, 2, 3.

Fig. 4
Fig. 4

Δ λ opt / λ 0 versus reference beam direction, where Δ λ o p t is the difference between the optimum reading and recording wavelengths, and λ 0 is the recording wavelength. The conditions for the calculations are listed in Tables 1, 2, 3.

Fig. 5
Fig. 5

Δ Ξ opt and Δ ξ opt versus reference beam direction. The dotted and solid curves show Δ Ξ opt and Δ ξ opt , respectively. The conditions for the calculation are listed in Tables 1, 2, 3.

Tables (3)

Tables Icon

Table 1 Directions of Reference and Signal Beams at 25 ° C

Tables Icon

Table 2 Medium Parameters

Tables Icon

Table 3 Simulation Conditions

Equations (60)

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Φ 0 = E 0 + Ψ 0 2 ,
B 0 = E 0 Ψ 0 2 .
G x = γ x ( T 1 - T 0 ) ,
G z = γ z ( T 1 - T 0 ) + s ,
n 1 = n 0 [ 1 + ν ( T 1 - T 0 ) ] ,
Δ n = n 0 ν ( T 1 - T 0 ) .
Ξ 0 = Φ 0 + B 0 ,
Ξ 0 = E 0 .
Ξ 1 = Φ 1 + B 1 ,
Δ Ξ = Δ Φ + Δ B .
tan Φ 0 = x 0 z 0 ,
tan Φ 1 = x 0 ( 1 + G x ) z 0 ( 1 + G z ) .
Δ Φ = ( G x - G z ) sin Φ 0 cos Φ 0 ,
Δ Φ = 1 2 ( G x - G z ) sin ( 2 Φ 0 ) .
sin B 0 = λ 0 2 n 0 Λ 0 .
sin B 1 = λ 1 2 n 1 Λ 1 ,
Δ B = tan B 0 ( Δ λ λ 0 - Δ n n 0 - Δ Λ Λ 0 ) .
Λ 0 = l 0 cos Φ 0 ,
Λ 1 = l 0 ( 1 + G x ) cos Φ 1 ,
Δ Λ Λ 0 = [ G x + G z 2 + G x - G z 2 cos ( 2 Φ 0 ) ] .
Δ B = tan B 0 [ Δ λ λ 0 - Δ n n 0 - G x + G z 2 - G x - G z 2 cos ( 2 Φ 0 ) ] .
Δ Ξ = ( G x - G z ) sin ( 2 Φ 0 - B 0 ) 2 cos B 0 + ( Δ λ λ 0 - Δ n n 0 - G x + G z 2 ) tan B 0 .
Δ Ξ = ( G x - G z ) sin ( E 0 + 3 Ψ 0 2 ) 2 cos ( E 0 - Ψ 0 2 ) + ( Δ λ λ 0 - Δ n n 0 - G x + G z 2 ) tan ( E 0 - Ψ 0 2 ) .
Δ Ξ opt = ( G x - G z ) sin ( E 0 + 3 Ψ 0 a 2 ) 2 cos ( E 0 - Ψ 0 a 2 ) + ( Δ λ opt λ 0 - Δ n n 0 - G x + G z 2 ) tan ( E 0 - Ψ 0 a 2 ) ,
Δ Ξ opt = ( G x - G z ) sin ( E 0 + 3 Ψ 0 b 2 ) 2 cos ( E 0 - Ψ 0 b 2 ) + ( Δ λ opt λ 0 - Δ n n 0 - G x + G z 2 ) tan ( E 0 - Ψ 0 b 2 ) .
Δ λ opt λ 0 = Δ n n 0 + G x + G z 2 + U ( G x - G z ) ,
Δ λ opt λ 0 = [ ν + γ x + γ z 2 + U ( γ x - γ z ) ] ( T 1 - T 0 ) + s ( 1 2 - U ) ,
U = cos ( E 0 + Ψ 0 a + Ψ 0 b 2 ) cos ( Ψ 0 a - Ψ 0 b 2 ) + 1 2 cos ( Ψ 0 a + Ψ 0 b ) .
0.0498 < E 0 + Ψ 0 a + Ψ 0 b 2 < 0.3255 π 10 .
0.95 < cos ( E 0 + Ψ 0 a + Ψ 0 b 2 ) < 1.
2 ν + ( 1 + 2 U ) γ x + ( 1 2 U ) γ z = 0.
Δ Ξ o p t = V ( γ x γ z ) ( T T 0 ) s V ,
V = sin ( E 0 + Ψ 0 a + Ψ 0 b 2 ) cos ( Ψ 0 a - Ψ 0 b 2 ) - 1 2 sin ( Ψ 0 a + Ψ 0 b ) .
0.05 < sin ( E 0 + Ψ 0 a + Ψ 0 b 2 ) < 0.32 ,
sin ξ 0 = n 0 sin Ξ 0 ,
sin ξ opt = n 1 sin Ξ opt ,
ξ opt = ξ 0 + Δ ξ opt ,
Ξ opt = Ξ 0 + Δ Ξ opt .
Δ ξ opt = [ n 0 V ( γ x - γ z ) cos Ξ 0 cos ξ 0 + n 0 ν sin Ξ 0 cos ξ 0 ] ( T 1 - T 0 ) - n 0 s V cos Ξ 0 cos ξ 0 .
X 0 = Φ 0 - B 0 ,
X 1 = Φ 1 - B 1 .
Δ X = Δ Φ - Δ B .
Δ X = 1 2 ( G x - G z ) sin ( 2 Φ 0 ) - tan B 0 [ Δ λ opt λ 0 - Δ n n 0 - G x + G z 2 - G x - G z 2 cos ( 2 Φ 0 ) ] .
Δ X = ( G x - G z ) [ sin ( E 0 + 3 Ψ 0 2 ) 2 cos ( E 0 - Ψ 0 2 ) - U tan ( E 0 - Ψ 0 2 ) ] ,
G x - G z = ( γ x - γ z ) ( T 1 - T 0 ) - s .
sin χ 0 = n 0 sin X 0 ,
sin χ 1 = ( n 0 + Δ n ) sin ( X 0 + Δ X ) .
sin χ 1 = sin ψ 0 + n 0 ( cos Ψ 0 ) Δ X + ( sin Ψ 0 ) Δ n .
u f = sin ψ 0 = n 0 sin Ψ 0 ,
w f = sin χ 1 = n 1 sin X 1 .
w f = u f ( 1 + Δ n n 0 ) + n 0 2 - ( u f ) 2 Δ X ,
Ψ 0 = arcsin ( u n 0 f ) .
w f = 0.993 u f + 0.0009.
( Δ λ opt λ 0 - Δ n n 0 - G x + G z 2 ) [ tan ( E 0 - Ψ 0 a 2 ) - tan ( E 0 - Ψ 0 b 2 ) ] = - ( G x - G z ) 2 [ sin ( E 0 + 3 Ψ 0 a 2 ) cos ( E 0 - Ψ 0 a 2 ) - sin ( E 0 + 3 Ψ 0 b 2 ) cos ( E 0 - Ψ 0 b 2 ) ] .
tan A - tan B = sin ( A - B ) cos A cos B .
Δ λ opt λ 0 = Δ n n 0 + G x + G z 2 + U ( G x - G z ) ,
U = sin ( E 0 + 3 Ψ 0 a 2 ) cos ( E 0 - Ψ 0 b 2 ) - cos ( E 0 - Ψ 0 a 2 ) sin ( E 0 + 3 Ψ 0 b 2 ) 2 sin ( Ψ 0 a - Ψ 0 b 2 ) .
Δ λ opt λ 0 = [ ν + γ x + γ z 2 + U ( γ x - γ z ) ] ( T 1 - T 0 ) + s ( 1 2 - U ) .
U = [ sin ( E 0 + 3 Ψ 0 a - Ψ 0 b 2 ) + sin ( 3 Ψ 0 a + Ψ 0 b 2 ) ] - [ sin ( E 0 + - Ψ 0 a + 3 Ψ 0 b 2 ) + sin ( Ψ 0 a + 3 Ψ 0 b 2 ) ] 4 sin ( Ψ 0 a - Ψ 0 b 2 ) , = [ sin ( E 0 + 3 Ψ 0 a - Ψ 0 b 2 ) - sin ( E 0 + - Ψ 0 a + 3 Ψ 0 b 2 ) ] + [ sin ( 3 Ψ 0 a + Ψ 0 b 2 ) - sin ( Ψ 0 a + 3 Ψ 0 b 2 ) ] 4 sin ( Ψ 0 a - Ψ 0 b 2 ) , = 2 cos ( E 0 + Ψ 0 a + Ψ 0 b 2 ) sin ( Ψ 0 a - Ψ 0 b ) + 2 cos ( Ψ 0 a + Ψ 0 b ) sin ( Ψ 0 a - Ψ 0 b 2 ) 4 sin ( Ψ 0 a - Ψ 0 b 2 ) .
U = cos ( E 0 + Ψ 0 a + Ψ 0 b 2 ) cos ( Ψ 0 a - Ψ 0 b 2 ) + 1 2 cos ( Ψ 0 a + Ψ 0 b ) .

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