Abstract

A hologram multiplexing technique that uses random wave fronts generated by photorefractive beam fanning is investigated. A storage photorefractive crystal generates various random wave fronts to be used as reference beams without the external diffusers such as ground glass and multimode optical fiber that are generally employed. We experimentally demonstrate hologram multiplexing with six images and show that the stored holograms can be selectively retrieved. We also simulate photorefractive beam fanning inside a BaTiO3 crystal, in particular regarding the correlation properties of the fanning beams for the first time to our knowledge, and reveal the conditions of incidence of an object beam and a reference beam required for suppressing image degradation, implementing low-cross-talk retrieval, and producing a large number of stored holograms.

© 2005 Optical Society of America

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2004 (1)

M. Bunsen, A. Okamoto, Y. Takayama, “Hologram multiplexing with photorefractive beam-fanning speckle,” Opt. Commun. 235, 41–47 (2004).
[CrossRef]

2002 (1)

T. Nakada, A. Okamoto, K. Sato, “Reconfigurable free-space all-optical interconnection with beam-fanning switch in photorefractive crystal,” Opt. Commun. 208, 69–77 (2002).
[CrossRef]

2001 (1)

2000 (1)

1999 (1)

1998 (4)

1996 (1)

1995 (1)

1994 (4)

1993 (3)

1992 (2)

1991 (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

1990 (1)

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its breaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

1988 (1)

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–31 (1984).
[CrossRef]

1982 (1)

Adibi, A.

Aharoni, A.

Barbastathis, G.

Bashaw, M. C.

Boj, S.

Bunsen, M.

M. Bunsen, A. Okamoto, Y. Takayama, “Hologram multiplexing with photorefractive beam-fanning speckle,” Opt. Commun. 235, 41–47 (2004).
[CrossRef]

Burr, G. W.

D. Psaltis, G. W. Burr, “Holographic data storage,” Computer 31, 52–60 (1998).
[CrossRef]

Buse, K.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–31 (1984).
[CrossRef]

Dai, J.

P. Xie, P. Wang, J. Dai, H. Zhang, “Effect of random volume scattering on image amplification and beam fanning in photorefractive materials,” J. Opt. Soc. Am. B 15, 1889–1894 (1998).
[CrossRef]

P. Xie, Y. Hong, J. Dai, Y. Zhu, “Theoretical and experimental studies of fanning effects in photorefractive crystal,” J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Denz, C.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Fainman, Y.

Fischer, B.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its breaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–31 (1984).
[CrossRef]

Ford, J. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hagler, M. O.

He, Q. B.

Heanue, J. F.

Hesselink, L.

Hong, Y.

P. Xie, Y. Hong, J. Dai, Y. Zhu, “Theoretical and experimental studies of fanning effects in photorefractive crystal,” J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Kang, Y. H.

Kim, K. H.

Kral, E. L.

Lee, B.

Lee, H. S.

Lee, S. H.

Levene, M.

Levya, V.

Leyva, V.

Li, H.

Markov, V.

Midwinter, J. E.

Millerd, J.

Mok, F. H.

Nakada, T.

T. Nakada, A. Okamoto, K. Sato, “Reconfigurable free-space all-optical interconnection with beam-fanning switch in photorefractive crystal,” Opt. Commun. 208, 69–77 (2002).
[CrossRef]

Norrie, M.

Okamoto, A.

M. Bunsen, A. Okamoto, Y. Takayama, “Hologram multiplexing with photorefractive beam-fanning speckle,” Opt. Commun. 235, 41–47 (2004).
[CrossRef]

T. Nakada, A. Okamoto, K. Sato, “Reconfigurable free-space all-optical interconnection with beam-fanning switch in photorefractive crystal,” Opt. Commun. 208, 69–77 (2002).
[CrossRef]

T. Yoshida, A. Okamoto, Y. Takayama, K. Sato, “Operable conditions of the beam-fanning novelty filter for the c axis and the incident angle,” Appl. Opt. 39, 5940–5948 (2000).
[CrossRef]

Ophir, Y.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its breaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Orlov, S.

Pauliat, G.

S. Boj, G. Pauliat, G. Roosen, “Dynamic holographic memory showing readout, refreshing, and updating capabilities,” Opt. Lett. 17, 438–440 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Psaltis, D.

Rakuljic, G.

Rakuljic, G. A.

Roosen, G.

S. Boj, G. Pauliat, G. Roosen, “Dynamic holographic memory showing readout, refreshing, and updating capabilities,” Opt. Lett. 17, 438–440 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Sato, K.

T. Nakada, A. Okamoto, K. Sato, “Reconfigurable free-space all-optical interconnection with beam-fanning switch in photorefractive crystal,” Opt. Commun. 208, 69–77 (2002).
[CrossRef]

T. Yoshida, A. Okamoto, Y. Takayama, K. Sato, “Operable conditions of the beam-fanning novelty filter for the c axis and the incident angle,” Appl. Opt. 39, 5940–5948 (2000).
[CrossRef]

Segev, M.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its breaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Selviah, D. R.

Takayama, Y.

M. Bunsen, A. Okamoto, Y. Takayama, “Hologram multiplexing with photorefractive beam-fanning speckle,” Opt. Commun. 235, 41–47 (2004).
[CrossRef]

T. Yoshida, A. Okamoto, Y. Takayama, K. Sato, “Operable conditions of the beam-fanning novelty filter for the c axis and the incident angle,” Appl. Opt. 39, 5940–5948 (2000).
[CrossRef]

Tao, S.

Trolinge, J.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Walkup, J. F.

Wang, P.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–31 (1984).
[CrossRef]

Xie, P.

P. Xie, P. Wang, J. Dai, H. Zhang, “Effect of random volume scattering on image amplification and beam fanning in photorefractive materials,” J. Opt. Soc. Am. B 15, 1889–1894 (1998).
[CrossRef]

P. Xie, Y. Hong, J. Dai, Y. Zhu, “Theoretical and experimental studies of fanning effects in photorefractive crystal,” J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Yariv, A.

Yeh, P.

Yin, S.

F. Yu, S. Yin, Photorefractive Optics: Materials, Properties and Applications (Academic, San Diego, Calif., 2000).

Yoshida, T.

Yu, F.

F. Yu, S. Yin, Photorefractive Optics: Materials, Properties and Applications (Academic, San Diego, Calif., 2000).

Zhang, H.

Zhu, Y.

P. Xie, Y. Hong, J. Dai, Y. Zhu, “Theoretical and experimental studies of fanning effects in photorefractive crystal,” J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Appl. Opt. (6)

Computer (1)

D. Psaltis, G. W. Burr, “Holographic data storage,” Computer 31, 52–60 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–31 (1984).
[CrossRef]

J. Appl. Phys. (1)

P. Xie, Y. Hong, J. Dai, Y. Zhu, “Theoretical and experimental studies of fanning effects in photorefractive crystal,” J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (4)

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its breaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase coding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

T. Nakada, A. Okamoto, K. Sato, “Reconfigurable free-space all-optical interconnection with beam-fanning switch in photorefractive crystal,” Opt. Commun. 208, 69–77 (2002).
[CrossRef]

M. Bunsen, A. Okamoto, Y. Takayama, “Hologram multiplexing with photorefractive beam-fanning speckle,” Opt. Commun. 235, 41–47 (2004).
[CrossRef]

Opt. Lett. (8)

Science (1)

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Other (3)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

F. Yu, S. Yin, Photorefractive Optics: Materials, Properties and Applications (Academic, San Diego, Calif., 2000).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (16)

Fig. 1
Fig. 1

Generation of beam fanning. (a) Generation of the scattered beam. (b) Two-beam coupling of the scattered beam and the incident beam. (c) Broadening of the beam like a fan inside the crystal.

Fig. 2
Fig. 2

Conceptual diagram of hologram multiplexing with a random wave front generated by photorefractive beam fanning: (a) recording, (b) retrieval.

Fig. 3
Fig. 3

Experimental setup: PRC, photorefractive crystal; M1–M4, mirrors; HWP1, HWP2, half-wave plates; P, polarizer; PBS, polarizing beam splitter; L1–L6, lenses.

Fig. 4
Fig. 4

Hologram recording with an object beam and a random wave front generated by beam fanning.

Fig. 5
Fig. 5

Selectively reconstructed images from six multiplexed holograms.

Fig. 6
Fig. 6

Optical geometry for analysis of beam fanning.

Fig. 7
Fig. 7

Profile of input Gaussian beam. (a) Spatial intensity distribution at z = 0 mm. The beam radius (1/e width of the amplitude) is 100 μm. (b) Angular intensity distribution of (a).

Fig. 8
Fig. 8

Calculated intensity distribution in BaTiO3 crystal (φ = 45°): (a) angular intensity distribution, (b) spatial intensity distribution.

Fig. 9
Fig. 9

Calculated angular intensity distribution of the fanning beam for various values of φ at z = 5 mm. (a) Angular intensity distribution. Beam fanning scarcely occurs when φ = 0°. Therefore the curve for φ = 0° does not appear in this figure. (b) Enlarged view of (a) near θ = 0°.

Fig. 10
Fig. 10

Calculated spatial intensity distribution in BaTiO3 crystal (φ = 90°).

Fig. 11
Fig. 11

Sample phase function of the scattered beam. w and N are assumed to be 10 μm and 1000, respectively, in the analyses that follow.

Fig. 12
Fig. 12

Square of calculated autocorrelation function of a propagating beam in a BaTiO3 crystal (φ = 45°).

Fig. 13
Fig. 13

Incident intensity distribution at z = 0 for various values of δi. A1(y, z) is generated by the incident beam with δi = 0.

Fig. 14
Fig. 14

Calculated cross-correlation coefficient for z(φ = 45°).

Fig. 15
Fig. 15

Calculated cross-correlation coefficient for the amount of horizontal shift of the incident position (z = 5 mm, φ = 45°).

Fig. 16
Fig. 16

Experimental result of normalized diffraction efficiency for δi0.

Equations (6)

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f ( q , z ) = - A ( y , z ) exp ( - i 2 π q y ) d y ,
d f ( q , z ) d z = 1 I 0 - γ ( q , q ) f ( q , z ) 2 d q f ( q , z ) ,
γ ( q , q ) - ω 2 n o 3 r eff ( q , q ) 2 c 2 ϕ ( q ) k g ( k B T / e ) 1 + ( k g 2 / k D 2 ) e ^ T ( q ) e ^ ( q ) ,
r eff ( q , q ) = e ^ T ( q ) { ɛ ˜ s [ R ˜ k g ( q , q ) k g ( q , q ) ] ɛ ˜ s } e ^ ( q ) n o 3 ,
ϕ ( q ) = k ( q ) cos θ .
C C = A 1 ( y , z ) A 2 * ( y , z ) d y [ A 1 ( y , z ) 2 d y A 2 ( y , z ) 2 d y ] 1 / 2 .

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