Abstract

The influence of the recording conditions, including the widths of the recording beams, the width ratio of the recording beams, and the recording angles, on the properties of crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals is studied. A theoretical model that combines the band transport model with two-dimensional coupled-wave theory is proposed. The numerical calculations of the space-charge field, the intensity profiles of the diffracted beam, and the diffraction efficiency are presented.

© 2006 Optical Society of America

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  1. W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
    [CrossRef]
  2. D. G. Papazoglou, M. Loulakis, G. Siganakis, and N. A. Vainos, "Holographic read-write projector of video images," Opt. Express 10, 280-285 (2002).
    [PubMed]
  3. T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
    [CrossRef]
  4. L. Y. Ren, L. L. Liu, D. Liu, J. F. Zu, and Z. Luan, "Recording and fixing dynamics of nonvolatile photorefractive holograms in LiNbO3:Fe:Mn crystals," J. Opt. Soc. Am. B 20, 2162-2173 (2003).
    [CrossRef]
  5. C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
    [CrossRef]
  6. K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
    [CrossRef]
  7. Y. W. Liu, L. R. Liu, and C. H. Zhou, "Prescription for optimizing holograms in LiNbO3:Fe:Mn," Opt. Lett. 25, 551-553 (2000).
    [CrossRef]
  8. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  9. A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
    [CrossRef]
  10. S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
    [CrossRef]
  11. P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
    [CrossRef]
  12. R. P. Kenan, "Theory of crossed-beam diffraction gratings," IEEE. J. Quantum. Electron. QE 14, 924-930 (1978).
    [CrossRef]
  13. L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820-822 (1977).
    [CrossRef]
  14. G. Notni and R. Kowarschik, "Diffraction analysis of three-dimensional volume gratings with arbitrary boundaries," J. Opt. Soc. Am. A 6, 1682-1691 (1989).
    [CrossRef]
  15. M. G. Maharam, T. K. Gaylord, R. Magnusson, "Diffraction characteristics of three-dimensional crossed-beam volume gratings," J. Opt. Soc. Am. 70, 437-442 (1980).
    [CrossRef]
  16. P. St. J. Russell and L. Solymar, "The properties of holographic overlap gratings," Opt. Acta. 26, 329-347 (1979).
  17. Y. P. Yang, A. Adibi, and D. Psaltis, "Comparison of transmission and the 90-degree holographic recording geometry," Appl. Opt. 42, 3418-3427 (2003).
    [CrossRef] [PubMed]
  18. Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
    [CrossRef]

2005 (1)

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

2004 (4)

A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
[CrossRef]

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

2003 (3)

2002 (1)

2000 (1)

1998 (1)

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
[CrossRef]

1989 (1)

1985 (1)

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

1980 (1)

1979 (1)

P. St. J. Russell and L. Solymar, "The properties of holographic overlap gratings," Opt. Acta. 26, 329-347 (1979).

1978 (1)

R. P. Kenan, "Theory of crossed-beam diffraction gratings," IEEE. J. Quantum. Electron. QE 14, 924-930 (1978).
[CrossRef]

1977 (1)

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820-822 (1977).
[CrossRef]

1969 (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Adibi, A.

Y. P. Yang, A. Adibi, and D. Psaltis, "Comparison of transmission and the 90-degree holographic recording geometry," Appl. Opt. 42, 3418-3427 (2003).
[CrossRef] [PubMed]

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
[CrossRef]

Banerjee, P. P.

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

Burr, G. W.

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

Buse, K.

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
[CrossRef]

Chai, Z. F.

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

Chatterjee, M. R.

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

Chen, J. B.

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

Chiou, A. E. T.

W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
[CrossRef]

Dai, C. X.

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

Dong, Q. M.

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

M. G. Maharam, T. K. Gaylord, R. Magnusson, "Diffraction characteristics of three-dimensional crossed-beam volume gratings," J. Opt. Soc. Am. 70, 437-442 (1980).
[CrossRef]

Kenan, R. P.

R. P. Kenan, "Theory of crossed-beam diffraction gratings," IEEE. J. Quantum. Electron. QE 14, 924-930 (1978).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Kowarschik, R.

Kukhtarev, N.

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
[CrossRef]

Kukhtareva, T.

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

Liu, D.

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
[CrossRef]

L. Y. Ren, L. L. Liu, D. Liu, J. F. Zu, and Z. Luan, "Recording and fixing dynamics of nonvolatile photorefractive holograms in LiNbO3:Fe:Mn crystals," J. Opt. Soc. Am. B 20, 2162-2173 (2003).
[CrossRef]

Liu, Dai A.

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

Liu, L.

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

Liu, L. L.

Liu, L. R.

A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
[CrossRef]

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

Y. W. Liu, L. R. Liu, and C. H. Zhou, "Prescription for optimizing holograms in LiNbO3:Fe:Mn," Opt. Lett. 25, 551-553 (2000).
[CrossRef]

Liu, Y. W.

Loulakis, M.

Luan, Z.

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

L. Y. Ren, L. L. Liu, D. Liu, J. F. Zu, and Z. Luan, "Recording and fixing dynamics of nonvolatile photorefractive holograms in LiNbO3:Fe:Mn crystals," J. Opt. Soc. Am. B 20, 2162-2173 (2003).
[CrossRef]

Magnusson, R.

Maharam, M. G.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Notni, G.

Papazoglou, D. G.

Psaltis, D.

Y. P. Yang, A. Adibi, and D. Psaltis, "Comparison of transmission and the 90-degree holographic recording geometry," Appl. Opt. 42, 3418-3427 (2003).
[CrossRef] [PubMed]

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
[CrossRef]

Ren, L. Y.

Siganakis, G.

Solymar, L.

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820-822 (1977).
[CrossRef]

Su, W. C.

W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
[CrossRef]

Sun, C. C.

W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
[CrossRef]

Tao, S. Q.

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

Vainos, N. A.

Wang, B.

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

Yan, A. M.

A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
[CrossRef]

Yang, Y. P.

Zhou, C. H.

Zu, J. F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820-822 (1977).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

IEEE. J. Quantum. Electron. (1)

R. P. Kenan, "Theory of crossed-beam diffraction gratings," IEEE. J. Quantum. Electron. QE 14, 924-930 (1978).
[CrossRef]

J. Mod. Opt. (1)

S. Q. Tao, B. Wang, G. W. Burr, and J. B. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Nature (1)

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in double doped lithium niobite crystals," Nature 393, 665-668 (1998).
[CrossRef]

Opt. Acta. (1)

P. St. J. Russell and L. Solymar, "The properties of holographic overlap gratings," Opt. Acta. 26, 329-347 (1979).

Opt. Commun. (1)

C. X. Dai, L. Liu, D. Liu, Z. F. Chai, and Z. Luan, "Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals," Opt. Commun. 248, 27-33 (2005).
[CrossRef]

Opt. Eng. (2)

W. C. Su, C. C. Sun, N. Kukhtarev, and A. E. T. Chiou, "Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry," Opt. Eng. 42, 9-10 (2003).
[CrossRef]

P. P. Banerjee, M. R. Chatterjee, N. Kukhtarev, and T. Kukhtareva, "Volume holographic recording and readout for 90-deg geometry," Opt. Eng. 43, 2053-2060 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (2)

Q. M. Dong, L. R. Liu, Dai A. Liu, and C. X. Dai, "Grating spacing dependence of nonvolatile holographic recording with arbitrary charge transport lengths," Optik 115, 427-431 (2004).
[CrossRef]

A. M. Yan, L. R. Liu, and D. Liu, "Polarizing properties of crossed-beam volume holographic gratings," Optik 115, 159-163 (2004).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Recording geometry for a crossed-beam photorefractive grating in LiNbO 3 : Fe : Mn crystal.

Fig. 2
Fig. 2

Spatial distribution of the SCF at the end of fixing: (a) w = 0.1   mm , (b) w = 0.5   mm , (c) w = 1.0   mm , (d) w = 2.0   mm .

Fig. 3
Fig. 3

Intensity profile of the diffracted beam along the grating boundary at the end of fixing: (a) w = 0.1   mm , (b) w = 0.5   mm , (c) w = 1.0   mm , (d) w = 2.0   mm .

Fig. 4
Fig. 4

Diffraction efficiency at the end of fixing as a function of w.

Fig. 5
Fig. 5

Spatial distribution of the SCF at the end of fixing: (a) β = 1 / 10 , (b) β = 1 / 2 , (c) β = 1 / 1 , (d) β = 2 / 1 .

Fig. 6
Fig. 6

Intensity profile of the diffracted beam along the grating boundary at the end of fixing: (a) β = 1 / 10 , (b) β = 1 / 2 , (c) β = 1 / 1 , (d) β = 2 / 1 .

Fig. 7
Fig. 7

Diffraction efficiency at the end of fixing as a function of β.

Fig. 8
Fig. 8

Spatial distribution of the SCF at the end of fixing: (a) θ out = 10 ° , (b) θ out = 20 ° , (c) θ out = 30 ° , (d) θ out = 45 ° .

Fig. 9
Fig. 9

Intensity profile of the diffracted beam along the grating boundary at the end of fixing for various θ out .

Fig. 10
Fig. 10

Diffraction efficiency at the end of fixing as a function of θ out .

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

E 1 ( r ) = A 1 ( x , z ) exp ( i K 1 r ) ,
E 2 ( r ) = A 2 ( x , z ) exp ( i K 2 r ) ,
N D 0 - t = g D N D 0 - + γ D N e 0 ( N D N D 0 - ) ,
N S 0 - t = g S N S 0 - + γ S N e 0 ( N S N S 0 - ) ,
N e 0 = g D N D 0 - + g S N S 0 - γ D ( N D N D 0 - ) + γ S ( N S N S 0 - ) .
N D 1 - t = g D N D 1 - S D , L m I L 0 N D 0 - + γ D N e 1 × ( N D N D 0 - ) γ D N e 0 N D 1 - ,
N S 1         t = g S N S 1         S S , L m I L 0 N S 0         + γ S N e 1 × ( N S N S 0         ) γ S N e 0 N S 1         ,
N e 1 = { ( g D + γ D N e 0 ) N D 1 - + ( g S + γ S N e 0 ) N S 1 - ( e μ N e 0 / ε ε 0 ) ( N D 1 - + N S 1 - ) i k g / e × [ κ D N D 1 - + κ S N S 1 - + ( κ D , L N D 0 - + κ S , L N S 0 - ) m I L 0 ] + ( S D , L N D 0 - + S S , L N S 0 - ) m I L 0 } γ D ( N D N D 0 - ) + γ S ( N S N S 0 - ) + e μ N e 0 / ε ε 0 + K B T μ k g 2 / e ,
E S C = i e ε ε 0 k g ( N D 1         + N S 1         + N e 1 ).
n 1   exp ( i φ E ) = n o 3 γ 13 E S C 2 ,
cos   θ A 1 x + sin   θ A 1 z + i n 1 π λ A 2   exp ( i φ E ) + α red 2 A 1 = 0 ,
cos  θ A 2 x sin   θ A 2 z + i n 1 π λ A 1   exp ( i φ E ) + α red 2 A 2 = 0 ,
sin 2 θ A 1 ξ + i n 1 π λ A 2   exp ( i φ E ) + α red 2 A 1 = 0 ,
sin 2 θ A 2 η + i n 1 π λ A 1   exp ( i φ E ) + α red 2 A 2 = 0.
DE  =   P out S P out R + P out S ,

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