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.

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]

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)

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]

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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