Abstract

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.

© 2007 Optical Society of America

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  1. G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Volume holographic data storage at an areal density of 250gigapixels/in.2," Opt. Lett. 26, 444-446 (2001).
    [CrossRef]
  2. S. Breer and K. Buse, "Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate," Appl. Phys. B 66, 339-345 (1998).
    [CrossRef]
  3. G. Barbastathis, M. Balberg, and D. J. Brady, "Confocal microscopy with a volume holographic filter," Opt. Lett. 24, 811-813 (1999).
    [CrossRef]
  4. G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. S. Tao, B. Wang, G. W. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
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  15. S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), pp. 136 (in Chinese).
  16. D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
    [CrossRef]
  17. P. Günter and J.-P. Huignard, "Photorefractive effects and materials," in Fundamental Phenomena, P.Günter and J.-P.Huignard, eds., Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, 1988), pp. 7-70.

2006 (1)

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

2004 (1)

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

2001 (1)

1999 (2)

G. Barbastathis, M. Balberg, and D. J. Brady, "Confocal microscopy with a volume holographic filter," Opt. Lett. 24, 811-813 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

1998 (2)

1993 (1)

1992 (2)

1983 (1)

1979 (1)

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

1976 (1)

D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
[CrossRef]

1969 (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2047 (1969).

Athale, R. A.

Balberg, M.

Barbastathis, G.

Brady, D.

Brady, D. J.

Breer, S.

S. Breer and K. Buse, "Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate," Appl. Phys. B 66, 339-345 (1998).
[CrossRef]

Brost, G. A.

Burr, G. W.

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

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Volume holographic data storage at an areal density of 250gigapixels/in.2," Opt. Lett. 26, 444-446 (2001).
[CrossRef]

Buse, K.

S. Breer and K. Buse, "Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate," Appl. Phys. B 66, 339-345 (1998).
[CrossRef]

Chen, A. G.-S.

Chen, J.

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

Cooke, D. J.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981), 164-253.

Coufal, H.

Ding, Y.

Edwin, R. P.

D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
[CrossRef]

Gallmann, L.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Gaylord, T. K.

Günter, P.

P. Günter and J.-P. Huignard, "Photorefractive effects and materials," in Fundamental Phenomena, P.Günter and J.-P.Huignard, eds., Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, 1988), pp. 7-70.

Guo, R.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), pp. 136 (in Chinese).

Hill, K. B.

Hoffnagle, J. A.

Hu, Z.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Huignard, J.-P.

P. Günter and J.-P. Huignard, "Photorefractive effects and materials," in Fundamental Phenomena, P.Günter and J.-P.Huignard, eds., Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, 1988), pp. 7-70.

Jefferson, C. M.

Jurich, M.

Kanan, A.

Keller, U.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2047 (1969).

Ling, Z.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), pp. 136 (in Chinese).

Liu, D.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Liu, L.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Liu, S.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), pp. 136 (in Chinese).

Macfarlane, R. M.

Matuschek, N.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Moharam, M. G.

Nolte, D. D.

Qu, W.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Raj, K.

Riccius, H. D.

D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
[CrossRef]

Rodriguez, G.

Russell, P. St. J.

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

Shelby, R. M.

Smith, D. S.

D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
[CrossRef]

Solymar, L.

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

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981), 164-253.

Steinmeyer, G.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Sutter, D. H.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Tao, S.

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

Wang, B.

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

Wang, C.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Weiner, A. M.

Yan, A.

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

Zheng, Z.

Appl. Phys. B (1)

S. Breer and K. Buse, "Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate," Appl. Phys. B 66, 339-345 (1998).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2047 (1969).

J. Mod. Opt. (2)

C. Wang, L. Liu, A. Yan, D. Liu, Z. Hu, and W. Qu, "Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout," J. Mod. Opt. 53, 1931-1945 (2006).
[CrossRef]

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

J. Opt. Soc. Am. (1)

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

Opt. Acta (1)

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

Opt. Commun. (1)

D. S. Smith, H. D. Riccius, and R. P. Edwin, "Refractive indices of lithium niobate," Opt. Commun. 17, 332-335 (1976).
[CrossRef]

Opt. Lett. (5)

Science (1)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Other (3)

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981), 164-253.

P. Günter and J.-P. Huignard, "Photorefractive effects and materials," in Fundamental Phenomena, P.Günter and J.-P.Huignard, eds., Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, 1988), pp. 7-70.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), pp. 136 (in Chinese).

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Figures (9)

Fig. 1
Fig. 1

(a) Recording the overlapping VHG with the o- or e-polarized continuous beam. (b) Reading the developed overlapping VHG with a UPB.

Fig. 2
Fig. 2

Normalized intensity distributions of the diffracted pulsed beams in the temporal domain along the output boundary (a) for the o-o case and (b) for the o-e case, where W S = 0.3 mm , R W = 1 , θ 0 = π 18 .

Fig. 3
Fig. 3

Normalized intensity distributions of the diffracted pulsed beams in the temporal domain along the output boundary (a) for the o-o case and (b) for the o-e case, where W S = 0.3 mm , R W = 2 , θ 0 = π 18 .

Fig. 4
Fig. 4

Normalized intensity distributions of the diffracted pulsed beams in the temporal domain along the output boundary (a) for the o-o cases and (b) for the o-e cases, where W S = 1 mm , R W = 1 , θ 0 = π 18 .

Fig. 5
Fig. 5

Normalized intensity distributions of the diffracted pulsed beams in the temporal domain along the output boundary (a) for the o-o cases and (b) for the o-e cases, where W S = 0.3 mm , R W = 1 , θ 0 = π 6 .

Fig. 6
Fig. 6

Diffraction efficiency distributions of the diffracted pulsed beams along the u S axis on the output face of the grating for the four recording and reading polarization cases, where (a) W S = 0.3 mm , R W = 1 , θ 0 = π 18 ; (b) W S = 0.3 mm , R W = 2 , θ 0 = π 18 ; (c) W S = 1 mm , R W = 1 , θ 0 = π 18 ; (d) W S = 0.3 mm , R W = 1 , θ 0 = π 6 .

Fig. 7
Fig. 7

Variation of η Tol with Δ τ , where W S = 0.3 mm , R W = 1 , θ 0 = π 18 .

Fig. 8
Fig. 8

Variation of η Tol with W S for the input UPB with (a) Δ τ = 30 fs , (b) Δ τ = 100 fs , (c) Δ τ = 200 fs , and (d) for the CW readout, where R W = 1 , θ 0 = π 18 .

Fig. 9
Fig. 9

Variation of η Tol with R W for the input UPB with (a) Δ τ = 30 fs , (b) Δ τ = 100 fs , (c) Δ τ = 300 fs , and (d) for the CW readout, where W S = 0.3 mm , θ 0 = π 18 .

Equations (26)

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E i 0 = A i 0 exp ( j β 0 p i 0 ) e i 0 ,
u 0 ( t ) = exp ( j ω 0 t t 2 T 2 ) e 1 ,
E 0 ( λ ) = π T exp { [ π T c ( 1 λ 1 λ 0 ) ] 2 } .
ε r ( λ ) = ε r 0 ( λ ) + ε r 1 ( e 10 e 20 ) cos [ β 0 ( p 10 p 20 ) ] ,
E ( λ ) = E 1 ( λ ) + E 2 ( λ ) = i = 1 2 { A i 1 e i + A i 2 p i 0 + A i 3 ( e i × p i 0 ) } exp ( j β p i 0 ) ,
A 11 p 10 + j κ ( e 10 e 20 ) e 1 2 exp ( j K ) { ( e 1 e 2 ) A 21 + e 1 ( e 2 × p 20 ) A 23 } = 0 ,
A 21 p 20 + j κ ( e 10 e 20 ) e 2 2 exp ( j K ) { ( e 1 e 2 ) A 11 + e 2 ( e 1 × p 10 ) A 13 } = 0 ,
( u R u S ) = 1 W S ( sin θ 0 cos θ 0 sin θ 0 cos θ 0 ) ( x z ) ,
n g = n g o = n o ( λ 0 ) λ 0 d n o ( λ ) d λ λ = λ 0
n g = n g e = n e ( λ 0 ) λ 0 d n e ( λ ) d λ λ = λ 0
A 11 u S = j κ W S exp ( j K ) A 21 ,
A 21 u R = j κ exp ( j K ) A 11 ,
E 1 ( u R , 1 , λ ) = E 0 ( λ ) E 0 ( λ ) κ W S exp ( j δ W S u R ) × 0 u R 1 u R τ J 1 ( 2 κ W S u R τ ) exp ( j δ W S τ ) d τ ,
E 2 ( R W , u S , λ ) = j E 0 ( λ ) κ W S exp ( j δ W S u S ) × 0 R W J 0 ( 2 κ W S u S ( τ R W ) ) exp ( j δ W S τ ) d τ .
I 1 ( u R , 1 , λ ) = E 1 ( u R , 1 , λ ) 2 ,
I 2 ( R W , u S , λ ) = E 2 ( R W , u S , λ ) 2 .
u 1 ( u R , 1 , t ) = E 1 ( u R , 1 , λ ) exp ( j 2 π c t λ ) [ 2 π c λ 2 ] d λ ,
u 2 ( R W , u S , t ) = E 2 ( R W , u S , λ ) exp ( j 2 π c t λ ) [ 2 π c λ 2 ] d λ .
η ( R W , u S ) = I 2 ( R W , u S , λ ) 2 π c λ 2 d λ R W I 0 ( λ ) 2 π c λ 2 d λ .
η Tol = 1 0 η ( R W , u S ) d u S .
η CW = 1 J 0 2 ( 2 κ W S R W ) J 1 2 ( 2 κ W S R W ) .
Δ λ G ( R W , u S ) = K ¯ λ 0 2 π n g tan θ 0 W S R W + u S ,
n 1 o o = n o 3 ( λ 0 ) γ 13 E SC 2 ,
n 1 o e = [ γ 13 n o 4 ( λ 0 ) sin 2 θ 0 + γ 33 n e 4 ( λ 0 ) cos 2 θ 0 ] E SC [ 2 n e ( λ 0 ) ] ,
n 1 e o = [ cos 2 θ 0 sin 2 θ 0 ] n o 3 ( λ 0 ) γ 13 E SC 2 ,
n 1 e e = [ cos 2 λ 0 sin 2 θ 0 ] [ γ 13 n o 4 ( λ 0 ) sin 2 θ 0 + γ 33 n e 4 ( λ 0 ) cos 2 θ 0 ] E SC [ 2 n e ( λ 0 ) ] ,

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