Abstract

The multilayer coupled wave theory is extended to systematically investigate the diffraction properties of multilayer volume holographic gratings (MVHGs) under ultrashort laser pulse readout. Solutions for the diffracted and transmitted intensities, diffraction efficiency, and the grating bandwidth are obtained in transmission MVHGs. It is shown that the diffraction characteristics depend not only on the input pulse duration but also on the number and thickness of grating layers and the gaps between holographic layers. This analysis can be implemented as a useful tool to aid with the design of multilayer volume grating-based devices employed in optical communications, pulse shaping, and processing.

© 2008 Optical Society of America

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  1. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894-937 (1985).
    [CrossRef]
  2. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981).
  3. S. Wu, T. K. Gaylord, E. N. Glytsis, and Y. Wu, “Angular sensitivities of volume gratings for substrate-mode optical interconnects,” Appl. Opt. 44, 4447-4453 (2005).
    [CrossRef] [PubMed]
  4. K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
    [CrossRef]
  5. D. Yang, H. Wang, X. Guo, J. Zhao, and H. Xiang, “Wavelength demultiplexing with layered multiple Bragg gratings in LiNbO3:Fe crystal,” Appl. Opt. 46, 5604-5607 (2007).
    [CrossRef] [PubMed]
  6. D. V. Raymond and H. Lambertus, “Dynamic multiple wavelength filter using a stratified volume holographic optical element,” U.S. patent 5,640,256 (June 17, 1997).
  7. D. M. Chambers, G. P. Nordin, and S. Kim, “Fabrication and analysis of a three-layer stratified volume diffractive optical element high-efficiency grating,” Opt. Express 11, 27-38 (2003).
    [CrossRef] [PubMed]
  8. A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. 49, 85-88 (1980).
  9. G. P. Nordin, R. V. Johnson, and A. R. Tanguay, “Diffraction properties of stratified volume holographic optical elements,” J. Opt. Soc. Am. A 9, 2206-2217 (1992).
    [CrossRef]
  10. D. M. Chambers and G. P. Nordin, “Stratified volume diffractive optical elements as high-efficiency gratings,” J. Opt. Soc. Am. A 16, 1184-1193 (1999).
    [CrossRef]
  11. R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235-249 (1986).
  12. G. A. Rakuljic and V. Leyva, “Volume holographic narrow-band optical filter,” Opt. Lett. 18, 459-461 (1993).
    [CrossRef] [PubMed]
  13. H. Kogelink, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2047 (1969).
  14. V. A. Komotskii and V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. 63, 239-242 (1987).
  15. R. D. Vre and L. Hesselink, “Analysis of photorefractive stratified volume holographic optical elements,” J. Opt. Soc. Am. B 11, 1800-1808 (1994).
    [CrossRef]
  16. Y. Ding, D. D. Nolte, Z. Zheng, A. Kanan, A. M. Weiner, and G. A. Brost, “Bandwidth study of volume holography in photorefractive InP:Fe for femtosecond pulse readout at 1.5 μm,” J. Opt. Soc. Am. B 15, 2763-2768 (1998).
    [CrossRef]
  17. C. Wang, L. Liu, A. Yan, D. Liu, D. Li, and W. Qu, “Pulse shaping properties of volume holographic gratings in anisotropic media,” J. Opt. Soc. Am. A 23, 3191-3196 (2006).
    [CrossRef]
  18. A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
    [CrossRef]
  19. 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.
  20. D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332-335 (1976).
    [CrossRef]
  21. S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

2007 (2)

D. Yang, H. Wang, X. Guo, J. Zhao, and H. Xiang, “Wavelength demultiplexing with layered multiple Bragg gratings in LiNbO3:Fe crystal,” Appl. Opt. 46, 5604-5607 (2007).
[CrossRef] [PubMed]

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

2006 (1)

2005 (1)

2003 (1)

1999 (1)

1998 (1)

1997 (1)

K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1987 (1)

V. A. Komotskii and V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. 63, 239-242 (1987).

1986 (1)

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235-249 (1986).

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)

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. 49, 85-88 (1980).

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. Kogelink, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2047 (1969).

Brost, G. A.

Chambers, D. M.

Chen, G.

S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

Cooke, D. J.

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

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]

Gaylord, T. K.

Glytsis, E. N.

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, X.

Hesselink, L.

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.

Jannson, T.

K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
[CrossRef]

Johnson, R. V.

G. P. Nordin, R. V. Johnson, and A. R. Tanguay, “Diffraction properties of stratified volume holographic optical elements,” J. Opt. Soc. Am. A 9, 2206-2217 (1992).
[CrossRef]

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235-249 (1986).

Kanan, A.

Kim, S.

Kogelink, H.

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

Komotskii, V. A.

V. A. Komotskii and V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. 63, 239-242 (1987).

Lambertus, H.

D. V. Raymond and H. Lambertus, “Dynamic multiple wavelength filter using a stratified volume holographic optical element,” U.S. patent 5,640,256 (June 17, 1997).

Leyva, V.

Li, D.

Liu, D.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

C. Wang, L. Liu, A. Yan, D. Liu, D. Li, and W. Qu, “Pulse shaping properties of volume holographic gratings in anisotropic media,” J. Opt. Soc. Am. A 23, 3191-3196 (2006).
[CrossRef]

Liu, J.

S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

Liu, L.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

C. Wang, L. Liu, A. Yan, D. Liu, D. Li, and W. Qu, “Pulse shaping properties of volume holographic gratings in anisotropic media,” J. Opt. Soc. Am. A 23, 3191-3196 (2006).
[CrossRef]

Luan, Z.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

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]

Nikulin, V. F.

V. A. Komotskii and V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. 63, 239-242 (1987).

Nolte, D. D.

Nordin, G. P.

Qu, W.

Rakuljic, G. A.

Raymond, D. V.

D. V. Raymond and H. Lambertus, “Dynamic multiple wavelength filter using a stratified volume holographic optical element,” U.S. patent 5,640,256 (June 17, 1997).

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]

Shi, S.

S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

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.

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

Spariosu, K.

K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
[CrossRef]

Tanguay, A. R.

G. P. Nordin, R. V. Johnson, and A. R. Tanguay, “Diffraction properties of stratified volume holographic optical elements,” J. Opt. Soc. Am. A 9, 2206-2217 (1992).
[CrossRef]

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235-249 (1986).

Tengara, I.

K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
[CrossRef]

Vre, R. D.

Wang, C.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

C. Wang, L. Liu, A. Yan, D. Liu, D. Li, and W. Qu, “Pulse shaping properties of volume holographic gratings in anisotropic media,” J. Opt. Soc. Am. A 23, 3191-3196 (2006).
[CrossRef]

Wang, H.

Weiner, A. M.

Wu, S.

Wu, Y.

Xiang, H.

Yakimovich, A. P.

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. 49, 85-88 (1980).

Yan, A.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

C. Wang, L. Liu, A. Yan, D. Liu, D. Li, and W. Qu, “Pulse shaping properties of volume holographic gratings in anisotropic media,” J. Opt. Soc. Am. A 23, 3191-3196 (2006).
[CrossRef]

Yang, D.

Zhao, J.

Zhao, W.

S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

Zheng, Z.

Zhou, Y.

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

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

J. Opt. A, Pure Appl. Opt. (1)

A. Yan, L. Liu, D. Liu, Y. Zhou, Z. Luan, and C. Wang, “Analysis of an ultrashort pulsed finite beam diffracted by volume gratings,” J. Opt. A, Pure Appl. Opt. 9, 66-72 (2007).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

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. Eng. (1)

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235-249 (1986).

Opt. Express (1)

Opt. Lett. (1)

Opt. Spectrosc. (2)

V. A. Komotskii and V. F. Nikulin, “Theoretical analysis of diffraction of a Gaussian optical beam by a system of two diffraction gratings,” Opt. Spectrosc. 63, 239-242 (1987).

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. 49, 85-88 (1980).

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]

Proc. SPIE (1)

K. Spariosu, I. Tengara, and T. Jannson, “Stratified volume diffractive elements: modeling and applications,” Proc. SPIE 3133, 101-109 (1997).
[CrossRef]

Other (4)

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

D. V. Raymond and H. Lambertus, “Dynamic multiple wavelength filter using a stratified volume holographic optical element,” U.S. patent 5,640,256 (June 17, 1997).

S. Shi, G. Chen, W. Zhao, and J. Liu, Nonlinear Optics (Xi'An, 2003), pp. 371 (in Chinese).

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.

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Figures (6)

Fig. 1
Fig. 1

Model of a system of multilayer volume holographic gratings read by an ultrashort laser pulse.

Fig. 2
Fig. 2

Normalized spectral distributions of the diffraction intensity in the two-layer system read by an ultrashort laser pulse at τ = 50 fs : (a) T 1 = T 2 = 0.5 T 0 , and the relative distance between layers d 1 T 0 = 0 , 0.3 , 0.6 , 0.9 , (b) d 1 = 0.5 T 0 , T 1 + T 2 = T 0 , and the relative thickness between two gratings T 1 T 2 = 0.1 0.9 , 0.2 0.8 , 0.3 0.7 , 0.5 0.5 , (c) T 1 = T 2 = 0.5 T 0 , d 1 = 0.1 T 0 , and the grating period Λ = 1 , 3, and 5.

Fig. 3
Fig. 3

Variations of the diffraction bandwidth as a function of τ with the same parameters as Figs. 2a, 2b.

Fig. 4
Fig. 4

Normalized spectral distributions of the diffraction intensity in the two-, five-, and eleven-layer systems of MVHGs with identical holographic gratings separated by gaps of equal magnitude ( T i = 0.5 T 0 and d i = 0.1 T 0 ) at τ = 50 fs .

Fig. 5
Fig. 5

Variation of the total diffraction intensity η Tol in the two-layer system as a function of τ with the same parameters as Figs. 2a, 2b.

Fig. 6
Fig. 6

Variation of the total diffraction intensity η Tol as a function of τ in the two-, five-, and eleven-layer systems of MVHGs with the same parameters as Fig. 3.

Equations (24)

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n ( ω ) = n 0 ( ω ) + n 1 cos ( K r ) n 1 n 0 ( ω ) ,
E ( x , z , ω ) = e ̂ r R i ( z , ω ) exp ( j k r r ) + e ̂ s S i ( z , ω ) exp ( j k s r ) ,
E ( x , z , ω ) = e ̂ r R i ( ω ) exp ( j k r 0 r ) + e ̂ s S i ( ω ) exp ( j k s 0 r ) ,
[ R i r S i r ] = [ m i 11 m i 12 m i 21 m i 22 ] × [ R i l S i l ] ,
where m i 11 = [ cos ( V T i ) + j ξ V sin ( V T i ) ] exp ( j ξ T i ) ,
m i 12 = j γ V C S C R sin ( V T i ) exp ( j ξ T i ) ,
m i 21 = j γ V C R C S sin ( V T i ) exp ( j ξ T i ) ,
m i 22 = [ cos ( V T i ) j ξ V sin ( V T i ) ] exp ( j ξ T i ) .
[ R ( i + 1 ) l S ( i + 1 ) l ] = [ D i ] × [ R i r S i r ] ,
[ D i ] = [ 1 0 0 exp ( j ϑ d i C S ) ] .
[ R ( T d , ω ) S ( T d , ω ) ] = [ M C ] × [ R 0 ( 0 , ω ) S 0 ( 0 , ω ) ] .
T d = i = 1 N T i + i = 1 N 1 d i ,
[ M C ] = M N D N 1 M N 1 D i M i D 1 M 1 ,
I R ( T d , ω ) = R ( T d , ω ) 2 , I S ( T d , ω ) = S ( T d , ω ) 2 .
η λ ( ω ) = [ C S I S ( T d , ω ) ] [ C R I 0 ( 0 , ω ) ] ,
η Tol = C S C R I S ( T d , ω ) d ω I 0 ( 0 , ω ) d ω .
n 1 = n 0 3 ( ω 0 ) γ 13 E sc 2 ,
n 2 ( λ ) = a 0 + a 1 λ 2 a 2 a 3 λ 2 ,
u 0 ( t ) = exp ( j ω 0 t ) exp ( 2 ln 2 t 2 τ 2 ) ,
U 0 ( ω ) = π τ 2 2 ln 2 exp [ τ 2 2 ln 2 ( ω ω 0 ) 2 4 ] ,
ϑ = π v p Λ 2 n ( ω 0 ) v g Δ λ ,
v p = c n ( ω 0 ) ,
v g = c n ( ω 0 ) λ 0 d n ( ω ) d λ λ = λ 0
Δ λ G = 16 π ξ ¯ n ( ω 0 ) cos θ K 2 v g v p ,

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