Abstract

Based on Kogelnik’s coupled-wave theory and matrix optics, generation of femtosecond double pulses by modulating thickness of the buffer layer of two-layer volume holographic grating (TL-VHG) is discussed. Expressions of diffraction field when a femtosecond pulse incidents on the TL-VHG are deduced. Simulation results show when thickness of the buffer layer increases from 6mm to 11mm or even larger, one incident pulse splits into double femtosecond pulses with the same duration and peak intensity, and pulse interval is linearly proportional to the thickness. The reason of these phenomena is due to the interference of diffraction waves reconstructed from two gratings and phase shift resulting from the buffer layer thickness. Time-delay of diffracted double pulses is explained by group time delay of periodic media. It is shown that the slope of the pulse interval with respect to the thickness of buffer layer is 2 times of that of pulse time-delay. Furthermore, we demonstrate it is possible to control the output double pulses’ duration and pulse interval by varying the grating thickness.

© 2013 Optical Society of America

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References

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2011

2010

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

2009

A. Yan, L. Liu, Y. Zhi, D. Liu, and J. Sun, “Bragg diffraction of multiplayer volume holographic gratings under ultrashort laser pulse readout,” J. Opt. Soc. Am. A26(1), 135–141 (2009).
[CrossRef]

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

2007

2006

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

2005

T. Nagata, M. Kamata, and M. Obara, “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett.86(25), 251103 (2005).
[CrossRef]

B. Wang, J. Jiang, D. M. Chambers, J. Cai, and G. P. Nordin, “Stratified waveguide grating coupler for normal fiber incidence,” Opt. Lett.30(8), 845–847 (2005).
[CrossRef] [PubMed]

2003

2001

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

2000

1999

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulse,” IEEE J. Quantum Electron.35(4), 501–509 (1999).
[CrossRef]

D. M. Chambers and G. P. Nordin, “Stratified volume diffractive optical elements as high-efficiency gratings,” J. Opt. Soc. Am. A16(5), 1184–1193 (1999).
[CrossRef]

1996

1995

1994

R. De Vré and L. Hesselink, “Analysis of photorefractive stratified volume holographic optical elements,” J. Soc. Opt. Am. B11(9), 1800–1808 (1994).
[CrossRef]

1993

A. Granger, L. Song, and R. A. Lessard, “Multiple beam generation using a stratified volume holographic grating,” Appl. Opt.32(14), 2534–2537 (1993).
[CrossRef] [PubMed]

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

1992

1988

1984

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

1980

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

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

Acioli, L. H.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

Bañares, L.

Bosco, C. A. C.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

Brener, I.

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

Cai, J.

Calvo, M. L.

Chambers, D. M.

Che, W.

Cheben, P.

Chuang, S. L.

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

De Vré, R.

R. De Vré and L. Hesselink, “Diffraction analysis of layered structures of photorefractive gratings,” J. Opt. Soc. Am. A13(2), 285–295 (1996).
[CrossRef]

R. De Vré and L. Hesselink, “Analysis of photorefractive stratified volume holographic optical elements,” J. Soc. Opt. Am. B11(9), 1800–1808 (1994).
[CrossRef]

Felinto, D.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

Granger, A.

Guo, X.

Han, B.

Han, F.

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Hernández-Garay, M. P.

Hesselink, L.

R. De Vré and L. Hesselink, “Diffraction analysis of layered structures of photorefractive gratings,” J. Opt. Soc. Am. A13(2), 285–295 (1996).
[CrossRef]

R. De Vré and L. Hesselink, “Analysis of photorefractive stratified volume holographic optical elements,” J. Soc. Opt. Am. B11(9), 1800–1808 (1994).
[CrossRef]

Hsu, K. Y.

Iaconis, C.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulse,” IEEE J. Quantum Electron.35(4), 501–509 (1999).
[CrossRef]

Ishige, Y.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Iwai, S.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Izquierdo, J. G.

Jiang, J.

Johnson, R. V.

Kamata, M.

T. Nagata, M. Kamata, and M. Obara, “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett.86(25), 251103 (2005).
[CrossRef]

Kim, S.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

Lessard, R. A.

Lin, S. H.

Liu, D.

A. Yan, L. Liu, Y. Zhi, D. Liu, and J. Sun, “Bragg diffraction of multiplayer volume holographic gratings under ultrashort laser pulse readout,” J. Opt. Soc. Am. A26(1), 135–141 (2009).
[CrossRef]

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Liu, L.

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

A. Yan, L. Liu, Y. Zhi, D. Liu, and J. Sun, “Bragg diffraction of multiplayer volume holographic gratings under ultrashort laser pulse readout,” J. Opt. Soc. Am. A26(1), 135–141 (2009).
[CrossRef]

Luo, M. S.

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

Magnusson, R.

Martínez-Matos, O.

Mirovitskii, D. I.

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

Nagata, T.

T. Nagata, M. Kamata, and M. Obara, “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett.86(25), 251103 (2005).
[CrossRef]

Nordin, G. P.

Nuss, M. C.

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

Obara, M.

T. Nagata, M. Kamata, and M. Obara, “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett.86(25), 251103 (2005).
[CrossRef]

Okamoto, H.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Okimoto, Y.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Planken, P. C.

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

Qi, Y.

Rostovtseva, N. V.

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

Serov, O. B.

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

Song, L.

Sun, J.

A. Yan, L. Liu, Y. Zhi, D. Liu, and J. Sun, “Bragg diffraction of multiplayer volume holographic gratings under ultrashort laser pulse readout,” J. Opt. Soc. Am. A26(1), 135–141 (2009).
[CrossRef]

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Tanaka, S.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Tanguay, A. R.

Tokura, Y.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Vaveliuk, P.

Vianna, S. S.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

Walmsley, I. A.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulse,” IEEE J. Quantum Electron.35(4), 501–509 (1999).
[CrossRef]

Wan, L.

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Wang, B.

Wang, H.

Wang, K. P.

Wang, L.

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Wang, S. S.

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, Y. Zhi, D. Liu, and J. Sun, “Bragg diffraction of multiplayer volume holographic gratings under ultrashort laser pulse readout,” J. Opt. Soc. Am. A26(1), 135–141 (2009).
[CrossRef]

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Yan, X.

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Yang, C.

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Yang, D.

Yeh, P.

Zel’dovich, B. Y.

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

Zhang, G.

Zhao, J.

Zhi, Y.

Zhu, R.

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Zou, H.

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. B

A. Yan, L. Liu, L. Wang, D. Liu, J. Sun, and L. Wan, “Pulse shaping and diffraction properties of multi-layers reflection volume holographic gratings,” Appl. Phys. B96(1), 71–77 (2009).
[CrossRef]

Appl. Phys. Lett.

T. Nagata, M. Kamata, and M. Obara, “Optical waveguide fabrication with double pulse femtosecond lasers,” Appl. Phys. Lett.86(25), 251103 (2005).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

IEEE J. Quantum Electron.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulse,” IEEE J. Quantum Electron.35(4), 501–509 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Soc. Opt. Am. B

R. De Vré and L. Hesselink, “Analysis of photorefractive stratified volume holographic optical elements,” J. Soc. Opt. Am. B11(9), 1800–1808 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

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

Optik

C. Yang, X. Yan, R. Zhu, H. Zou, and F. Han, “Diffraction study of volume holographic gratings in dispersive photorefractive material for femtosecond pulse readout,” Optik121(12), 1138–1143 (2010).
[CrossRef]

Phys. Rev. A

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Accumulative effects in temporal coherent control,” Phys. Rev. A64(6), 063413 (2001).
[CrossRef]

Phys. Rev. B Condens. Matter

M. S. Luo, S. L. Chuang, P. C. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B Condens. Matter48(15), 11043–11050 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. Iwai, Y. Ishige, S. Tanaka, Y. Okimoto, Y. Tokura, and H. Okamoto, “Coherent control of charge and lattice dynamics in a photoinduced neutral-to-ionic transition of a charge-transfer compound,” Phys. Rev. Lett.96(5), 057403 (2006).
[CrossRef] [PubMed]

Sov. J. Quantum Electron.

B. Y. Zel’dovich, D. I. Mirovitskii, N. V. Rostovtseva, and O. B. Serov, “Characteristics of two-layer phase holograms,” Sov. J. Quantum Electron.14(3), 364–369 (1984).
[CrossRef]

Other

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2002).

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Figures (7)

Fig. 1
Fig. 1

Diagram of recording and reconstruction structure of TL-VHG: (a) Recording of VHGs in two grating layers with two coherent plane waves s and r; (b) Readout of the recorded TL-VHG with a femtosecond pulse u(t), and the transmitted and diffracted pulses are denoted by R(t) and S(t).

Fig. 2
Fig. 2

Instantaneous intensity distribution of the incident femtosecond Gaussian pulse when Δτ = 100fs.

Fig. 3
Fig. 3

Distributions of instantaneous diffracted intensity of TL-VHG when thickness of the buffer layer changes from (a): 0 mm to 0.8mm, (b): 1mm to 3.5mm.

Fig. 4
Fig. 4

Distributions of instantaneous diffraction intensity of TL-VHG when the thickness of buffer layer changes in the range of (a): 4mm to 6mm, (b): 7mm to 11mm.

Fig. 5
Fig. 5

Diagram of pulse interval of diffracted double pulses with respect to the thickness of buffer layer.

Fig. 6
Fig. 6

Time-delay of diffraction pulse with respect to the thickness of buffer layer of TL-VHG.

Fig. 7
Fig. 7

Distributions of instantaneous diffraction intensity of TL-VHG when thickness of the buffer layer is fixed at d = 7mm, while the thickness of two gratings changes from 1mm to 6mm.

Equations (18)

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

n= n 0 + n 1 cos( K r ) n 1 << n 0 .
U(0,ω)= 1 2π u(z=0,t) exp(jωt)dt= T 2 π exp[ T 2 (ω ω 0 ) 2 4 ].
E i (z,ω)= R i (z,ω)exp(j k gr r )+ S i (z,ω)exp(j k gd r ),
R i ' (z,ω)=jν S i (z,ω) C d / C r , S i ' (z,ω)+2jξ S i (z,ω)=jν R i (z,ω) C r / C d .
[ R ir S ir ]=[ m i11 m i12 m i21 m i22 ]×[ R il S il ]=[ M i ][ R il S il ].
m i11 =exp(jξ T i )[cos( ξ 2 + ν 2 T i )+ jξ ξ 2 + ν 2 sin( ξ 2 + ν 2 T i )], m i12 =j ν ξ 2 + ν 2 C d C r exp(jξ T i )sin( ξ 2 + ν 2 T i ), m i21 =j ν ξ 2 + ν 2 C r C d exp(jξ T i )sin( ξ 2 + ν 2 T i ), m i22 =exp(jξ T i )[cos( ξ 2 + ν 2 T i ) jξ ξ 2 + ν 2 sin( ξ 2 + ν 2 T i )].
[ R 2l S 2l ]=[ D ]×[ R 1r S 1r ],
[ D ]=[ 1 0 0 exp(2jζd) ],
ζ= k gd k gr 2 .
[ R(T,ω) S(T,ω) ]=[ M 2 ][D][ M 1 ][ U(0,ω) 0 ].
T= T 1 +d+ T 2 .
S(T,t)= S(T,ω) exp(jωt)dω,
I S (T,t)= | S(T,t) | 2 .
Δ λ G = 3 2 Λ T ( 2 n 0 Λ ) 2 λ 0 2 .
Δ ω P = 2πc λ 0 2 Δ λ p .
S(T,ω)=( M 221 M 111 + M 222 M 121 e 2jζd )U(0,ω),
V g =l ( ϕ ω ) 1 ,
τ g = l V g = ϕ ω .

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