Abstract

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO3 crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.

© 2006 Optical Society of America

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    [CrossRef]

2004

X. Yang, B. Yang, and B. Yu, "Diffraction study of photorefractive hologram under ultrashort pulse readout," Optik (Stuttgart) 115, 512-516 (2004).
[CrossRef]

1998

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]

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

1997

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

1995

1993

1992

1976

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

1969

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

Athale, R. A.

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: Lasers Opt. 66, 339-345 (1998).
[CrossRef]

Brost, G. A.

Buse, K.

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

Chen, A. G.-S.

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]

Günter, P.

P. Günter and J.-P. Huignard, "Photoreactive 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), p. 100 (in Chinese).

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

Hill, K. B.

Huignard, J.-P.

P. Günter and J.-P. Huignard, "Photoreactive 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.

Kanan, A.

Kogelnik, H.

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

Leaird, D. E.

Ling, Z.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), p. 100 (in Chinese).

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

Liu, S.

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), p. 100 (in Chinese).

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

Montemezzani, G.

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

Nolte, D. D.

Paek, E. G.

Purchase, K. G.

Raj, K.

Reitze, D. H.

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.

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]

Teng, S.

S. Teng, Applications of the Diffraction in Optical Communication and Optical Information Processing (Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences, 2004), pp. 104-121 (in Chinese).

Weiner, A. M.

Weiner, M.

Yang, B.

X. Yang, B. Yang, and B. Yu, "Diffraction study of photorefractive hologram under ultrashort pulse readout," Optik (Stuttgart) 115, 512-516 (2004).
[CrossRef]

Yang, X.

X. Yang, B. Yang, and B. Yu, "Diffraction study of photorefractive hologram under ultrashort pulse readout," Optik (Stuttgart) 115, 512-516 (2004).
[CrossRef]

Yu, B.

X. Yang, B. Yang, and B. Yu, "Diffraction study of photorefractive hologram under ultrashort pulse readout," Optik (Stuttgart) 115, 512-516 (2004).
[CrossRef]

Zgonik, M.

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

Zheng, Z.

Appl. Phys. B: Lasers Opt.

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

Bell Syst. Tech. J.

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

J. Opt. Soc. Am. B

Opt. Commun.

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

Opt. Lett.

Optik (Stuttgart)

X. Yang, B. Yang, and B. Yu, "Diffraction study of photorefractive hologram under ultrashort pulse readout," Optik (Stuttgart) 115, 512-516 (2004).
[CrossRef]

Phys. Rev. E

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

Other

S. Liu, R. Guo, and Z. Ling, Photorefractive Nonlinear Optics (Chinese Standard, 1992), p. 100 (in Chinese).

P. Günter and J.-P. Huignard, "Photoreactive 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), p. 136 (in Chinese).

S. Teng, Applications of the Diffraction in Optical Communication and Optical Information Processing (Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences, 2004), pp. 104-121 (in Chinese).

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Figures (5)

Fig. 1
Fig. 1

Model of a volume holographic grating in an anisotropic crystal read by the o or e component of a UPB with arbitrary linear polarization state.

Fig. 2
Fig. 2

Variation of the grating bandwidth Δ ω G i and Δ ω G o Δ ω G e with the grating space Λ, where d = 1 mm , E S C = 5.0 × 10 6 Vm 1 in a Li Nb O 3 crystal.

Fig. 3
Fig. 3

Variation of the diffraction bandwidth Δ ω S i with the bandwidth ratio R b w , where Λ = 3 μ m , d = 1 mm , and E S C = 5.0 × 10 6 Vm 1 in a Li Nb O 3 crystal.

Fig. 4
Fig. 4

Temporal intensity distributions (a) of the o diffracted pulsed beams, (b) of the e diffracted pulsed beams, (c) of the o transmitted pulsed beams, and (d) of the e transmitted pulsed beams vary with the polarization angle φ at Δ τ inp = 20 fs , Λ = 3 μ m , d = 1 mm , and E S C = 5.0 × 10 6 Vm 1 .

Fig. 5
Fig. 5

Variation of the total diffraction efficiency η Tot with the polarization angle φ and the TFWHM Δ τ inp of the input UPB, where d = 1 mm and Λ = 3 μ m .

Equations (23)

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K S i = K R i K Δ K i ,
cos θ i d R i ( z , ω ) d z = j κ i ( ω ) S i ( z , ω ) exp ( i Δ K i z ) ,
cos θ i d S i ( z , ω ) d z = j κ i ( ω ) R i ( z , ω ) exp ( i Δ K i z ) , ( i = o or e ) ,
tan δ e = n e 2 ( ω 0 ) n o 2 ( ω 0 ) 2 [ n o 2 ( ω 0 ) cos 2 θ e + n e 2 ( ω 0 ) sin 2 θ e ] sin 2 θ e .
κ i ( ω ) = ω 4 c e R i ε 1 e S i 2 n i ( ω ) cos δ i
Δ K i = K tan θ i c K 2 2 ω n i ( ω ) cos θ i .
Δ K i = Δ ω K 2 c 2 cos θ i ω 0 2 n g i n i 2 ( ω 0 ) ,
n g i = n i ( ω 0 ) + ω d n i ( ω ) d ω ω = ω 0 = n i ( λ 0 ) λ 0 d n i ( ω ) d λ λ = λ 0
S i ( d , ω ) = j R i ( 0 , ω ) exp ( j ξ i ) sin ( v i 2 ξ i 2 ) 1 2 ( 1 + ξ i 2 v i 2 ) 1 2 ,
R i ( d , ω ) = R i ( 0 , ω ) exp ( j ξ i ) [ cos ( v i 2 + ξ i 2 ) 1 2 + j sin ( v i 2 + ξ i 2 ) 1 2 ( 1 + v i 2 ξ i 2 ) 1 2 ] ,
υ i = ω d 4 c cos θ i e R i ε i e S i n i ( ω ) cos δ i ,
ξ i = Δ K i d 2 .
I S i ( d , ω ) = S i ( d , ω ) 2 , I R i ( d , ω ) = R i ( d , ω ) 2
I s i ( d , t ) = s i ( d , t ) 2 , I r i ( d , t ) = r i ( d , t ) 2
Δ ω G i = 4 cos θ i ω 0 2 ξ ¯ i d K 2 c n i 2 ( ω 0 ) n g i
Δ ω range = Δ ω S o Δ ω S e .
R b w = Δ ω inp Δ ω G i
η Tot = I S o ( d , ω ) d ω + I S e ( d , ω ) d ω U 0 ( ω ) 2 d ω .
u 0 ( t ) = exp ( i ω 0 t t 2 T 2 ) ,
U 0 ( ω ) = 1 2 π T exp [ T 2 ( ω ω 0 ) 2 4 ] .
υ i = ω d n 1 i 2 c cos θ i ,
n 1 o = n o 3 ( λ 0 ) γ 13 E S C 2 ,
n 1 e = cos 2 θ e [ γ 13 n o 4 ( λ 0 ) sin 2 θ e + γ 33 n e 0 4 ( λ 0 ) cos 2 θ e ] E S C [ 2 n e ( λ 0 ) cos δ e ] ,

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