Abstract

Some of the theoretical models in the literature describing the mechanism of hologram formation in photopolymer materials predict the existence of higher harmonics in the Fourier expansion of the recorded refractive index. Nevertheless, quantitative information is only obtained for the first harmonic of the refractive index using Kogelnik’s Coupled Wave Theory. In this work we apply the Rigorous Coupled Wave Theory to demonstrate that when recording phase diffraction gratings in PVA/acrylamide photopolymer materials, a second order grating is also recorded in the hologram even when the material is exposed to a sinusoidal interference pattern. The influence of this second order grating on the efficiency of the first order for replay at the first on-Bragg angular replay condition is studied and the size of the 2nd harmonic examined.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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Appl. Opt. (4)

Appl. Phys. B (1)

C. García, A. Fimia, I. Pascual, �??Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: mechanism of polymerization,�?? Appl. Phys. B 72, 311-316 (2001).
[CrossRef]

Bell Sys. Technol. J. (1)

H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Sys. Technol. J. 48, 2909-2947 (1969).

J. Appl. Phys. (1)

V. L. Colvin, R. G. Larson, A. L. Harris, M. L. Schilling, �??Quantitative model of volume hologram formation in photopolymers,�?? J. Appl. Phys. 81, 5913-5923 (1997).
[CrossRef]

J. Mod. Opt. (1)

G. Zhao, P. Mouroulis, �??Diffusion model of hologram formation in dry photopolymer materials,�?? J. Mod. Opt. 41, 1929-1939 (1994).
[CrossRef]

J. Opt. A: Pure and Appl. Opt (1)

J. T. Sheridan, M. Downey, F. T. O�??Neill, �??Diffusion based model of holographic grating formation in photopolymers: Generalised non-local material responses,�?? J. Opt. A: Pure and Appl. Opt. 3, 477-488 (2001).
[CrossRef]

J. Opt. Am. B (1)

C. Neipp, S. Gallego, M. Ortuño, A. Márquez, M. �?lvarez, A. Beléndez and I. Pascual, �??Fist harmonic diffusion based model applied to PVA/acrylamide based photopolymer,�?? J. Opt. Am. B (submitted).

J. Opt. Soc. Am. (1)

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

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

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

S. Wu and E. N. Glytsis, "Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and rigorous coupled-wave analysis," J. Opt. Soc. Am. B. 20, 1177-1188 (2003).
[CrossRef]

Opt. Commun. (2)

G. Zhao, P. Mourolis, �??Second order grating formation in dry holographic photopolymers,�?? Opt. Commun. 115, 528-532 (1995).
[CrossRef]

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, V. V. Lemeshko, �??Spatial transfer of matter as a method of holographic recording in photoformers,�?? Opt. Commun. 174, 391-404 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

J. R. Lawrence, F. T. O�??Neill, J. T. Seridan, �??Photopolymer holographic recording material,�?? Optik (Stuttgart, The International Journal for Light and Electron Optics) 112, 449-463 (2001).
[CrossRef]

Other (2)

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

R. R. A. Syms, Practical Volume Holography (Clarendon Press, Oxford, 1990).

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Figures (4)

Fig. 1.
Fig. 1.

Relative error of the first order efficiency, at first Bragg angle condition, for transmission diffraction gratings of different spatial frequencies for different values of the ratio ε2 /ε1 : 1/2, 1/4 and 1/8.

Fig. 2.
Fig. 2.

Angular responses of the first and second order efficiency for a transmission diffraction grating recorded on PVA/acrylamide photopolymer material with a spatial frequency of 545 lines/mm and a thickness of 73 µm.

Fig. 3.
Fig. 3.

Angular responses of the first and second order efficiency for a transmission diffraction grating recorded on PVA/acrylamide photopolymer material with a spatial frequency of 545 lines/mm and a thickness of 105 µm.

Fig. 4.
Fig. 4.

Angular responses of the first and second order efficiency for a transmission diffraction grating recorded on PVA/acrylamide photopolymer material with a spatial frequency of 1125 lines/mm and a thickness of 33 µm.

Tables (3)

Tables Icon

Table 1. Parameters of the theoretical simulations for transmission diffraction gratings recorded on PVA/Acrylamide photopolymers

Tables Icon

Table 2. Values of ε2 /ε1 for a transmission grating with a spatial frequency of 545 lines/mm predicted by the diffusion models presented in Refs. [9,11].

Tables Icon

Table 3. Values of ε2 /ε1 for a transmission grating with a spatial frequency of 1125 lines/mm predicted by the diffusion models presented in Refs. [9,11].

Equations (16)

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ε ( x , z ) = h ε h exp [ j h K · r ]
K = 2 π Λ
ε ( x ) = h ε h exp [ j h K x ]
E 1 = exp [ j ( k x 0 x + k z 0 z ) ] + i R i exp [ j ( k xi x k zi 1 z ) ]
E 3 = i T i exp { j [ k xi x k zi 3 ( z d ) ] }
k xi = k x 0 i K
k zi 1 = ( k 0 2 ε 1 k xi 2 ) 1 2 1 = 1 , 3
E 2 y = i S yi ( z ) exp ( j k xi x )
H 2 x = j ( ε 0 μ 0 ) 1 2 i U xi ( z ) exp ( j k xi x )
S yi z = k 0 U xi
U xi z = ( k xi 2 k 0 ) S yi k 0 p ε ( i p ) S yp
η u R = R i R i * Re ( k zi 1 k z 0 )
η i T = T i T i * Re ( k zi 3 k z 0 )
ε ( x ) = ε 0 + ε 1 cos [ Kx ] + ε 2 cos [ 2 Kx ]
Error = η ( 1 ) η ( 2 ) η ( 2 )
ν = π ε 1 d λ 0 2 ε 0 1 2 cos θ

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