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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First-harmonic diffusion-based model applied to a polyvinyl-alcohol– acrylamide-based photopolymer

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J. Opt. Soc. Am. B 20(10) 2052-2060 (2003)

References

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  1. J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart, The International Journal for Light and Electron Optics)  112, 449–463 (2001).
    [Crossref]
  2. F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials using analytic non-local diffusion models,” Appl. Opt. 41, 845–852 (2002).
    [Crossref]
  3. R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
    [Crossref]
  4. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
    [Crossref]
  5. S. Piazzolla and B. Jenkins, “Holographic grating formation in photopolymers,” Opt. Lett. 21, 1075–1077 (1996).
    [Crossref] [PubMed]
  6. V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
    [Crossref]
  7. G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
    [Crossref]
  8. C. Neipp, S. Gallego, M. Ortuño, A. Márquez, M. Álvarez, A. Beléndez, and I. Pascual, “Fist harmonic diffusion based model applied to PVA/acrylamide based photopolymer,” J. Opt. Am. B (submitted).
  9. J. T. Sheridan and J. R. Lawrence, “Non-local response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17, 1108–1114 (2000).
    [Crossref]
  10. J. T. Sheridan, M. Downey, and 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]
  11. J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Adjusted intensity non-local diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621–629 (2002).
    [Crossref]
  12. G. Zhao and P. Mourolis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 115, 528–532 (1995).
    [Crossref]
  13. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Technol. J. 48, 2909–2947 (1969).
  14. M. G. Moharam and T. K. Gaylord, “Rigurous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  15. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficienct implementation of the rigurous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [Crossref]
  16. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).
  17. R. R. A. Syms, Practical Volume Holography (Clarendon Press, Oxford, 1990).
  18. S. Blaya, L. Carretero, R. Mallavia, A. Fimia, M Ulibarrena, and D. Levy, “Optimization of an acrylamide-based dry film used for holographic recording,” Appl. Opt. 37, 7604 (1998).
    [Crossref]
  19. C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
    [Crossref]
  20. C. García, A. Fimia, and 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]
  21. S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
    [Crossref] [PubMed]
  22. 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]

2003 (2)

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

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]

2002 (2)

2001 (3)

J. T. Sheridan, M. Downey, and 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]

C. García, A. Fimia, and 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]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart, The International Journal for Light and Electron Optics)  112, 449–463 (2001).
[Crossref]

2000 (2)

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

J. T. Sheridan and J. R. Lawrence, “Non-local response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17, 1108–1114 (2000).
[Crossref]

1999 (1)

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
[Crossref]

1998 (1)

1997 (1)

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[Crossref]

1996 (1)

1995 (2)

1994 (1)

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[Crossref]

1991 (1)

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[Crossref]

1981 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Technol. J. 48, 2909–2947 (1969).

Adhami, R. R.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[Crossref]

Álvarez, M.

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

Beléndez, A.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

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

Blaya, S.

Carretero, L.

Colvin, V. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[Crossref]

Cooke, D. J.

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

Downey, M.

J. T. Sheridan, M. Downey, and 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]

Fimia, A.

C. García, A. Fimia, and 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]

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
[Crossref]

S. Blaya, L. Carretero, R. Mallavia, A. Fimia, M Ulibarrena, and D. Levy, “Optimization of an acrylamide-based dry film used for holographic recording,” Appl. Opt. 37, 7604 (1998).
[Crossref]

Gallego, S.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

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

García, C.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

C. García, A. Fimia, and 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]

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
[Crossref]

Gaylord, T. K.

Glytsis, E. N.

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]

Grann, E. B.

Gregory, D. A.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[Crossref]

Harris, A. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[Crossref]

Jenkins, B.

Karpov, G. M.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Technol. J. 48, 2909–2947 (1969).

Lanteigne, D. J.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[Crossref]

Larson, R. G.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[Crossref]

Lawrence, J. R.

Lemeshko, V. V.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

Levy, D.

Mallavia, R.

Márquez, A.

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

Moharam, M. G.

Mourolis, P.

G. Zhao and P. Mourolis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 115, 528–532 (1995).
[Crossref]

Mouroulis, P.

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[Crossref]

Neipp, C.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

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

O’Neill, F. T.

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials using analytic non-local diffusion models,” Appl. Opt. 41, 845–852 (2002).
[Crossref]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Adjusted intensity non-local diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621–629 (2002).
[Crossref]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart, The International Journal for Light and Electron Optics)  112, 449–463 (2001).
[Crossref]

J. T. Sheridan, M. Downey, and 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]

Obukhovsky, V. V.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

Ortuño, M.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

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

Pascual, I.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer,” Opt. Express 11, 181–190 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-181
[Crossref] [PubMed]

C. García, A. Fimia, and 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]

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
[Crossref]

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

Piazzolla, S.

Pommet, D. A.

Schilling, M. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[Crossref]

Sheridan, J. T.

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Adjusted intensity non-local diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621–629 (2002).
[Crossref]

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials using analytic non-local diffusion models,” Appl. Opt. 41, 845–852 (2002).
[Crossref]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart, The International Journal for Light and Electron Optics)  112, 449–463 (2001).
[Crossref]

J. T. Sheridan, M. Downey, and 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. T. Sheridan and J. R. Lawrence, “Non-local response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17, 1108–1114 (2000).
[Crossref]

Smirnova, T. N.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

Solymar, L.

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

Syms, R. R. A.

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

Ulibarrena, M

Wu, S.

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]

Zhao, G.

G. Zhao and P. Mourolis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 115, 528–532 (1995).
[Crossref]

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[Crossref]

Appl. Opt. (2)

Appl. Opt.s (1)

C. García, A. Fimia, and I. Pascual, “Diffraction efficiency and signal-to-noise ratio of diffuse-object holograms in real time in polyvinyl alcohol photopolymers,” Appl. Opt.s 38, 5548 (1999).
[Crossref]

Appl. Phys. B (1)

C. García, A. Fimia, and 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, and 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 and 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, and 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. 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]

Microwave Opt. Technol. Lett. (1)

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[Crossref]

Opt. Commun. (2)

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun. 174, 391–404 (2000).
[Crossref]

G. Zhao and P. Mourolis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 115, 528–532 (1995).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart, The International Journal for Light and Electron Optics)  112, 449–463 (2001).
[Crossref]

Other (3)

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

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)

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

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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