Abstract

The kinetics of photosensitive polymer holographic recording materials are examined assuming a material that exhibits nonideal kinetic behavior. Previously, a linear relationship between monomer concentration and polymerization was assumed when deriving the nonlocal polymer-driven diffusion (NPDD) model. This is consistent with ideal kinetic conditions in which chain termination is governed by a bimolecular process. However, these models have been reported to disagree with experimental results. In a limiting case of nonideal kinetics it is assumed that primary termination is dominant. In this case the NPDD model must be modified to incorporate a quadratic relationship between the monomer concentration and the polymerization rate. By use of a multiharmonic expansion method of solution the predictions of ideal (bimolecular or linear) and nonideal (primary or quadratic) kinetic models are compared. By using these models we carried out numerical fits to experimental growth curves of gratings recorded in an acrylamide-based cross-linked photopolymer system. Superior fits are achieved by use of the primary termination model. Physical parameters such as the diffusion constant are extracted and compared with results previously reported in the literature.

© 2005 Optical Society of America

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References

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  1. S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, "Design, fabrication, and performance of preferential-order volume grating waveguide couplers," Appl. Opt. 39, 1223-1232 (2000).
    [CrossRef]
  2. A. Sato, M. Scepanovic, and R. K. Kostuk, "Holographic edge-illuminated polymer Bragg gratings for dense wavelength division optical filters at 1550 nm," Appl. Opt. 42, 778-784 (2003).
    [CrossRef] [PubMed]
  3. L. Dahr, A. Hale, K. Curtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, "Photopolymer recording media for high density holographic data storage," in Conference Digest, Optical Data Storage 2000 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 158-160.
  4. G. Zhao and P. Mouroulis, "Diffusion model of hologram formation in dry photopolymer materials," J. Mod. Opt. 41, 1929-1939 (1994).
    [CrossRef]
  5. J. T. Sheridan and J. R. Lawrence, "Nonlocal-response diffusion model of holographic recording in photopolymer," J. Opt. Soc. Am. A 17, 1108-1114 (2000).
    [CrossRef]
  6. J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Adjusted intensity nonlocal diffusion model of photopolymer grating formation," J. Opt. Soc. Am. B 19, 621-629 (2002).
    [CrossRef]
  7. J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
    [CrossRef]
  8. H. Kogelnik, "Coupled wave theory for thick holographic gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
    [CrossRef]
  9. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981).
    [CrossRef]
  10. C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
    [CrossRef]
  11. I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
    [CrossRef]
  12. V. Moreau, Y. Renotte, and Y. Lion, "Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model," Appl. Opt. 41, 3427-3435 (2002).
    [CrossRef] [PubMed]
  13. J. H. Kwon, H. C. Hwang, and K. C. Woo, "Analysis of temporal behavior of beams diffracted by volume gratings formed in photopolymers," J. Opt. Soc. Am. B 16, 1651-1657 (1999).
    [CrossRef]
  14. G. Odian, Principles of Polymerization (Wiley, New York, 1991).
  15. C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
    [CrossRef]
  16. W. L. Wilson, InPhase Technologies, 2000 Pike Road, Longmont, Colo. (personal communication, June 2003).
  17. J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
    [CrossRef]
  18. H.-G. Elias, An Introduction to Polymer Science (VCH Verlag GmbH, Weinheim, Germany, 1997).
  19. W. J. Tomlinson, "Organic photochemical refractive-index systems," in Advances in Photochemistry , Vol. 12, G. S. Hammond, K. Gollnick, and J. N. Pitts, eds. (Wiley, New York, 1980).
  20. E. El-Sheikh, C. Penny, F. Bakomska, R. Liu, A. Kamel, and J. Sticken, "Intelligent tutoring for polymer composite molding," presented at the Symposium on Low-Cost, High Speed Polymer Composites Processing, Michigan State University, Lansing, Mich., June 1, 1997, http://islnotes.cps.msu.edu/trp/back/fre_gel.html.
  21. P. Munk, Introduction to Molecular Science (Wiley, New York, 1989).
  22. S.-D. 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]
  23. J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
    [CrossRef]
  24. F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).
  25. S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
    [CrossRef]

2004 (1)

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

2003 (4)

A. Sato, M. Scepanovic, and R. K. Kostuk, "Holographic edge-illuminated polymer Bragg gratings for dense wavelength division optical filters at 1550 nm," Appl. Opt. 42, 778-784 (2003).
[CrossRef] [PubMed]

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

S.-D. 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]

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

2002 (2)

2001 (2)

J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
[CrossRef]

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
[CrossRef]

2000 (4)

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).

C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
[CrossRef]

S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, "Design, fabrication, and performance of preferential-order volume grating waveguide couplers," Appl. Opt. 39, 1223-1232 (2000).
[CrossRef]

J. T. Sheridan and J. R. Lawrence, "Nonlocal-response diffusion model of holographic recording in photopolymer," J. Opt. Soc. Am. A 17, 1108-1114 (2000).
[CrossRef]

1999 (1)

1998 (1)

I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

1994 (1)

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

1981 (1)

1969 (1)

H. Kogelnik, "Coupled wave theory for thick holographic gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
[CrossRef]

Acebal, P.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Alvarez, M. L.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

Aubrecht, I.

I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

Beléndez, A.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

Blaya, S.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
[CrossRef]

Carretero, L.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Downey, M.

J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
[CrossRef]

Fernández-Pousa, C. R.

C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
[CrossRef]

Fimia, A.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Gallego, S.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Hwang, H. C.

Kelly, J. V.

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick holographic gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
[CrossRef]

Kostuk, R. K.

Koudela, I.

I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

Kwon, J. H.

Lawrence, J. R.

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Adjusted intensity nonlocal 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 parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
[CrossRef]

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).

J. T. Sheridan and J. R. Lawrence, "Nonlocal-response diffusion model of holographic recording in photopolymer," J. Opt. Soc. Am. A 17, 1108-1114 (2000).
[CrossRef]

Lion, Y.

Madrigal, R. F.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Mallavia, R.

C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
[CrossRef]

Miller, M.

I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

Moharam , M. G.

Moreau, V.

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.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

O'Neill, F. T.

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Adjusted intensity nonlocal diffusion model of photopolymer grating formation," J. Opt. Soc. Am. B 19, 621-629 (2002).
[CrossRef]

J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
[CrossRef]

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
[CrossRef]

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).

Ortuno, M.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

Pascual, I.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

Renotte, Y.

Sato, A.

Scepanovic, M.

Schultz, S. M.

Sheridan, J. T.

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Adjusted intensity nonlocal diffusion model of photopolymer grating formation," J. Opt. Soc. Am. B 19, 621-629 (2002).
[CrossRef]

J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
[CrossRef]

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
[CrossRef]

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).

Sheridan , J. T.

Ulibarrena, M.

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Woo, K. C.

Wu , S.-D.

Zhao , G.

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

Appl. Opt. (3)

Appl. Phys. B: Lasers Opt. (2)

C. R. Fernández-Pousa, R. Mallavia, and S. Blaya, "Holographic determination of the irradiance dependence of linear-chain polymerization rates in photopolymer dry films," Appl. Phys. B: Lasers Opt. 70, 537-542 (2000).
[CrossRef]

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal, and A. Fimia, "Photopolymerization model for holographic gratings formation in photopolymers," Appl. Phys. B: Lasers Opt. 77, 639-662 (2003).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick holographic gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
[CrossRef]

J. Appl. Phys. (1)

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, "Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model," J. Appl. Phys. 90, 3142-3148 (2001).
[CrossRef]

J. Mod. Opt. (3)

C. Neipp, M. L. Alvarez, S. Gallego, M. Ortuno, J. T. Sheridan, I. Pascual, and A. Beléndez, "Angular responses of the first diffracted order in over-modulated volume diffraction gratings," J. Mod. Opt. 51, 1149-1162 (2004).
[CrossRef]

I. Aubrecht, M. Miller, and I. Koudela, "Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth," J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

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 Appl. Opt. (1)

J. T. Sheridan, M. Downey, and F. T. O'Neill, "Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses," J. Opt. A, Pure Appl. Opt. 3, 477-488 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Optik (Stuttgart) (1)

F. T. O'Neill, J. R. Lawrence, and J. T. Sheridan, "Automated recording and testing of holographic optical element arrays," Optik (Stuttgart) 111, 459-467 (2000).

Proc. SPIE (1)

J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, "Holographic photopolymer materials with nonlocal and nonlinear response," in Organic Holographic Materials and Applications, K. Meerholz, ed., Proc. SPIE 5216, 127-138 (2003).
[CrossRef]

Other (7)

H.-G. Elias, An Introduction to Polymer Science (VCH Verlag GmbH, Weinheim, Germany, 1997).

W. J. Tomlinson, "Organic photochemical refractive-index systems," in Advances in Photochemistry , Vol. 12, G. S. Hammond, K. Gollnick, and J. N. Pitts, eds. (Wiley, New York, 1980).

E. El-Sheikh, C. Penny, F. Bakomska, R. Liu, A. Kamel, and J. Sticken, "Intelligent tutoring for polymer composite molding," presented at the Symposium on Low-Cost, High Speed Polymer Composites Processing, Michigan State University, Lansing, Mich., June 1, 1997, http://islnotes.cps.msu.edu/trp/back/fre_gel.html.

P. Munk, Introduction to Molecular Science (Wiley, New York, 1989).

G. Odian, Principles of Polymerization (Wiley, New York, 1991).

W. L. Wilson, InPhase Technologies, 2000 Pike Road, Longmont, Colo. (personal communication, June 2003).

L. Dahr, A. Hale, K. Curtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, "Photopolymer recording media for high density holographic data storage," in Conference Digest, Optical Data Storage 2000 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 158-160.

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Figures (5)

Fig. 1
Fig. 1

Variation in the polymerization rate as a function of time (arbitrary units).

Fig. 2
Fig. 2

Harmonic amplitudes of monomer concentration with α=0 and σ=0, predicted by (a) model II, RII=1 and (b) model III, RIII=1 mol/cm3.

Fig. 3
Fig. 3

Harmonic amplitudes of polymer concentration where α=0 and σ=0 as predicted by (a) model II, RII=50 and (b) model III, RIII=50 mol/cm3.

Fig. 4
Fig. 4

Spatial distribution of polymer concentrations, where RIII=1 mol/cm3 mol and α=0.1. Solid curve, σ=0; long dashed curve, σ=1/64; short dashed curve σ=1/32, where σ is the normalized nonlocal length.

Fig. 5
Fig. 5

Fit to experimental data by use of estimated parameters given in Table 2. Spatial frequency=1250 lines/mm. Error bars are included to allow for the possibility of ±10% experimental error.

Tables (2)

Tables Icon

Table 1 Characteristic Parameters Extracted from Fits to Experimental Data with Model II

Tables Icon

Table 2 Best-Fit Parameters Extracted from Fits to Experimental Data with Model III

Equations (48)

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

F0=κI0γ(x),
IkdR,
Rd=d[R]/dt=kd[I],
R+MkiM1,
Mn+MkpMn+1,
Rr=fkd[I].
Ri=d[M1]/dt=ki[R][M],
d[R]/dt=fkd[I]-ki[R][M]=0.
Ri=ki[R][M]=fkd[I].
Mn+MmktcMn+m
Mn+MmktdMn+Mm.
Rt=kt[M]2,
fkd[I]=kt[M]2.
[M]stat=(fkd[I]/kt)1/2.
Rp=-d[M]/dt=kp[M][M],
Rp=kp(fkd/kt)1/2[I]1/2[M].
Ri=fΦIa,
Ia(x)=I(x)[1-exp(-Zd)]=I(x)(1-T),
[M]=fΦI(x)(1-T)kt1/2.
Rp=kp[M]fΦI(x)(1-T)kt1/2.
Rp=constant×[M]·l1/2,
Rp=constant×[M]β·lγ.
IkdR,
R+MkiM1.
Mn+MkpMn+1.
Mn+RktpMnR.
Ri=ki[R][M],
Rp=kp[M][M],
Rtp=ktp[M][R],
[M]=kiktp[M],
Rp=kpki[M]2ktp.
Rp=-[M]t=kp[M]βfΦI(x)(1-T)ktγ.
-[M]t=D 2[M]x2+Q[1+V cos(Kx)]γ[M]β,
Q=kpΦI0(1-T)ktγ.
u(x, t)t=x D(x, t) u(x, t)x--+0tR(x, x; t, t)F(x, t)×[u(x, t)]βdtdx.
R(x, x)=12πσ exp-(x-x)22σ,
du0(ξ)dξ=-14{4f0u0(ξ)2+(2f0+f2)u1(ξ)2+2(f0)u2(ξ)2+2f0u3(ξ)2+2u1(ξ)[(f1+f3)u2(ξ)+f2u3(ξ)]+4u0(ξ)[f1u1(ξ)+f2u2(ξ)+f3u3(ξ)]+2f1u2(ξ)u3(ξ)},
du1(ξ)dξ=-R Ch[ξ]u1(ξ)-R Sh[ξ]u2(ξ)-S14{4f1u0(ξ)2+3(f1+f3)u1(ξ)2+(2f1+f3)u2(ξ)2+2(2f0+f2)u2(ξ)u3(ξ)+2f1u3(ξ)2+4u0(ξ)[(2f0+f2u1)(ξ)+(f1+f3)u2(ξ)+f2u3(ξ)]+2u1(ξ)[2(f0+f2)u2(ξ)+(f1+2f3)u3(ξ)]},
du2(ξ)dξ=-R Sh[ξ][u1(ξ)+3u3(ξ)]-4R Ch[ξ]u2(ξ)-S24{4f2u0(ξ)2+2(f0+f2)u1(ξ)2+3f2u2(ξ)2+2(f1+2f3)u2(ξ)u3(ξ)+2f2u3(ξ)2+4u0(ξ)[(f1+f3)u1(ξ)+2f0u2(ξ)+f1u3(ξ)]+2u1(ξ)[(2f1+f3)u2(ξ)+(2f0+f2)u3(ξ)]},
du3(ξ)dξ=-3R Sh[ξ]u2(ξ)-9R Ch[ξ]u3(ξ)-S34{4f3u0(ξ)2+(f1+2f3)u1(ξ)2+(f1+2f3)u2(ξ)2+4f2u2(ξ)u3(ξ)+3f3u3(ξ)2+4u0(ξ)[f2u1(ξ)+f1u2(ξ)+2f0u3(ξ)]+2u1(ξ)[(2f0+f2)u2(ξ)+2f1u3(ξ)]},
Ch[ξ]=exp[-αF0t(1-V+1+V)/2]×cosh[αF0t(1+V-1-V)/2];
Sh[ξ]=exp[-αF0t(1-V+1+V)/2]×sinh[αF0t(1+V-1-V)/2];
N0(ξ)=14 0ξ{4f0u0(ξ)2+(2f0+f2)u1(ξ)2+2(f0)u2(ξ)2+2f0u3(ξ)2+2f1u2(ξ)u3(ξ)×2u1(ξ)[(f1+f3)u2(ξ)+f2u3(ξ)]+4u0(ξ)[f1u1(ξ)+f2u2(ξ)+f3u3(ξ)]}dξ,
N1(ξ)=S14 0ξ{4f1u0(ξ)2+(3f1+f3)u1(ξ)2+(2f1+f3)u2(ξ)2+2(2f0+f2)u2(ξ)u3(ξ)+2f1u3(ξ)2+4u0(ξ)[(2f0+f)u1(ξ)+(f1+f3)u2(ξ)+f2u3(ξ)]+2u1(ξ)[2(f0+f2)u2(ξ)+(f1+2f3)u3(ξ)]}dξ,
N2(ξ)=S24 0ξ{4f2u0(ξ)2+2(f0+f2)u1(ξ)2+3f2u2(ξ)2+2(f1+2f3)u2(ξ)u3(ξ)+2f2u3(ξ)2+4u0(ξ)[(f1+f3)u1(ξ)+2f0u2(ξ)+f1u3(ξ)]+2u1(ξ)[2(f1+f3)u2(ξ)+(2f0+f2)u3(ξ)]}dξ,
N3(ξ)=S34 0ξ{4f3u0(ξ)2+(f1+2f3)u1(ξ)2+(f1+2f3)u2(ξ)2+4f2u2(ξ)u3(ξ)+3f3u3(ξ)2+4u0(ξ)[f2u1(ξ)+f1u2(ξ)+2f0u3(ξ)]+2u1(ξ)[(2f0+f2)u2(ξ)+2f1u3(ξ)]}dξ.
n(x, ξ)=Cpi=0MNi(ξ)cos(iKx)+Cmi=0Mui(ξ)cos(iKx),
Cp=n1sN1s,

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