Abstract

The photochemical processes present during free-radical-based holographic grating formation are examined. A kinetic model is presented, which includes, in a more nearly complete and physically realistic way, most of the major photochemical and nonlocal photopolymerization-driven diffusion effects. These effects include: (i) non-steady-state kinetics (ii) spatially and temporally nonlocal polymer chain growth (iii) time varying photon absorption (iv) diffusion controlled viscosity effects (v) multiple termination mechanisms, and (vi) inhibition. The convergence of the predictions of the resulting model is then examined. Comparisons with experimental results are carried out in Part II of this series of papers [J. Opt. Soc. Am. B 26, 1746 (2009) ].

© 2009 Optical Society of America

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  1. M. R. Gleeson, S. Liu, R. R. McLeod, and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. Part II. Experimental validation,” J. Opt. Soc. Am. B 26, 1746-1754 (2009).
    [CrossRef]
  2. G. Manivannan and R. A. Lessard, “Trends in holographic recording materials,” Trends Polym. Sci. 2, 282-290 (1994).
  3. J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik 112, 449-463 (2001).
    [CrossRef]
  4. M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerisation in the formation of holographic gratings,” J. Opt. A 10, 024008 (2009).
    [CrossRef]
  5. S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
    [CrossRef]
  6. A. C. Sullivan, M. W. Grabowski, and R. R. McLeod, “Three-dimensional direct-write lithography into photopolymer,” Appl. Opt. 46, 295-301 (2007).
    [CrossRef] [PubMed]
  7. J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
    [CrossRef] [PubMed]
  8. J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
    [CrossRef]
  9. M. R. Gleeson, “Analysis of the photochemical kinetics in photopolymers for holographic data storage and hybrid photonic circuits,” Ph.D. thesis (University College Dublin, 2008).
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    [CrossRef]
  11. M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
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    [CrossRef]
  15. J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
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  16. M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
    [CrossRef]
  17. C. H. Bamford, A. D. Jenkins, and R. Johnston, “Termination by primary radicals in vinyl polymerization,” Trans. Faraday Soc. 55, 1451-1460 (1959).
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  19. M. D. Goodner and C. N. Bowman, “Modeling primary radical termination and its effects on autoacceleration in photopolymerization kinetics,” Macromolecules 32, 6552-6559 (1999).
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  21. A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
    [CrossRef]
  22. A. K. O'Brien and C. N. Bowman, “Modeling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15(2), 176-182 (2006).
    [CrossRef]
  23. M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
    [CrossRef]
  24. L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
    [CrossRef]
  25. T. Manabe, T. Utsumi, and S. Okamura, “Behavior of primary radicals in vinyl polymerization,” J. Polym. Sci. 58(166), 121-146 (1962).
    [CrossRef]
  26. C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).
  27. A. K. Doolittle, “Studies in Newtonian flow II. The dependence of the viscosity of liquids on free-space,” J. Appl. Phys. 22, 1471-1475 (1951).
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  28. A. Bondi, “Free volumes and free rotation in simple liquids and liquid saturated hydrocarbons,” J. Phys. Chem. 58, 929-939 (1954).
    [CrossRef]
  29. F. L. Marten and A. E. Hamielec, “High-conversion diffusion-controlled polymerization of styrene, Part 1,” J. Appl. Polym. Sci. 27(2), 489-505 (1982).
    [CrossRef]
  30. C. N. Bowman and N. A. Peppas, “Coupling of kinetics and volume relaxation during polymerizations of multiacrylates and multimethacrylates,” Macromolecules 24, 1914-1920 (1991).
    [CrossRef]
  31. M. L. Williams, R. F. Landel, and J. D. Ferry, “Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Phys. Rev. 98, 1549-1549 (1955).
    [CrossRef]
  32. K. A. Berchtold, T. M. Lovestead, and C. N. Bowman, “Coupling chain length dependent and reaction diffusion controlled termination in the free radical polymerization of multivinyl (meth)acrylates,” Macromolecules 35, 7968-7975 (2002).
  33. I. Aubrecht, M. Miler, 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).
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    [CrossRef]
  38. 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]
  39. 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]
  40. J. V. Kelly, F. T. ONeill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407-416 (2005).
    [CrossRef]
  41. J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
    [PubMed]
  42. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2945 (1969).
  43. 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]
  44. C. Neipp, A. Belendez, S. Gallego, M. Ortuno, I. Pascual, and J. T. Sheridan, “Angular responses of the first and second diffracted orders in transmission diffraction grating recorded on photopolymer material,” Opt. Express 11, 1835-1843 (2003).
    [CrossRef] [PubMed]
  45. J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
    [CrossRef]
  46. R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
    [CrossRef]

2009 (2)

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerisation in the formation of holographic gratings,” J. Opt. A 10, 024008 (2009).
[CrossRef]

M. R. Gleeson, S. Liu, R. R. McLeod, and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. Part II. Experimental validation,” J. Opt. Soc. Am. B 26, 1746-1754 (2009).
[CrossRef]

2008 (3)

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
[CrossRef]

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

2007 (4)

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
[CrossRef]

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

A. C. Sullivan, M. W. Grabowski, and R. R. McLeod, “Three-dimensional direct-write lithography into photopolymer,” Appl. Opt. 46, 295-301 (2007).
[CrossRef] [PubMed]

2006 (4)

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

A. K. O'Brien and C. N. Bowman, “Modeling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15(2), 176-182 (2006).
[CrossRef]

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[CrossRef]

2003 (2)

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 77, 639-662 (2003).
[CrossRef]

C. Neipp, A. Belendez, S. Gallego, M. Ortuno, I. Pascual, and J. T. Sheridan, “Angular responses of the first and second diffracted orders in transmission diffraction grating recorded on photopolymer material,” Opt. Express 11, 1835-1843 (2003).
[CrossRef] [PubMed]

2002 (2)

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]

K. A. Berchtold, T. M. Lovestead, and C. N. Bowman, “Coupling chain length dependent and reaction diffusion controlled termination in the free radical polymerization of multivinyl (meth)acrylates,” Macromolecules 35, 7968-7975 (2002).

2001 (1)

J. R. Lawrence, F. T. O'Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik 112, 449-463 (2001).
[CrossRef]

2000 (2)

T. Trentler, J. Boyd, and V. Colvin, “Epoxy resin photopolymer composites for volume holography,” Chem. Mater. 12, 1431-1438 (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 (2)

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]

M. D. Goodner and C. N. Bowman, “Modeling primary radical termination and its effects on autoacceleration in photopolymerization kinetics,” Macromolecules 32, 6552-6559 (1999).
[CrossRef]

1998 (2)

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[CrossRef]

I. Aubrecht, M. Miler, 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]

1997 (2)

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]

M. D. Goodner, H. R. Lee, and C. N. Bowman, “Method for determining the kinetic parameters in diffusion-controlled free-radical homopolymerizations,” Ind. Eng. Chem. Res. 36, 1247-1252 (1997).
[CrossRef]

1996 (1)

C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).

1994 (1)

G. Manivannan and R. A. Lessard, “Trends in holographic recording materials,” Trends Polym. Sci. 2, 282-290 (1994).

1993 (1)

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

1991 (1)

C. N. Bowman and N. A. Peppas, “Coupling of kinetics and volume relaxation during polymerizations of multiacrylates and multimethacrylates,” Macromolecules 24, 1914-1920 (1991).
[CrossRef]

1985 (1)

H. K. Mahabadi, “Effects of chain-length dependence of termination rate-constant on the kinetics of free-radical polymerization. Part 1. Evaluation of an analytical expression relating the apparent rate-constant of termination to the number-average degree of polymerization,” Macromolecules 18, 1319-1324 (1985).
[CrossRef]

1982 (1)

F. L. Marten and A. E. Hamielec, “High-conversion diffusion-controlled polymerization of styrene, Part 1,” J. Appl. Polym. Sci. 27(2), 489-505 (1982).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2945 (1969).

1962 (1)

T. Manabe, T. Utsumi, and S. Okamura, “Behavior of primary radicals in vinyl polymerization,” J. Polym. Sci. 58(166), 121-146 (1962).
[CrossRef]

1959 (1)

C. H. Bamford, A. D. Jenkins, and R. Johnston, “Termination by primary radicals in vinyl polymerization,” Trans. Faraday Soc. 55, 1451-1460 (1959).
[CrossRef]

1955 (1)

M. L. Williams, R. F. Landel, and J. D. Ferry, “Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Phys. Rev. 98, 1549-1549 (1955).
[CrossRef]

1954 (1)

A. Bondi, “Free volumes and free rotation in simple liquids and liquid saturated hydrocarbons,” J. Phys. Chem. 58, 929-939 (1954).
[CrossRef]

1951 (1)

A. K. Doolittle, “Studies in Newtonian flow II. The dependence of the viscosity of liquids on free-space,” J. Appl. Phys. 22, 1471-1475 (1951).
[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 77, 639-662 (2003).
[CrossRef]

Amatguerri, F.

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

Aubrecht, I.

I. Aubrecht, M. Miler, 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]

Bamford, C. H.

C. H. Bamford, A. D. Jenkins, and R. Johnston, “Termination by primary radicals in vinyl polymerization,” Trans. Faraday Soc. 55, 1451-1460 (1959).
[CrossRef]

Belendez, A.

Berchtold, K. A.

K. A. Berchtold, T. M. Lovestead, and C. N. Bowman, “Coupling chain length dependent and reaction diffusion controlled termination in the free radical polymerization of multivinyl (meth)acrylates,” Macromolecules 35, 7968-7975 (2002).

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 77, 639-662 (2003).
[CrossRef]

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[CrossRef]

Bondi, A.

A. Bondi, “Free volumes and free rotation in simple liquids and liquid saturated hydrocarbons,” J. Phys. Chem. 58, 929-939 (1954).
[CrossRef]

Bowman, C. N.

A. K. O'Brien and C. N. Bowman, “Modeling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15(2), 176-182 (2006).
[CrossRef]

K. A. Berchtold, T. M. Lovestead, and C. N. Bowman, “Coupling chain length dependent and reaction diffusion controlled termination in the free radical polymerization of multivinyl (meth)acrylates,” Macromolecules 35, 7968-7975 (2002).

M. D. Goodner and C. N. Bowman, “Modeling primary radical termination and its effects on autoacceleration in photopolymerization kinetics,” Macromolecules 32, 6552-6559 (1999).
[CrossRef]

M. D. Goodner, H. R. Lee, and C. N. Bowman, “Method for determining the kinetic parameters in diffusion-controlled free-radical homopolymerizations,” Ind. Eng. Chem. Res. 36, 1247-1252 (1997).
[CrossRef]

C. N. Bowman and N. A. Peppas, “Coupling of kinetics and volume relaxation during polymerizations of multiacrylates and multimethacrylates,” Macromolecules 24, 1914-1920 (1991).
[CrossRef]

Boyd, J.

T. Trentler, J. Boyd, and V. Colvin, “Epoxy resin photopolymer composites for volume holography,” Chem. Mater. 12, 1431-1438 (2000).
[CrossRef]

Bunning, T. J.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[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 77, 639-662 (2003).
[CrossRef]

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[CrossRef]

Close, C. E.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
[CrossRef]

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
[CrossRef] [PubMed]

Colvin, V.

T. Trentler, J. Boyd, and V. Colvin, “Epoxy resin photopolymer composites for volume holography,” Chem. Mater. 12, 1431-1438 (2000).
[CrossRef]

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]

Connors, K. A.

K. A. Connors, Chemical Kinetics: The Study of Reaction Rates in Solutions (Wiley-VCH, 1990).

Decker, C.

C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).

Decker, D.

C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).

Doolittle, A. K.

A. K. Doolittle, “Studies in Newtonian flow II. The dependence of the viscosity of liquids on free-space,” J. Appl. Phys. 22, 1471-1475 (1951).
[CrossRef]

Elzaouk, B.

C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).

Ferry, J. D.

M. L. Williams, R. F. Landel, and J. D. Ferry, “Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Phys. Rev. 98, 1549-1549 (1955).
[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 77, 639-662 (2003).
[CrossRef]

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[CrossRef]

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

Gallego, S.

Galstian, T.

S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
[CrossRef]

A. V. Galstyan, R. S. Hakobyan, S. Harbour, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials,” Electronic-Liquid Crystal Communications (2004). Available at http://e_lc.org/Documents/T.V Galstian_2004_05_05_11_13_17.

Galstyan, A. V.

A. V. Galstyan, R. S. Hakobyan, S. Harbour, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials,” Electronic-Liquid Crystal Communications (2004). Available at http://e_lc.org/Documents/T.V Galstian_2004_05_05_11_13_17.

Gleeson, M. R.

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerisation in the formation of holographic gratings,” J. Opt. A 10, 024008 (2009).
[CrossRef]

M. R. Gleeson, S. Liu, R. R. McLeod, and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. Part II. Experimental validation,” J. Opt. Soc. Am. B 26, 1746-1754 (2009).
[CrossRef]

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
[CrossRef] [PubMed]

M. R. Gleeson, “Analysis of the photochemical kinetics in photopolymers for holographic data storage and hybrid photonic circuits,” Ph.D. thesis (University College Dublin, 2008).

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M. D. Goodner and C. N. Bowman, “Modeling primary radical termination and its effects on autoacceleration in photopolymerization kinetics,” Macromolecules 32, 6552-6559 (1999).
[CrossRef]

M. D. Goodner, H. R. Lee, and C. N. Bowman, “Method for determining the kinetic parameters in diffusion-controlled free-radical homopolymerizations,” Ind. Eng. Chem. Res. 36, 1247-1252 (1997).
[CrossRef]

Grabowski, M. W.

Hakobyan, R. S.

A. V. Galstyan, R. S. Hakobyan, S. Harbour, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials,” Electronic-Liquid Crystal Communications (2004). Available at http://e_lc.org/Documents/T.V Galstian_2004_05_05_11_13_17.

Hamielec, A. E.

F. L. Marten and A. E. Hamielec, “High-conversion diffusion-controlled polymerization of styrene, Part 1,” J. Appl. Polym. Sci. 27(2), 489-505 (1982).
[CrossRef]

Harbour, S.

S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
[CrossRef]

A. V. Galstyan, R. S. Hakobyan, S. Harbour, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials,” Electronic-Liquid Crystal Communications (2004). Available at http://e_lc.org/Documents/T.V Galstian_2004_05_05_11_13_17.

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]

Hwang, H. C.

Jenkins, A. D.

C. H. Bamford, A. D. Jenkins, and R. Johnston, “Termination by primary radicals in vinyl polymerization,” Trans. Faraday Soc. 55, 1451-1460 (1959).
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C. H. Bamford, A. D. Jenkins, and R. Johnston, “Termination by primary radicals in vinyl polymerization,” Trans. Faraday Soc. 55, 1451-1460 (1959).
[CrossRef]

Kasala, K.

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

Kelly, J. V.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
[CrossRef]

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
[CrossRef]

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
[CrossRef]

J. V. Kelly, F. T. ONeill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407-416 (2005).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2945 (1969).

Koudela, I.

I. Aubrecht, M. Miler, 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.

Landel, R. F.

M. L. Williams, R. F. Landel, and J. D. Ferry, “Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Phys. Rev. 98, 1549-1549 (1955).
[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.

Lee, H. R.

M. D. Goodner, H. R. Lee, and C. N. Bowman, “Method for determining the kinetic parameters in diffusion-controlled free-radical homopolymerizations,” Ind. Eng. Chem. Res. 36, 1247-1252 (1997).
[CrossRef]

Lessard, R. A.

G. Manivannan and R. A. Lessard, “Trends in holographic recording materials,” Trends Polym. Sci. 2, 282-290 (1994).

Liu, S.

M. R. Gleeson, S. Liu, R. R. McLeod, and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. Part II. Experimental validation,” J. Opt. Soc. Am. B 26, 1746-1754 (2009).
[CrossRef]

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

Lopez, N.

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
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K. A. Berchtold, T. M. Lovestead, and C. N. Bowman, “Coupling chain length dependent and reaction diffusion controlled termination in the free radical polymerization of multivinyl (meth)acrylates,” Macromolecules 35, 7968-7975 (2002).

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 77, 639-662 (2003).
[CrossRef]

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Belendez, and A. Fimia, “Theoretical and experimental study of the bleaching of a dye in a film-polymerization process,” Appl. Opt. 37, 4496-4499 (1998).
[CrossRef]

Mahabadi, H. K.

H. K. Mahabadi, “Effects of chain-length dependence of termination rate-constant on the kinetics of free-radical polymerization. Part 1. Evaluation of an analytical expression relating the apparent rate-constant of termination to the number-average degree of polymerization,” Macromolecules 18, 1319-1324 (1985).
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Mallavia, R.

Manabe, T.

T. Manabe, T. Utsumi, and S. Okamura, “Behavior of primary radicals in vinyl polymerization,” J. Polym. Sci. 58(166), 121-146 (1962).
[CrossRef]

Manivannan, G.

G. Manivannan and R. A. Lessard, “Trends in holographic recording materials,” Trends Polym. Sci. 2, 282-290 (1994).

Marten, F. L.

F. L. Marten and A. E. Hamielec, “High-conversion diffusion-controlled polymerization of styrene, Part 1,” J. Appl. Polym. Sci. 27(2), 489-505 (1982).
[CrossRef]

Mateos, F.

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

McLeod, R. R.

Miler, M.

I. Aubrecht, M. Miler, 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]

Natarajan, L. V.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[CrossRef]

Neipp, C.

O'Brien, A. K.

A. K. O'Brien and C. N. Bowman, “Modeling the effect of oxygen on photopolymerization kinetics,” Macromol. Theory Simul. 15(2), 176-182 (2006).
[CrossRef]

Odian, G.

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

O'Duill, S.

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

Okamura, S.

T. Manabe, T. Utsumi, and S. Okamura, “Behavior of primary radicals in vinyl polymerization,” J. Polym. Sci. 58(166), 121-146 (1962).
[CrossRef]

ONeill, F. T.

O'Neill, F. T.

Ortuno, M.

Pascual, I.

Peppas, N. A.

C. N. Bowman and N. A. Peppas, “Coupling of kinetics and volume relaxation during polymerizations of multiacrylates and multimethacrylates,” Macromolecules 24, 1914-1920 (1991).
[CrossRef]

Pineda, J.

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

Rewari, A.

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

Sabol, D.

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

Saravanamuttu, K.

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

Sastre, R.

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

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.

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerisation in the formation of holographic gratings,” J. Opt. A 10, 024008 (2009).
[CrossRef]

M. R. Gleeson, S. Liu, R. R. McLeod, and J. T. Sheridan, “Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions. Part II. Experimental validation,” J. Opt. Soc. Am. B 26, 1746-1754 (2009).
[CrossRef]

M. R. Gleeson, D. Sabol, S. Liu, C. E. Close, J. V. Kelly, and J. T. Sheridan, “Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length,” J. Opt. Soc. Am. B 25, 396-406 (2008).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling for holographic data storage,” J. Opt. A 10, 115203 (2008).
[CrossRef]

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

S. Harbour, J. V. Kelly, T. Galstian, and J. T. Sheridan, “Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals,” Opt. Commun. 278, 28-33 (2007).
[CrossRef]

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,” J. Opt. Soc. Am. B 23, 2079-2088 (2006).
[CrossRef]

J. V. Kelly, F. T. ONeill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407-416 (2005).
[CrossRef]

J. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,” Opt. Express 13, 6990-7004 (2005).
[CrossRef] [PubMed]

C. Neipp, A. Belendez, S. Gallego, M. Ortuno, I. Pascual, and J. T. Sheridan, “Angular responses of the first and second diffracted orders in transmission diffraction grating recorded on photopolymer material,” Opt. Express 11, 1835-1843 (2003).
[CrossRef] [PubMed]

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,” Optik 112, 449-463 (2001).
[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]

Sullivan, A. C.

Sutherland, R. L.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[CrossRef]

Tondiglia, V. P.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[CrossRef]

Trentler, T.

T. Trentler, J. Boyd, and V. Colvin, “Epoxy resin photopolymer composites for volume holography,” Chem. Mater. 12, 1431-1438 (2000).
[CrossRef]

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 77, 639-662 (2003).
[CrossRef]

Utsumi, T.

T. Manabe, T. Utsumi, and S. Okamura, “Behavior of primary radicals in vinyl polymerization,” J. Polym. Sci. 58(166), 121-146 (1962).
[CrossRef]

Williams, M. L.

M. L. Williams, R. F. Landel, and J. D. Ferry, “Temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” Phys. Rev. 98, 1549-1549 (1955).
[CrossRef]

Woo, K. C.

Zhang, J.

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

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 77, 639-662 (2003).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2945 (1969).

Chem. Mater. (1)

T. Trentler, J. Boyd, and V. Colvin, “Epoxy resin photopolymer composites for volume holography,” Chem. Mater. 12, 1431-1438 (2000).
[CrossRef]

Ind. Eng. Chem. Res. (1)

M. D. Goodner, H. R. Lee, and C. N. Bowman, “Method for determining the kinetic parameters in diffusion-controlled free-radical homopolymerizations,” Ind. Eng. Chem. Res. 36, 1247-1252 (1997).
[CrossRef]

J. Am. Chem. Soc. (1)

J. Zhang, K. Kasala, A. Rewari, and K. Saravanamuttu, “Self-trapping of spatially and temporally incoherent white light in a photochemical medium,” J. Am. Chem. Soc. 128, 406-407 (2006).
[CrossRef] [PubMed]

J. Appl. Phys. (6)

M. R. Gleeson, S. Liu, S. O'Duill, and J. T. Sheridan, “Examination of the photoinitiation processes in photopolymer materials,” J. Appl. Phys. 104, 064917 (2008).
[CrossRef]

M. R. Gleeson, J. V. Kelly, D. Sabol, C. E. Close, S. Liu, and J. T. Sheridan, “Modelling the photochemical effects present during holographic grating formation in photopolymer materials,” J. Appl. Phys. 102, 023108 (2007).
[CrossRef]

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. V. Kelly, M. R. Gleeson, C. E. Close, F. T. O'Neill, J. T. Sheridan, S. Gallego, and C. Neipp, “Temporal response and first order volume changes during grating formation in photopolymers,” J. Appl. Phys. 99, 113105 (2006).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J. Bunning, “Phenomenological model of anisotropic volume hologram formation in liquid-crystal-photopolymer mixtures,” J. Appl. Phys. 96, 951-965 (2004).
[CrossRef]

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[CrossRef]

J. Appl. Polym. Sci. (1)

F. L. Marten and A. E. Hamielec, “High-conversion diffusion-controlled polymerization of styrene, Part 1,” J. Appl. Polym. Sci. 27(2), 489-505 (1982).
[CrossRef]

J. Macromol. Sci. Pure Appl. Chem. (1)

C. Decker, B. Elzaouk, and D. Decker, “Kinetic study of ultrafast photopolymerizations reactions,” J. Macromol. Sci. Pure Appl. Chem. A33(2), 173-190 (1996).

J. Mod. Opt. (2)

I. Aubrecht, M. Miler, 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]

A. Fimia, N. Lopez, F. Mateos, R. Sastre, J. Pineda, and F. Amatguerri, “Elimination of oxygen inhibition in photopolymer system used as holographic recording materials,” J. Mod. Opt. 40, 699-706 (1993).
[CrossRef]

J. Nanosci. Nanotechnol. (1)

J. T. Sheridan, M. R. Gleeson, C. E. Close, and J. V. Kelly, “Optical response of photopolymer materials for holographic data storage applications,” J. Nanosci. Nanotechnol. 7, 232-242 (2007).
[PubMed]

J. Opt. A (2)

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerisation in the formation of holographic gratings,” J. Opt. A 10, 024008 (2009).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Predictions of the amplitudes of the first two harmonics of monomer concentration, u 0 and u 1 , when 4 (solid curve), 8 (short-dashed curve), and 12 (long-dashed curve), harmonics are retained during the simulations.

Fig. 2
Fig. 2

Amplitudes of polymer concentration, N 0 and N 1 , when 4 (solid curve), 8 (short-dashed curve), and 12 (long-dashed curve), harmonics are retained.

Fig. 3
Fig. 3

Comparison of the simulated growth curves for the holographic grating refractive index modulation, for a 2 mW cm 2 exposure, for 4 (full curve), 8 (short-dashed curve), and 12 (long-dashed curve) harmonics.

Equations (48)

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R p = k p M M = k p φ R i k t M ,
I h ν 2 R ,
R + M k i M 1 , chain initiator .
M n + M k p M n + 1 , growing polymer chain.
M n + M m k tc M n + m , dead polymer,
M n + M m k td M n + M m , dead polymer,
M n + R k tp M n R , dead polymer.
R + Z k z , R ( R + Z , and or R Z ) , scavenged radical,
M n + Z k z , M ( M n + Z , and or M n Z ) , dead polymer.
R i ( x , t ) = R i ( t ) [ 1 + V cos ( K x ) ] = 2 Φ I a ( t ) [ 1 + V cos ( K x ) ] ,
I a ( t ) = I 0 d { [ exp ( ε d A 0 ) 1 ] exp ( ε φ I 0 t ) 1 + [ exp ( ε d A 0 ) 1 ] exp ( ε φ I 0 t ) } ,
k p = k p 0 1 + exp [ A p ( 1 f v 1 f c p v ) ] ,
k t = k t 0 1 + { R D k p M k t 0 + exp [ A t ( 1 f v 1 f c t v ) ] } 1 ,
f v = f m v φ m + f p v ( 1 φ m ) ,
d Z ( x , t ) d t = d d x [ D z d Z ( x , t ) d x ] k z , R Z ( x , t ) R ( x , t ) k z , M Z ( x , t ) M ( x , t ) ,
k z = k z , 0 exp ( E z R T ) ,
d R ( x , t ) d t = R i ( x , t ) k i R ( x , t ) u ( x , t ) k t p R ( x , t ) M ( x , t ) k z R ( x , t ) Z ( x , t ) ,
d M ( x , t ) d t = k i R ( x , t ) u ( x , t ) 2 k t [ M ( x , t ) ] 2 k t p R ( x , t ) M ( x , t ) k z Z ( x , t ) M ( x , t ) ,
d u ( x , t ) d t = d d x [ D m ( x , t ) d u ( x , t ) d x ] k i R ( x , t ) u ( x , t ) G ( x , x ) F ( x , t ) u ( x , t ) d x ,
G ( x , x ) = 1 2 π σ exp [ ( x x ) 2 2 σ ] ,
F ( x , t ) = F 0 [ 1 + V cos ( K x ) ] γ = κ ( I 0 ) γ [ 1 + V cos ( K x ) ] γ ,
F ( x , t ) = k p M ( x , t ) ,
X ( x , t ) = j = 0 X j ( t ) cos ( j K x ) ,
Z 0 ( t = 0 ) = Z 0 ,
u 0 ( t = 0 ) = U 0 ,
u j > 0 ( t = 0 ) = R j 0 ( t = 0 ) = M j 0 ( t = 0 ) = 0 .
d R 0 ( t ) d t = R i ( t ) k t p [ M 0 ( t ) R 0 ( t ) + 1 2 M 1 ( t ) R 1 ( t ) + 1 2 M 2 ( t ) R 2 ( t ) + 1 2 M 3 ( t ) R 3 ( t ) ] k i [ R 0 ( t ) u 0 ( t ) + 1 2 R 1 ( t ) u 1 ( t ) + 1 2 R 2 ( t ) u 2 ( t ) + 1 2 R 3 ( t ) u 3 ( t ) ] k z [ R 0 ( t ) Z 0 ( t ) + 1 2 R 1 ( t ) Z 1 ( t ) ] ,
d R 1 ( t ) d t = V R i ( t ) k t p { M 1 ( t ) R 0 ( t ) + [ M 0 ( t ) + 1 2 M 2 ( t ) ] R 1 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] R 2 ( t ) + 1 2 M 2 ( t ) R 3 ( t ) } k i { R 1 ( t ) u 0 ( t ) + [ R 0 ( t ) + 1 2 R 2 ( t ) ] u 1 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 2 ( t ) + R 2 ( t ) u 3 ( t ) } k z [ R 1 ( t ) Z 0 ( t ) + R 0 ( t ) Z 1 ( t ) + 1 2 R 2 ( t ) Z 1 ( t ) ] ,
d R 2 ( t ) d t = k t p { M 2 ( t ) R 0 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] R 1 ( t ) + M 0 ( t ) R 2 ( t ) + 1 2 M 1 ( t ) R 3 ( t ) } k i { R 2 ( t ) u 0 ( t ) 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 1 ( t ) + R 0 ( t ) u 2 ( t ) + 1 2 R 1 ( t ) u 3 ( t ) } k z { R 2 ( t ) Z 0 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] Z 1 ( t ) } ,
d R 3 ( t ) d t = k t p [ M 3 ( t ) R 0 ( t ) + 1 2 M 2 ( t ) R 1 ( t ) + 1 2 M 1 ( t ) R 2 ( t ) + M 0 ( t ) R 3 ( t ) ] k i [ R 3 ( t ) u 0 ( t ) + 1 2 R 2 ( t ) u 1 ( t ) + 1 2 R 1 ( t ) u 2 ( t ) + 1 2 R 0 ( t ) u 3 ( t ) ] k z [ R 3 ( t ) Z 0 ( t ) + 1 2 R 2 ( t ) Z 1 ( t ) ] .
d M 0 ( t ) d t = k i 2 [ 2 R 0 ( t ) u 0 ( t ) + R 1 ( t ) u 1 ( t ) + R 2 ( t ) u 2 ( t ) + R 3 ( t ) u 3 ( t ) ] k t [ 2 M 0 ( t ) 2 + M 1 ( t ) 2 + M 2 ( t ) 2 + M 3 ( t ) 2 ] k t p 2 [ 2 M 0 ( t ) R 0 ( t ) + M 1 ( t ) R 1 ( t ) + M 2 ( t ) R 2 ( t ) + M 3 ( t ) R 3 ( t ) ] k z [ 2 M 0 ( t ) Z 0 ( t ) + M 1 ( t ) Z 1 ( t ) ] ,
d M 1 ( t ) d t = 2 k t [ 2 M 0 ( t ) M 1 ( t ) + M 1 ( t ) M 2 ( t ) + M 2 ( t ) M 3 ( t ) ] k t p [ M 1 ( t ) R 0 ( t ) + [ M 0 ( t ) + 1 2 M 2 ( t ) ] R 1 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] R 2 ( t ) + 1 2 M 2 ( t ) R 3 ( t ) ] + k i { R 1 ( t ) u 0 ( t ) + [ R 0 ( t ) + 1 2 R 2 ( t ) ] u 1 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 2 ( t ) + 1 2 R 2 ( t ) u 3 ( t ) } 2 k z [ M 1 ( t ) Z 0 ( t ) + M 0 ( t ) Z 1 ( t ) + 1 2 M 2 ( t ) Z 1 ( t ) ] ,
d M 2 ( t ) d t = k t [ M 1 ( t ) 2 + 4 M 0 ( t ) M 2 ( t ) + 2 M 1 ( t ) M 3 ( t ) ] k t p { M 2 ( t ) R 0 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] R 1 ( t ) + M 0 ( t ) R 2 ( t ) + 1 2 M 1 ( t ) R 3 ( t ) } + k i { R 2 ( t ) u 0 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 1 ( t ) + R 0 ( t ) u 2 ( t ) + 1 2 R 1 ( t ) u 3 ( t ) } k z [ 2 M 2 ( t ) Z 0 ( t ) + M 1 ( t ) Z 1 ( t ) + M 3 ( t ) Z 1 ( t ) ] ,
d M 3 ( t ) d t = 2 k t [ M 1 ( t ) M 2 ( t ) + 2 M 0 ( t ) M 3 ( t ) ] k t p [ M 3 ( t ) R 0 ( t ) + 1 2 M 2 ( t ) R 1 ( t ) + 1 2 M 1 ( t ) R 2 ( t ) + 1 2 M 0 ( t ) R 3 ( t ) ] + k i [ R 3 ( t ) u 0 ( t ) + 1 2 R 2 ( t ) u 1 ( t ) + 1 2 R 1 ( t ) u 2 ( t ) + R 0 ( t ) u 3 ( t ) ] k z [ 2 M 3 ( t ) Z 0 ( t ) + M 2 ( t ) Z 1 ( t ) ] .
d u 0 ( t ) d t = k p 2 [ 2 M 0 ( t ) u 0 ( t ) + M 1 ( t ) u 1 ( t ) + k p M 2 ( t ) u 2 ( t ) + M 3 ( t ) u 3 ( t ) ] k i 2 [ 2 R 0 ( t ) u 0 ( t ) + R 1 ( t ) u 1 ( t ) + k p R 2 ( t ) u 2 ( t ) + R 3 ( t ) u 3 ( t ) ] ,
d u 1 ( t ) d t = S 1 k p { M 1 ( t ) u 0 ( t ) + [ M 0 ( t ) + 1 2 M 2 ( t ) ] u 1 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] u 2 ( t ) + 1 2 M 2 ( t ) u 3 ( t ) } k i { R 1 ( t ) u 0 ( t ) + [ R 0 ( t ) + 1 2 R 2 ( t ) ] u 1 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 2 ( t ) + R 2 ( t ) u 3 ( t ) } K 2 { [ D m , 0 ( t ) 1 2 D m , 2 ( t ) ] u 1 ( t ) + [ D m , 1 ( t ) D m , 3 ( t ) ] u 2 ( t ) 3 2 D m , 2 ( t ) u 3 ( t ) } ,
d u 2 ( t ) d t = S 2 k p { M 2 ( t ) u 0 ( t ) + 1 2 [ M 1 ( t ) + M 3 ( t ) ] u 1 ( t ) + M 0 ( t ) u 2 ( t ) + 1 2 M 1 ( t ) u 3 ( t ) } k i { R 2 ( t ) u 0 ( t ) + 1 2 [ R 1 ( t ) + R 3 ( t ) ] u 1 ( t ) + R 0 ( t ) u 2 ( t ) + 1 2 R 1 ( t ) u 3 ( t ) } K 2 [ D m , 1 ( t ) u 1 ( t ) D m , 3 ( t ) u 1 ( t ) + 4 D m , 0 ( t ) u 2 ( t ) + 3 D m , 1 ( t ) u 3 ( t ) ] ,
d u 3 ( t ) d t = S 3 k p [ M 3 ( t ) u 0 ( t ) + 1 2 M 2 ( t ) u 1 ( t ) + 1 2 M 1 ( t ) u 2 ( t ) + M 0 ( t ) u 3 ( t ) ] k i [ R 3 ( t ) u 0 ( t ) + 1 2 R 2 ( t ) u 1 ( t ) + 1 2 R 1 ( t ) u 2 ( t ) + R 0 ( t ) u 3 ( t ) ] 3 K 2 [ 3 D m , 0 ( t ) u 3 ( t ) + D m , 1 ( t ) u 2 ( t ) + 1 2 D m , 2 ( t ) u 1 ( t ) ] ,
d Z 0 ( t ) d t = k z { [ 2 M 0 ( t ) + R 0 ( t ) ] Z 0 ( t ) + [ M 1 ( t ) + 1 2 R 1 ( t ) ] Z 1 ( t ) } ,
d Z 1 ( t ) d t = k z { [ 2 M 1 ( t ) + R 1 ( t ) ] Z 0 ( t ) + [ 2 M 0 ( t ) + M 2 ( t ) + R 0 ( t ) + 1 2 R 2 ( t ) ] Z 1 ( t ) } K 2 D z Z 1 ( t ) .
N ( x , t ) = 0 t + G ( x , x ) F ( x , t ) u ( x , t ) d x d t = 0 t + k p G ( x , x ) l = 0 M l ( t ) cos ( l K x ) j = 0 u j ( t ) cos ( j K x ) d x d t ,
N 0 ( t ) = 1 2 0 t k p [ 2 M 0 ( t ) u 0 ( t ) + M 1 ( t ) u 1 ( t ) + M 2 ( t ) u 2 ( t ) + M 3 ( t ) u 3 ( t ) ] d t ,
N 1 ( t ) = S 1 2 0 t k p { 2 M 1 ( t ) u 0 ( t ) + [ 2 M 0 ( t ) + M 2 ( t ) ] u 0 ( t ) + [ M 1 ( t ) + M 3 ( t ) ] u 2 ( t ) + M 2 ( t ) u 3 ( t ) } d t .
η ( t ) = sin 2 [ π d n 1 ( t ) λ cos θ ] ,
n 2 1 n 2 + 2 = φ ( m ) n m 2 1 n m 2 + 2 + φ ( p ) n p 2 1 n p 2 + 2 + φ ( b ) n b 2 1 n b 2 + 2 + φ ( H ) n H 2 1 n H 2 + 2 ,
φ ( m ) ( t ) + φ ( p ) ( t ) + φ ( b ) ( t ) + φ ( H ) ( t ) = 1 .
n 1 ( t ) = ( n dark 2 + 2 ) 2 6 n dark [ φ 1 ( m ) ( t ) ( n m 2 1 n m 2 + 2 n b 2 1 n b 2 + 2 ) + φ 1 ( p ) ( t ) ( n p 2 1 n p 2 + 2 n b 2 1 n b 2 + 2 ) ] ,
I 0 = I i ( λ N a h c ) T s f .

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