Abstract

The nonlocal polymerization-driven diffusion model (NPDD) has been shown to predict high spatial frequency cut-off in photopolymers and to accurately predict higher order grating components. We propose an extension to the NPDD model to account for the temporal response associated with polymer chain growth. An exponential response function is proposed to describe transient effects during the polymerization process. The extended model is then solved using a finite element technique and the nature of grating evolution examined in the case when illumination is stopped prior to the saturation of the grating recording process. Based on independently determined refractive index measurements we determine the temporal evolution of the refractive index modulation and the resulting diffraction efficiency using rigorous coupled wave theory. Material parameters are then extracted based on fits to experimental data for nonlinear and both ideal and non-ideal kinetic models.

© 2005 Optical Society of America

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2005 (5)

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: non-local polymerisation driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407–416 (2005).
[Crossref]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “Physical and effective optical thickness of holographic diffraction gratings recorded in photopolymers,” Opt. Express 131939 (2005)
[Crossref] [PubMed]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express 133543 (2005)
[Crossref] [PubMed]

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

2004 (4)

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

S. Massenot, J.-L. Kaiser, R. Chevallier, and Y. Renotte, “Study of the Dynamic Formation of Transmission Gratings Recorded in Photopolymers and Holographic Polymer-Dispersed Liquid Crystals,” Appl. Opt. 43, 5489–5497 (2004).
[Crossref] [PubMed]

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]

J. T. Sheridan, F. T. O’ Neill, and J. V. Kelly, “Holographic Data Storage: Optimized Scheduling using the Non-local Polymerization Driven Diffusion Model,” J. Opt. Soc. Am. B 21, 1443–1451 (2004).
[Crossref]

2003 (3)

2002 (1)

2001 (1)

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

2000 (3)

1999 (1)

1998 (1)

I. Aubrecht, M. Miller, and I. Koudela, “Recording of holographic 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]

J. Lougnot, P. Jost, and L. Lavielle, “Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process,” Pure and Applied Optics 6, 225–245 (1997).
[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)

A,

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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]

Aubrecht, I.

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

Beléndez, A.

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]

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]

Carr, A. J.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[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]

Chang, H. C.

Chevallier, R.

Close, C. E.

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[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]

Dahr, L.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Daniels, S. M.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

Dixon, C.

C. Dixon, Numerical Analysis, Blackie, (Glasgow and London, 1982).

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]

Gallego, S.

Galstian, T.

A.V. Galstyan, R. S. Hakobyan, S. H, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials” http://www.elc.org/Documents/T.__V_Galstian_2004_05_05_11_13_17.pdf

Galstyan, A.V.

A.V. Galstyan, R. S. Hakobyan, S. H, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials” http://www.elc.org/Documents/T.__V_Galstian_2004_05_05_11_13_17.pdf

Gaylord, T.

Gaylord, T.K.

Gleeson, M. R.

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

Glytsis, E.

Hakobyan, R. S.

A.V. Galstyan, R. S. Hakobyan, S. H, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials” http://www.elc.org/Documents/T.__V_Galstian_2004_05_05_11_13_17.pdf

Hale,

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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]

Hill, A.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Jost, P.

J. Lougnot, P. Jost, and L. Lavielle, “Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process,” Pure and Applied Optics 6, 225–245 (1997).
[Crossref]

Kaiser, J.-L.

Katz, H.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Kelly, J. V.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: non-local polymerisation driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407–416 (2005).
[Crossref]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “Physical and effective optical thickness of holographic diffraction gratings recorded in photopolymers,” Opt. Express 131939 (2005)
[Crossref] [PubMed]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express 133543 (2005)
[Crossref] [PubMed]

J. T. Sheridan, F. T. O’ Neill, and J. V. Kelly, “Holographic Data Storage: Optimized Scheduling using the Non-local Polymerization Driven Diffusion Model,” J. Opt. Soc. Am. B 21, 1443–1451 (2004).
[Crossref]

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

Kirk-Otmer,

Kirk-Otmer, Encyclopedia of Chemical Technology, Vol. 1, (Wiley, New York, 1991).

Koudela, I.

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

Kurtis, K.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Kwon, J. H.

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]

Lavielle, L.

J. Lougnot, P. Jost, and L. Lavielle, “Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process,” Pure and Applied Optics 6, 225–245 (1997).
[Crossref]

Lawrence, J. R.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[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, 621–624 (2002).
[Crossref]

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

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Automated recording and testing of holographic optical element arrays,” Optik 111,459–467 (2000).

Lougnot, J.

J. Lougnot, P. Jost, and L. Lavielle, “Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process,” Pure and Applied Optics 6, 225–245 (1997).
[Crossref]

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]

Márquez, A.

Massenot, S.

Miller, M.

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

Moharam, M. G.

Mouroulis, P.

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[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’ Neill, F. T.

O’Brien, G.

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

O’Neill, F. T.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: non-local polymerisation driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407–416 (2005).
[Crossref]

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[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, 621–624 (2002).
[Crossref]

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

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Automated recording and testing of holographic optical element arrays,” Optik 111,459–467 (2000).

J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

Odian, G.

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

Olsen, A.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Ortuno, M.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: non-local polymerisation driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407–416 (2005).
[Crossref]

J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

Ortuño, M.

Pascual, I.

Renotte, Y.

Rowsome, I. C.

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

S. H,

A.V. Galstyan, R. S. Hakobyan, S. H, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials” http://www.elc.org/Documents/T.__V_Galstian_2004_05_05_11_13_17.pdf

Schilling, M.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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]

Schnoes, M.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

Schultz, S.

Sheridan, J. T.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: non-local polymerisation driven diffusion under non-ideal kinetic conditions,” J. Opt. Soc. Am. B 22, 407–416 (2005).
[Crossref]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “Physical and effective optical thickness of holographic diffraction gratings recorded in photopolymers,” Opt. Express 131939 (2005)
[Crossref] [PubMed]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express 133543 (2005)
[Crossref] [PubMed]

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

J. T. Sheridan, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

J. T. Sheridan, F. T. O’ Neill, and J. V. Kelly, “Holographic Data Storage: Optimized Scheduling using the Non-local Polymerization Driven Diffusion Model,” J. Opt. Soc. Am. B 21, 1443–1451 (2004).
[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, 621–624 (2002).
[Crossref]

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Automated recording and testing of holographic optical element arrays,” Optik 111,459–467 (2000).

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]

J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

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]

Tackitt, M.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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]

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]

Wilson, W.

L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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 (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]

J. Appl. Phys. (2)

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]

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. (2)

I. Aubrecht, M. Miller, and I. Koudela, “Recording of holographic 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, J. V. Kelly, G. O’Brien, M. R. Gleeson, and F. T. O’Neill, “Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations,” J. Opt. A: Pure Appl. Opt. 61089–1096 (2004)
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (5)

Opt. Express (2)

Optik (2)

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

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Automated recording and testing of holographic optical element arrays,” Optik 111,459–467 (2000).

Proc. SPIE (2)

M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O’Neill, and J. T. Sheridan, “The Impact of Inhibition Processes during Grating Formation in Photopolymer Materials”, in Photonic Engineering, R. F. O’Dowd, ed., Proc. SPIE 5827, (2005).
[Crossref]

F. T. O’Neill, I. C. Rowsome, A. J. Carr, S. M. Daniels, M. R. Gleeson, J. V. Kelly, J. R. Lawrence, and J. T. Sheridan, “Photo-embossed optical elements and microfluidic lens fabrication”, in Photonic Engineering, T. J. Glynn, ed., Proc. SPIE 5827,. (2005).
[Crossref]

Pure and Applied Optics (1)

J. Lougnot, P. Jost, and L. Lavielle, “Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process,” Pure and Applied Optics 6, 225–245 (1997).
[Crossref]

Other (10)

A.V. Galstyan, R. S. Hakobyan, S. H, and T. Galstian, “Study of the inhibition period prior to the holographic grating formation in liquid crystal photopolymerizable materials” http://www.elc.org/Documents/T.__V_Galstian_2004_05_05_11_13_17.pdf

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J. V. Kelly, M. R. Gleeson, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Examination of the temporal and kinetic effects in acrylamide based photopolymer using the nonlocal polymer driven diffusion model (NPDD),” in Materials for Holographic and Optical Data Storage, V. Toal, ed., Proc SPIE, Holo 05,Bulgaria, (2005).

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L. Dahr, A, Hale, K. Kurtis, M. Schnoes, M. Tackitt, W. Wilson, A. Hill, M. Schilling, H. Katz, and A. Olsen, “Photopolymer Recording Media for High Density Data Storage,” in Proceedings of IEEE conference on Optical Data Storage Conference (Institute of Electrical and Electronics Engineers, Canada, 2000) pp. 158–160.

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

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Figures (5)

Fig. 1.
Fig. 1.

Harmonic coefficient amplitudes of polymer concentration for values of nonlocal temporal response parameter τ nD = (0.01, 0.05, 0.1), where R D = 50, σ D = 0 and β = 1.

Fig. 2.
Fig. 2.

(a) Polymer and (b) Monomer harmonic amplitudes for τ nD = (0.01, 0.05, 0.1) where R D=50, σ D = 0, α = 0, γ = 1/2 and β = 1.

Fig. 3.
Fig. 3.

Theoretical refractive index evolution where R D=50, σ D = 0, α = 0 and β = 1.

Fig. 4.
Fig. 4.

Diffraction efficiency evolution for short exposures. Exposure times are 1, 2, 3 and 5 seconds for (a), (b), (c) and (d) respectively.

Fig. 5.
Fig. 5.

Fit to experimental data using (a) the bimolecular termination model and (b) the primary termination model where the parameter values used are those given in Tables 4 and 5 for (i) 1 and (ii) 2 second exposures.

Tables (5)

Tables Icon

Table 1. Concentrations and volume fractions of photopolymer material components.

Tables Icon

Table 2. Refractive index measurements of material components.

Tables Icon

Table 3. Refractive index values of material components found in the literarure and those calculated from the results in table 2 in conjunction with the Lorentz-Lorenz relation.

Tables Icon

Table 4. Best fit parameters obtained for the ideal case of bimolecular termination, β = 1.

Tables Icon

Table 5. Best fit parameters obtained for the non-ideal case of primary termination, β = 2.

Equations (25)

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u x t t = x [ D x t u x t t ]
+ 0 t ( x , x ; t , t ) F ( x , t ) × [ u ( x , t ) ] β dt dx
u x t u x t + N x t H x t t
lim T max 0 { T t t } = δ ( t , t ) ,
t T ( t , t ) dt = 1 .
t T MAX t T ( t , t ) dt 1 ,
T ( t t ) = 1 τ n exp [ ( t t ) τ n ] .
u ( x D , t D ) t D = R D x D [ D D ( x D , t D ) u ( x D , t D ) x D ] + 0 t R ( x D , x D ; t D , t D ) F ( x D , t D ) u ( x D , t D ) dt D dx D
R ( x D , x D ; t D , t D ) = 1 2 π σ D exp [ ( x D x D ) 2 2 σ D ] × 1 τ nD exp [ ( t D t D ) τ nD ] ,
u i x D 1 2 Δ x ( u j + 1 u j 1 )
2 u i x 2 D 1 Δ x 2 ( u i + 1 2 u i + u i 1 ) ,
u j t D u j + 1 u j Δ t D ,
u i j [ 1 2 C 2 ( i , j 1 ) Δ t D Δ x D 2 ] u ( i , j 1 )
+ [ C 2 ( i , j 1 ) Δ t D Δ x D 2 + C 1 ( i , j 1 ) Δ t D Δ x D 2 ] u ( i + 1 , j 1 )
+ [ C 2 ( i , j 1 ) Δ t D Δ x D 2 C 1 ( i , j 1 ) Δ t D Δ x D 2 ] u ( i 1 , j 1 ) Δ t D C 3 ( i , j 1 )
C 1 ( i , j 1 ) = R D D D ( x D , i , t D , j 1 ) x D ,
C 2 ( i , j 1 ) = R D D D ( x D , i , t D , j 1 ) ,
C 3 ( i , j 1 ) = Δ x D 2 [ f D ( i , j 1 ) + 2 k = 2 N 1 f D ( k , j 1 ) + f D ( N , j 1 ) ]
f D ( k , j 1 ) = R ( x D , i , x D , k ) F ( x D , k ) u ( x D , k , t D , j 1 ) .
Δ t D 1 2 Δ x D 2 R D .
e 1 12 Δ t D 2 T ( τ ) × t D
N i j Δ t D 2 [ C 3 i 0 + 2 k = 1 j 1 C 3 i k + C 3 i j ] .
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 ( m ) + ϕ ( p ) + ϕ ( b ) + ϕ ( h ) = 1 ,
n 1 = ( n dark 2 + 2 ) 2 6 n dark [ ϕ 1 ( m ) ( n m 2 1 n m 2 + 2 n b 2 1 n b 2 + 2 ) + ϕ 1 ( p ) ( n p 2 1 n p 2 + 2 n b 2 1 n b 2 + 2 ) ] ,

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