Abstract

A general strategy for characterizing the reaction/diffusion kinetics of photopolymer media is proposed, in which key processes are decoupled and independently measured. This strategy enables prediction of a material’s potential refractive index change, solely on the basis of its chemical components. The degree to which a material does not reach this potential reveals the fraction of monomer that has participated in unwanted reactions, reducing spatial resolution and lifetime. This approach is demonstrated for a model material similar to commercial media, achieving quantitative predictions of refractive index response over three orders of exposure dose (~1 to ~103 mJ cm−2) and feature size (0.35 to 500 μm).

© 2014 Optical Society of America

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  29. 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(9), 5913–5923 (1997).
    [CrossRef]
  30. M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
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    [CrossRef] [PubMed]
  32. C. Decker, “Kinetic study and new applications of UV radiation curing,” Macromol. Rapid Commun.23(18), 1067–1093 (2002).
    [CrossRef]
  33. C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol.18(6), 1241–1244 (1985).
    [CrossRef]
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    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2013

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

2012

2009

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerization in the formation of holographic gratings,” J. Opt. A, Pure Appl. Opt.11(2), 024008 (2009).
[CrossRef]

2008

2005

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

2004

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, “Investigation of the diffusion processes in a self-processing acrylamide-based photopolymer system,” Appl. Opt.43(14), 2900–2905 (2004).
[CrossRef] [PubMed]

2002

C. Decker, “Kinetic study and new applications of UV radiation curing,” Macromol. Rapid Commun.23(18), 1067–1093 (2002).
[CrossRef]

2001

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg.17(5), S573–S577 (2001).
[PubMed]

2000

J. T. Sheridan and J. R. Lawrence, “Nonlocal-response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A17(6), 1108–1114 (2000).
[CrossRef] [PubMed]

T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater.12(5), 1431–1438 (2000).
[CrossRef]

1999

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, and F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett.24(7), 487–489 (1999).
[CrossRef] [PubMed]

1998

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[CrossRef]

I. Aubrecht, M. Miler, and I. Koudela, e.g.“Once monomer is converted to polymer, its diffusion is assumed to cease,” in “Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt.45(7), 1466–1477 (1998).

1997

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(9), 5913–5923 (1997).
[CrossRef]

S. Martin, C. A. Feely, and V. Toal, “Holographic recording characteristics of an acrylamide-based photopolymer,” Appl. Opt.36(23), 5757–5768 (1997).
[CrossRef] [PubMed]

1996

F. H. Mok, G. W. Burr, and D. Psaltis, “System metric for holographic memory systems,” Opt. Lett.21(12), 896–898 (1996).
[CrossRef] [PubMed]

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

1995

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun.115(5-6), 528–532 (1995).
[CrossRef]

1994

J. T. Gallo and C. M. Verber, “Model for the effects of material shrinkage on volume holograms,” Appl. Opt.33(29), 6797–6804 (1994).
[CrossRef] [PubMed]

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt.41(10), 1929–1939 (1994).
[CrossRef]

1985

C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol.18(6), 1241–1244 (1985).
[CrossRef]

1976

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

1971

W. S. Colburn and K. A. Haines, “Volume hologram formation in photopolymer materials,” Appl. Opt.10(7), 1636–1641 (1971).
[CrossRef] [PubMed]

P.-G. de Gennes, “Reptation of a polymer chain in the presence of fixed obstacles,” J. Chem. Phys.55(2), 572–579 (1971).
[CrossRef]

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

1965

W. Heller, “Remarks on refractive index mixture rules,” J. Phys. Chem.69(4), 1123–1129 (1965).
[CrossRef]

Askham, F.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Asua, M.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Aubrecht, I.

I. Aubrecht, M. Miler, and I. Koudela, e.g.“Once monomer is converted to polymer, its diffusion is assumed to cease,” in “Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt.45(7), 1466–1477 (1998).

Axelrod, D.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Baylor, M.-E.

Beal, D.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Beuermann, S.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Bowman, C. N.

Boyd, J. E.

T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater.12(5), 1431–1438 (2000).
[CrossRef]

Boyne, R. W.

Bruder, F.-K.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Buback, M.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Burr, G. W.

Castignolles, P.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Cerjan, B. W.

Charleux, B.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Chu, P. L.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

Colburn, W. S.

Cole, M.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Cole, M. C.

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

Colvin, V. L.

T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater.12(5), 1431–1438 (2000).
[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(9), 5913–5923 (1997).
[CrossRef]

Correa, I. C.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

Couch, C. L.

Cramer, N. B.

de Gennes, P.-G.

P.-G. de Gennes, “Reptation of a polymer chain in the presence of fixed obstacles,” J. Chem. Phys.55(2), 572–579 (1971).
[CrossRef]

Decker, C.

C. Decker, “Kinetic study and new applications of UV radiation curing,” Macromol. Rapid Commun.23(18), 1067–1093 (2002).
[CrossRef]

C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol.18(6), 1241–1244 (1985).
[CrossRef]

Deuber, F.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Dhal, P. K.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Dhar, L.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, and F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett.24(7), 487–489 (1999).
[CrossRef] [PubMed]

Duzick, T.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Elson, E.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Facke, T.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Feely, C. A.

Gallego, S.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Gallo, J. T.

Gambogi, J.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Gilbert, R. G.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Gleeson, M. R.

J. Guo, M. R. Gleeson, and J. T. Sheridan, “A review of the optimisation of photopolymer materials for holographic data storage,” Phys. Res. Int.2012, 803439 (2012).

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerization in the formation of holographic gratings,” J. Opt. A, Pure Appl. Opt.11(2), 024008 (2009).
[CrossRef]

Guo, J.

J. Guo, M. R. Gleeson, and J. T. Sheridan, “A review of the optimisation of photopolymer materials for holographic data storage,” Phys. Res. Int.2012, 803439 (2012).

Hagen, R.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Haines, K. A.

Hale, A.

Hamzavy, B.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Harris, A. L.

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[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(9), 5913–5923 (1997).
[CrossRef]

Harris, T. D.

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[CrossRef]

Heller, W.

W. Heller, “Remarks on refractive index mixture rules,” J. Phys. Chem.69(4), 1123–1129 (1965).
[CrossRef]

Hill, A.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Honel, D.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Horner, M. G.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Howard, R.

Hutchinson, R. A.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Ihas, B.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Ingwall, R. T.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Jallapuram, R.

Jenkins, A. D.

C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol.18(6), 1241–1244 (1985).
[CrossRef]

Jurberg, D.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Kagan, C. R.

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[CrossRef]

Kamysiak, K. K.

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

Katz, H. E.

Kelly, J.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Kelly, J. V.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

Kogure, M.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Kolb, E. S.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Koppel, D. E.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Koudela, I.

I. Aubrecht, M. Miler, and I. Koudela, e.g.“Once monomer is converted to polymer, its diffusion is assumed to cease,” in “Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt.45(7), 1466–1477 (1998).

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(9), 5913–5923 (1997).
[CrossRef]

Lawrence, J. R.

Leiza, J. R.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Li, H.-Y. S.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Mackara, S. R.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Martin, S.

McLeod, R. R.

Michaels, D.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Miler, M.

I. Aubrecht, M. Miler, and I. Koudela, e.g.“Once monomer is converted to polymer, its diffusion is assumed to cease,” in “Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt.45(7), 1466–1477 (1998).

Miller, S.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Minns, R. A.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Miranda, W. G.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

Mok, F. H.

Moore, E. D.

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

Mouroulis, P.

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun.115(5-6), 528–532 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt.41(10), 1929–1939 (1994).
[CrossRef]

Naydenova, I.

Neipp, C.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Neumann, M. G.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

Nikitin, A. N.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[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: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Ortuno, M.

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Peng, G. D.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

Pfiefer, C. R.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg.17(5), S573–S577 (2001).
[PubMed]

Psaltis, D.

Quirin, S.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Rolle, T.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Rueggeberg, F. A.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

Schild, H. G.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Schilling, F. C.

Schilling, M. L.

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, and F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett.24(7), 487–489 (1999).
[CrossRef] [PubMed]

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[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(9), 5913–5923 (1997).
[CrossRef]

Schlessinger, J.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Schmitt, C. C.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

Schnoes, M.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Schnoes, M. G.

Setthachayanon, S.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg.17(5), S573–S577 (2001).
[PubMed]

Sheridan, J. T.

J. Guo, M. R. Gleeson, and J. T. Sheridan, “A review of the optimisation of photopolymer materials for holographic data storage,” Phys. Res. Int.2012, 803439 (2012).

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerization in the formation of holographic gratings,” J. Opt. A, Pure Appl. Opt.11(2), 024008 (2009).
[CrossRef]

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

J. T. Sheridan and J. R. Lawrence, “Nonlocal-response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A17(6), 1108–1114 (2000).
[CrossRef] [PubMed]

Steijn, K. W.

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Toal, V.

Trentler, T.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Trentler, T. J.

T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater.12(5), 1431–1438 (2000).
[CrossRef]

Urness, A. C.

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

Vairon, J.-P.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

van Herk, A. M.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Verber, C. M.

Waldman, D. A.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerization methods for volume hologram recording,” Proc. SPIE2689, 127–141 (1996).
[CrossRef]

Wang, P.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Webb, W. W.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Weiser, M.-S.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

Wilson, W.

P. Wang, B. Ihas, M. Schnoes, S. Quirin, D. Beal, S. Setthachayanon, T. Trentler, M. Cole, F. Askham, D. Michaels, S. Miller, A. Hill, W. Wilson, and L. Dhar, “Photopolymer media for holographic storage at ~ 405 nm,” Proc. SPIE5380, 283–288 (2004).
[CrossRef]

Wu, B.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

Xiong, Z.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

Ye, C.

Zhao, G.

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun.115(5-6), 528–532 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt.41(10), 1929–1939 (1994).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48(9), 2909–2947 (1969).
[CrossRef]

Biophys. J.

D. Axelrod, D. E. Koppel, J. Schlessinger, E. Elson, and W. W. Webb, “Mobility measurement by analysis of fluorescence photobleaching recovery kinetics,” Biophys. J.16(9), 1055–1069 (1976).
[CrossRef] [PubMed]

Chem. Mater.

T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater.12(5), 1431–1438 (2000).
[CrossRef]

J. Appl. Phys.

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(9), 5913–5923 (1997).
[CrossRef]

J. Chem. Phys.

C. R. Kagan, T. D. Harris, A. L. Harris, and M. L. Schilling, “Submicron confocal Raman imaging of holograms in multicomponent photopolymers,” J. Chem. Phys.108(16), 6892–6896 (1998).
[CrossRef]

P.-G. de Gennes, “Reptation of a polymer chain in the presence of fixed obstacles,” J. Chem. Phys.55(2), 572–579 (1971).
[CrossRef]

J. Dent.

M. G. Neumann, W. G. Miranda, C. C. Schmitt, F. A. Rueggeberg, and I. C. Correa, “Molar extinction coefficients and the photon absorption efficiency of dental photoinitiators and light curing units,” J. Dent.33(6), 525–532 (2005).
[CrossRef] [PubMed]

J. Mod. Opt.

I. Aubrecht, M. Miler, and I. Koudela, e.g.“Once monomer is converted to polymer, its diffusion is assumed to cease,” in “Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth,” J. Mod. Opt.45(7), 1466–1477 (1998).

G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt.41(10), 1929–1939 (1994).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

M. R. Gleeson and J. T. Sheridan, “A review of the modelling of free-radical photopolymerization in the formation of holographic gratings,” J. Opt. A, Pure Appl. Opt.11(2), 024008 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Photopolym. Sci. Technol.

F.-K. Bruder, F. Deuber, T. Facke, R. Hagen, D. Honel, D. Jurberg, M. Kogure, T. Rolle, and M.-S. Weiser, “Full-color self-processing holographic photopolymers with high sensitivity in red-the first class of instant holographic photopolymers,” J. Photopolym. Sci. Technol.22(2), 257–260 (2009).
[CrossRef]

J. Phys. Chem.

W. Heller, “Remarks on refractive index mixture rules,” J. Phys. Chem.69(4), 1123–1129 (1965).
[CrossRef]

J. Refract. Surg.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg.17(5), S573–S577 (2001).
[PubMed]

JOSA B

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” JOSA B22(2), 407–416 (2005).
[CrossRef]

Light Sci. Appl.

A. C. Urness, E. D. Moore, K. K. Kamysiak, M. C. Cole, and R. R. McLeod, “Liquid deposition photolithography for submicrometer resolution three-dimensional index structuring with large throughput,” Light Sci. Appl.2(3), e56 (2013).
[CrossRef]

Macromol.

C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol.18(6), 1241–1244 (1985).
[CrossRef]

Macromol. Chem. Phys.

M. Asua, S. Beuermann, M. Buback, P. Castignolles, B. Charleux, R. G. Gilbert, R. A. Hutchinson, J. R. Leiza, A. N. Nikitin, J.-P. Vairon, and A. M. van Herk, “Critically evaluated rate coefficients for free‐radical polymerization, 5,” Macromol. Chem. Phys.205(16), 2151–2160 (2004).
[CrossRef]

Macromol. Rapid Commun.

C. Decker, “Kinetic study and new applications of UV radiation curing,” Macromol. Rapid Commun.23(18), 1067–1093 (2002).
[CrossRef]

Opt. Commun.

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun.115(5-6), 528–532 (1995).
[CrossRef]

Opt. Lett.

Opt. Mater. Express

Photonics Technology Letters, IEEE

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE11(3), 352–354 (1999).
[CrossRef]

Phys. Res. Int.

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Proc. SPIE

J. Gambogi, K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE2152, 282–293 (1994).
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Figures (10)

Fig. 1
Fig. 1

Bulk refractive index as a function of concentration of polymerized writing monomer, TBPA. Writing monomer is either dissolved into the liquid resin, or diffused into the thermoset matrix, with the in-diffusion process monitored gravimetrically. In either case, the sample is then flood-exposed and allowed to rest for >3 days to ensure complete polymerization; then bulk index is measured via Metricon 2010 prism coupler. The same refractive index relation holds in both cases: dashed line is a good (R2 = 0.992) linear fit to all data points. Therefore the solid matrix must be exhibiting nearly perfect volume displacement, just as the liquid resin is.

Fig. 2
Fig. 2

(a) Confocal Raman microspectroscopy yields concentration profiles of TBPA writing polymer, top, and urethane matrix polymer, bottom, within a gradient-index feature. The local densification of writing polymer causes a corresponding displacement of the host matrix, even over large scales (scale bars = 200 μm). (b) Spatial averages of those concentration profiles. (c) Writing polymer profile measured as a refractive index via phase-sensitive imaging and converted via Fig. 1 to concentration. This is compared to the confocal Raman result from (b), and to the prediction of the reaction/diffusion model discussed below.

Fig. 3
Fig. 3

(a) Holographically usable peak-to-mean refractive index modulation Δn, as a function of grating pitch Λ, compared to the ideal “formula limit” calculated from Fig. 1. For multiple weak exposures, this formula limit is simply Δn = n(6% TBPA) – n(0% TBPA), where 6% is the initial uniform TBPA concentration. (b) Distribution of polymerized TBPA at Λ = 0.70 μm and Λ = 0.35 μm, drawn to match the Δn scale in (a). For any exposure dose, three categories of writing oligomer are generated, in a ratio determined by Λ: (i) attached oligomer that is holographically patterned, (ii) attached oligomer that is spatially uniform, and (iii) mobile oligomer, which diffuses to become spatially uniform.

Fig. 4
Fig. 4

Species balance description of the set of reaction paths. As shown above, this set must be extended to separately track all of the following species: unconsumed photoinitiator PI; unreacted monomer M; mobile radicals Rmob and matrix-attached radicals Rfix (attached to chains of any length); and polymerized chain units Pmob and Pfix, belonging respectively to mobile or matrix-attached chains of any length.

Fig. 5
Fig. 5

a) Grating growth curves measured by Bragg diffraction, compared to predictions from the reaction/diffusion model without introduction of any additional fit parameters. Note that the apparent termination rate varies with Λ, since grating termination is actually governed by diffusional mechanisms that are successfully captured by the model. (i) Λ = 0.7 μm, exposure intensity I = 100 mW cm−2, exposure time t = 3 sec, ii) Λ = 5 μm, I = 100 mW cm−2, t = 1 sec, (iii) Λ = 0.7 μm, I = 10 mW cm−2, t = 3 sec. b) Growth curves of a grating’s fundamental and second spatial harmonics, when reaction and diffusion are strongly coupled. (Λ = 5 μm, I = 60 mW cm−2, t = 10 sec).

Fig. 6
Fig. 6

The dependence of glass transition temperature (Tg) on monomer conversion. a. The measured Tg of the photopolymer formulation with no writing monomer conversion. b. The measured Tg with 100% writing monomer conversion. All measurements are at 1 Hz, and Tg is defined as the tan(δ) peak.

Fig. 7
Fig. 7

(a) Raman spectra centered at 237 (cm−1) of unstructured sample with varying amounts of writing monomer. (b) The relationship between the writing monomer concentration and the integrated normalized spectra of the 237 (cm−1) spectral line.

Fig. 8
Fig. 8

Confocal Raman spectrum of the matrix and writing monomer independently. (a) Measured Raman spectrum of the matrix material. (b) Raman spectrum of tribromophenol, as reported by manufacturer Sigma-Aldrich.

Fig. 9
Fig. 9

The molecular weight distribution of unattached oligomers extracted from a photocured sample of the polymer, normalized to the peak value. Dashed lines show multiples of the molecular weight of the writing monomer.

Fig. 10
Fig. 10

Finding the diffusivity of monomer by fitting the in-diffusion of new monomer to a simple Fickian diffusion model. (a) The refractive index profile of the measured and simulated data. The green line is the simulated profile and the red line is the measured refractive index profile. (b) The dependence on the diffusion coefficient on the quality of the fit between the measure and simulated data.

Tables (2)

Tables Icon

Table 1 Model material formulation. Components are used as received, except TBPA which is purified by dissolving in methylene dichloride and filtering with a Millipore 0.5 micron pore membrane filter. Components 3-6 are mixed into the polyol at 60 °C, degassed, then mixed with isocyanate and cast between glass slides. For Fig. 1, initial concentration of writing monomer is varied from 0% to 6%, and writing monomer is later added or removed from the gelled matrix via bulk diffusion.

Tables Icon

Table 2 Reaction/diffusion equations based on the reaction paths in Fig. 4. I is the exposure intensity and 2ε is the radical quantum yield of the photoinitiator. For generality, both hydrogen abstraction and chain transfer are treated as first-order processes, rather than explicitly tracking the concentrations of matrix abstraction sites and of chain transfer agents.

Equations (3)

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n( φ writing polymer )= n matrix +( n writing polymer n matrix ) φ writing polymer
n( p writing polymer )= n matrix +( n writing polymer n matrix )( ρ total / ρ writing polymer ) p writing polymer n( p writing polymer )= n matrix +κ p writing polymer
n( p writing polymer )= n matrix +( n writing polymer n matrix )( ρ total / ρ writing polymer ) p writing polymer n( p writing polymer )= n matrix +κ p writing polymer

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