Quantitative modeling of the reaction/diffusion kinetics of two-chemistry diffusive photopolymers

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 ~10 mJ cm) and feature size (0.35 to 500 μm). ©2014 Optical Society of America OCIS codes: (090.0090) Holography; (090.2900) Optical storage materials; (090.7330) Volume gratings; (160.5335) Photosensitive materials; (160.5470) Polymers. References and links 1. H. J. Coufal, G. T. Sincerbox, and D. Psaltis, eds., Holographic Data Storage (Springer-Verlag, 2000). 2. Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” Photonics Technology Letters, IEEE 11(3), 352–354 (1999). 3. B. L. Booth and J. E. Marchegiano, “Waveguide properties and devices in photopolymer”, Optical Communication, 1988 (ECOC 88). Fourteenth European Conference on (Conf. Publ. No. 292), 589–590 (IET, 1988). 4. M.-E. Baylor, B. W. Cerjan, C. R. Pfiefer, R. W. Boyne, C. L. Couch, N. B. Cramer, C. N. Bowman, and R. R. McLeod, “Monolithic integration of optical waveguide and fluidic channel structures in a thiol-ene/methacrylate photopolymer,” Opt. Mater. Express 2(11), 1548–1555 (2012). 5. C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33(22), 2575–2577 (2008). 6. 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). 7. J. Gambogi, Jr., K. W. Steijn, S. R. Mackara, T. Duzick, B. Hamzavy, and J. Kelly, “Holographic optical element (HOE) imaging in DuPont holographic photopolymers,” Proc. SPIE 2152, 282–293 (1994). 8. 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. SPIE 5380, 283–288 (2004). 9. 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. SPIE 2689, 127– 141 (1996). 10. 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). 11. T. J. Trentler, J. E. Boyd, and V. L. Colvin, “Epoxy resin−photopolymer composites for volume holography,” Chem. Mater. 12(5), 1431–1438 (2000). 12. K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2011). 13. 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). #211355 $15.00 USD Received 5 May 2014; revised 14 Jul 2014; accepted 15 Jul 2014; published 22 Jul 2014 (C) 2014 OSA 1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001668 | OPTICAL MATERIALS EXPRESS 1668 14. 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). 15. H. M. Smith, Principles of Holography (Wiley, 1975). 16. 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 B 22(2), 407–416 (2005). 17. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41(10), 1929–1939 (1994). 18. J. T. Sheridan and J. R. Lawrence, “Nonlocal-response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17(6), 1108–1114 (2000). 19. W. S. Colburn and K. A. Haines, “Volume hologram formation in photopolymer materials,” Appl. Opt. 10(7), 1636–1641 (1971). 20. 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). 21. F. H. Mok, G. W. Burr, and D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21(12), 896–898 (1996). 22. J. T. Gallo and C. M. Verber, “Model for the effects of material shrinkage on volume holograms,” Appl. Opt. 33(29), 6797–6804 (1994). 23. W. Heller, “Remarks on refractive index mixture rules,” J. Phys. Chem. 69(4), 1123–1129 (1965). 24. 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). 25. P.-G. de Gennes, “Reptation of a polymer chain in the presence of fixed obstacles,” J. Chem. Phys. 55(2), 572– 579 (1971). 26. 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). 27. S. Martin, C. A. Feely, and V. Toal, “Holographic recording characteristics of an acrylamide-based photopolymer,” Appl. Opt. 36(23), 5757–5768 (1997). 28. 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). 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). 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). 31. M. G. Neumann, W. G. Miranda, Jr., 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). 32. C. Decker, “Kinetic study and new applications of UV radiation curing,” Macromol. Rapid Commun. 23(18), 1067–1093 (2002). 33. C. Decker and A. D. Jenkins, “Kinetic approach of oxygen inhibition in ultraviolet-and laser-induced polymerizations,” Macromol. 18(6), 1241–1244 (1985). 34. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001). 35. 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). 36. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969). 37. G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 115(5-6), 528–532 (1995).