Abstract

Cationic-induced two-photon photo-polymerization is demonstrated at 710 nm, using an isopropylthioxanthone/diarylidonium salt initiating system for the cationic polymerization of an epoxide. In-situ monitoring of the polymer conversion using interferometry allows for determination of the polymerization threshold J2th, polymerization rate R and its dependence of initiator’s concentration z. Best J2th achieved is 1 GW/cm2, with a dynamic range of > 100, i.e. the material can be fully polymerized at intensities > 100 times the threshold level without damage. The R is found to be proportional to the m=1.7 power of the intensity, or R=[C (J-J2th)]m=[C (J-J2th)]1.7, which implies a significantly stronger localization of the photochemical response than that of free radical photoinitiators. Both R and J2th significantly improve when the concentration z of the initiator (onium salt) increases, reduction of J2th exhibiting z-m trend.

© 2001 Optical Society of America

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  1. B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
    [Crossref]
  2. Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
    [Crossref]
  3. W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
    [Crossref]
  4. H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
    [Crossref]
  5. Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
    [Crossref]
  6. Y. Kawata, “Three-dimensional memory,” Proc. SPIE 4081, 76–85 (2000).
    [Crossref]
  7. R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
    [Crossref]
  8. K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
    [Crossref]
  9. D. Day, Gu Min, and A. Smallridge, “Use of two-photon excitation for erasable-rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948–950 (1999).
    [Crossref]
  10. H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
    [Crossref]
  11. S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
    [Crossref]
  12. C. Diamond, Y. Boiko, and S. Esener, “Two-photon holography in a 3D photopolymer host-guest matrix,” Opt. Express6, 64–68 (2000); http://www.opticsexpress.org/oearchive/source/18896.htm Errata: Opt. Express6, 109–110 (2000); http://www.opticsexpress.org/oearchive/source/19560.htm
    [Crossref] [PubMed]
  13. S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).
  14. Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).
  15. M. Shirai and M. Tsunooka, “Photoacid and photobase generators: chemistry and applications to polymeric materials,” Prog. Polym. Sci.,  21, 1–45 (1996).
    [Crossref]
  16. Y. Boiko, E. Tikhonov, and V. Shilov, “Photopolymerization studies by Michelson interferometer,” stored in and available from Ukr. Sci.-Research Inst. of Sci. and Technical Information (UkrNIINTI), Dep.No.2155, 17p., 15.09.1986 (in Russian).
  17. Y. Boiko, “Volume holographic optics recording in photopolymerizable layers,” Holographic Optics III - Principles and Applications, Proc. SPIE 1507, 318–327 (1991).
  18. G. Manivannan and J. Fouassier, “Primary process in the photosensitized polymerization of cationic monomers,” J. Polym. Sci. A: Polym. Chem.,  29,1113–1124 (1991).
    [Crossref]

2000 (7)

W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
[Crossref]

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

Y. Kawata, “Three-dimensional memory,” Proc. SPIE 4081, 76–85 (2000).
[Crossref]

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

1999 (6)

D. Day, Gu Min, and A. Smallridge, “Use of two-photon excitation for erasable-rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948–950 (1999).
[Crossref]

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

1996 (1)

M. Shirai and M. Tsunooka, “Photoacid and photobase generators: chemistry and applications to polymeric materials,” Prog. Polym. Sci.,  21, 1–45 (1996).
[Crossref]

1991 (2)

Y. Boiko, “Volume holographic optics recording in photopolymerizable layers,” Holographic Optics III - Principles and Applications, Proc. SPIE 1507, 318–327 (1991).

G. Manivannan and J. Fouassier, “Primary process in the photosensitized polymerization of cationic monomers,” J. Polym. Sci. A: Polym. Chem.,  29,1113–1124 (1991).
[Crossref]

Ananthavel, S.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

Ananthavel, S.P.

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Barlow, S.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Baur, J. W.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Boiko, Y.

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

Y. Boiko, “Volume holographic optics recording in photopolymerizable layers,” Holographic Optics III - Principles and Applications, Proc. SPIE 1507, 318–327 (1991).

Y. Boiko, E. Tikhonov, and V. Shilov, “Photopolymerization studies by Michelson interferometer,” stored in and available from Ukr. Sci.-Research Inst. of Sci. and Technical Information (UkrNIINTI), Dep.No.2155, 17p., 15.09.1986 (in Russian).

C. Diamond, Y. Boiko, and S. Esener, “Two-photon holography in a 3D photopolymer host-guest matrix,” Opt. Express6, 64–68 (2000); http://www.opticsexpress.org/oearchive/source/18896.htm Errata: Opt. Express6, 109–110 (2000); http://www.opticsexpress.org/oearchive/source/19560.htm
[Crossref] [PubMed]

Bowen, M.

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

Clark, C. M.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Clarson, S.J.

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

Cokgor,

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

Costa, J.

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

Cumpston, B.H.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Day, D.

Denny, L. R.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Diamond, C.

C. Diamond, Y. Boiko, and S. Esener, “Two-photon holography in a 3D photopolymer host-guest matrix,” Opt. Express6, 64–68 (2000); http://www.opticsexpress.org/oearchive/source/18896.htm Errata: Opt. Express6, 109–110 (2000); http://www.opticsexpress.org/oearchive/source/19560.htm
[Crossref] [PubMed]

Dvornikov, A.S.

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

Dyer, D.L.

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Ehrlich, J.E.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Erskine, L.L.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Esener, S.

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

C. Diamond, Y. Boiko, and S. Esener, “Two-photon holography in a 3D photopolymer host-guest matrix,” Opt. Express6, 64–68 (2000); http://www.opticsexpress.org/oearchive/source/18896.htm Errata: Opt. Express6, 109–110 (2000); http://www.opticsexpress.org/oearchive/source/19560.htm
[Crossref] [PubMed]

Esener, S.C.

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

Fouassier, J.

G. Manivannan and J. Fouassier, “Primary process in the photosensitized polymerization of cationic monomers,” J. Polym. Sci. A: Polym. Chem.,  29,1113–1124 (1991).
[Crossref]

Heikal, A.A.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Ishikawa, M.

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

Joshi, M.P.

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

Juodkazis, S.

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

Kannan, R.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Kawata, Y.

Y. Kawata, “Three-dimensional memory,” Proc. SPIE 4081, 76–85 (2000).
[Crossref]

Kirkpatrick, S. M.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Kuebler, S.M.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Lee, B.K.

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

Lee, I-Y.S.

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Liu, W.Y.

W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
[Crossref]

Manivannan, G.

G. Manivannan and J. Fouassier, “Primary process in the photosensitized polymerization of cationic monomers,” J. Polym. Sci. A: Polym. Chem.,  29,1113–1124 (1991).
[Crossref]

Marder, S.R.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Matsuo, S.

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

McCord-Maughon, D.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Min, Gu

Misawa, H.

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

Nakatsuka, H.

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

Nishii, J.

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

Perry, J.W.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Piyaket, R.

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

Prasad, P.N.

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

Pudavar, H.E.

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

Qin, J.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

Qin, Jinqui

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Reinhardt, B. A.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Reinhardt, B.A.

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

Rentzepis, P.M.

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

Rockel, H.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Rumi, M.

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Shilov, V.

Y. Boiko, E. Tikhonov, and V. Shilov, “Photopolymerization studies by Michelson interferometer,” stored in and available from Ukr. Sci.-Research Inst. of Sci. and Technical Information (UkrNIINTI), Dep.No.2155, 17p., 15.09.1986 (in Russian).

Shirai, M.

M. Shirai and M. Tsunooka, “Photoacid and photobase generators: chemistry and applications to polymeric materials,” Prog. Polym. Sci.,  21, 1–45 (1996).
[Crossref]

Sivaraman, R.

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

Smallridge, A.

Steckl, A.J.

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

Steenson, D.P.

W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
[Crossref]

Steer, M.B.

W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
[Crossref]

Stone, M. O.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Sun, H.

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

Sun, H.B.

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

Tikhonov, E.

Y. Boiko, E. Tikhonov, and V. Shilov, “Photopolymerization studies by Michelson interferometer,” stored in and available from Ukr. Sci.-Research Inst. of Sci. and Technical Information (UkrNIINTI), Dep.No.2155, 17p., 15.09.1986 (in Russian).

Tomlin, D. W.

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Tsunooka, M.

M. Shirai and M. Tsunooka, “Photoacid and photobase generators: chemistry and applications to polymeric materials,” Prog. Polym. Sci.,  21, 1–45 (1996).
[Crossref]

Tsurumachi, N.

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

Wang, M.

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

Watanabe, M.

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

Wu, Xiang-Li

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Yamane, Y.

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

Yamasaki, K.

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

Yong Ye, Jing

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

Appl. Phys. A (1)

S. M. Kirkpatrick, J. W. Baur, C. M. Clark, L. R. Denny, D. W. Tomlin, B. A. Reinhardt, R. Kannan, and M. O. Stone, “Holographic Recording Using Two-Photon Induced Photopolymerization,” Appl. Phys. A 69, 461–464 (1999).
[Crossref]

Appl. Phys. Lett. (4)

H.E. Pudavar, M.P. Joshi, P.N. Prasad, and B.A. Reinhardt, “High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout,” Appl. Phys. Lett. 74, 1338–1340 (1999).
[Crossref]

Jing Yong Ye, M. Ishikawa, Y. Yamane, N. Tsurumachi, and H. Nakatsuka, “Enhancement of two-photon excited fluorescence using one-dimensional photonic crystals,” Appl. Phys. Lett.,  75, 3605–3607 (1999).
[Crossref]

R. Sivaraman, S.J. Clarson, B.K. Lee, A.J. Steckl, and B.A. Reinhardt, “Photoluminescence studies and read/write process of a strong two-photon absorbing chromophore,” Appl. Phys. Lett. 77, 328–330 (2000).
[Crossref]

K. Yamasaki, S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000).
[Crossref]

Complex Mediums, Proc. SPIE (1)

Y. Boiko, M. Bowen, M. Wang, J. Costa, and S. Esener, “Threshold enhancement in two-photon photo-polymerization,” Complex Mediums, Proc. SPIE 4097, 254–263 (2000).

Holographic Optics III - Principles and Applications, Proc. SPIE (1)

Y. Boiko, “Volume holographic optics recording in photopolymerizable layers,” Holographic Optics III - Principles and Applications, Proc. SPIE 1507, 318–327 (1991).

J. Polym. Sci. A: Polym. Chem. (1)

G. Manivannan and J. Fouassier, “Primary process in the photosensitized polymerization of cationic monomers,” J. Polym. Sci. A: Polym. Chem.,  29,1113–1124 (1991).
[Crossref]

Micro- and Nano-photonic Materials and Devices, Proc. SPIE (1)

S.M. Kuebler, B.H. Cumpston, S. Ananthavel, S. Barlow, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, S.R. Marder, and J.W. Perry, “Three-dimensional microfabrication using two-photon activated chemistry,” Micro- and Nano-photonic Materials and Devices, Proc. SPIE 3937, 97–105 (2000).

Nature (1)

B.H. Cumpston, S.P. Ananthavel, S. Barlow, D.L. Dyer, J.E. Ehrlich, L.L. Erskine, A.A. Heikal, S.M. Kuebler, I-Y.S. Lee, D. McCord-Maughon, Jinqui Qin, H. Rockel, M. Rumi, Xiang-Li Wu, S.R. Marder, and J.W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature,  398 (6722), 51–54 (1999).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (4)

Y. Kawata, “Three-dimensional memory,” Proc. SPIE 4081, 76–85 (2000).
[Crossref]

Cokgor, R. Piyaket, S.C. Esener, A.S. Dvornikov, and P.M. Rentzepis, “Two-photon absorption induced photochromic reactions in spirobenzopyran-doped PMMA waveguides,” Proc. SPIE 3623, 92–103 (1999).
[Crossref]

W.Y. Liu, D.P. Steenson, and M.B. Steer, “Technique of microfabrication suitable for machining submillimeter-wave components,” Proc. SPIE 4088, 144–147 (2000).
[Crossref]

H. Misawa, S. Juodkazis, H. Sun, S. Matsuo, and J. Nishii, “Formation of photonic crystals by femtosecond laser microfabrication,” Proc. SPIE 4088, 29–32 (2000).
[Crossref]

Prog. Polym. Sci. (1)

M. Shirai and M. Tsunooka, “Photoacid and photobase generators: chemistry and applications to polymeric materials,” Prog. Polym. Sci.,  21, 1–45 (1996).
[Crossref]

Other (2)

Y. Boiko, E. Tikhonov, and V. Shilov, “Photopolymerization studies by Michelson interferometer,” stored in and available from Ukr. Sci.-Research Inst. of Sci. and Technical Information (UkrNIINTI), Dep.No.2155, 17p., 15.09.1986 (in Russian).

C. Diamond, Y. Boiko, and S. Esener, “Two-photon holography in a 3D photopolymer host-guest matrix,” Opt. Express6, 64–68 (2000); http://www.opticsexpress.org/oearchive/source/18896.htm Errata: Opt. Express6, 109–110 (2000); http://www.opticsexpress.org/oearchive/source/19560.htm
[Crossref] [PubMed]

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Figures (9)

Fig. 1.
Fig. 1.

Chemical structure of cationic sensitizer Isopropylthioxanthone (ITX; 2&4 isomer mixture; C16H14OS)

Fig. 2.
Fig. 2.

Schematic for in-situ interferometric monitoring of two-photon photopolymerization. Only the two-photon induced contribution to the local change of the refractive index, Δntotal, is contributing to the signal on the detector. This technique is “blind” to the single photon induced contribution to Δn. The dominant contribution is due to Δnpol=n(Npol) - nmon, i.e. Δnpol≫Δnthermal, Δnbleaching, Δnothers if any.

Fig. 3.
Fig. 3.

Change of two-photon initiated cationic photopolymerization rate (which is proportional to the slope of the curve as indicated by Eq. (12)) at different peak intensities J of the laser beam - (a) J=10 GW/cm2; (b) J=20 GW/cm2 - for low concentrations (z=0.5%) of the cationic initiator DAI (formulation K126:ITX:DAI=97:2.5:0.5). Vertical axis is in arbitrary units of I using Eq. (8). Horizontal axis is exposure time in seconds. The polymerization rate Rlin is proportional to the slope of the beginning stages of exposure. Initial zero shift is due to background contribution after the beam is turned on. . Differences in appearance are not essential here, which is commented on in the text of the article.

Fig. 4.
Fig. 4.

Change of two-photon initiated cationic photopolymerization rate (which is proportional to the slope of the curve as indicated by Eq. (12)) at different peak intensities J of the laser beam - (a) J=10 GW/cm2; (b) J=20 GW/cm2 - for high concentrations (z=1.5%) of the cationic initiator DAI (formulation K126:ITX:DAI=96:2.5:1.5). Vertical axis is in arbitrary units of I using Eq. (8). Horizontal axis is exposure time in seconds. The polymerization rate Rlin is proportional to the slope of the beginning stages of exposure. Initial zero shift is due to background contribution after the beam is turned on.

Fig. 5.
Fig. 5.

Saturation of two-photon initiated cationic photopolymerization rate at near-threshold laser intensity. Formulation is K126:ITX:DAI=96:2.5:1.5. Vertical axis is in arbitrary units of I from using Eq. (8). Horizontal axis is exposure time in seconds. The polymerization rate Rlin is proportional to the slope of the beginning stages of exposure. Initial zero shift is due to background contribution after the beam is turned on.

Fig. 6.
Fig. 6.

Dynamic range of two-photon cationic photopolymerizable formulation K126:ITX:DAI=x:y:z, where x:y:z=96:2.5:1.5 for Series1 and x:y:z=97:2.5:0.5 for Series2. Points A and B are near-threshold conditions for each respective Series; upper plot is on a linear scale (a); lower plot is on a power m=1.7 scale (b), Jmax=300 GW/cm2.

Fig. 7.
Fig. 7.

Polymerization rate increase with the increase of the light intensity i for single-photon initiated polymerization reactions: (a) cationic photo-polymerization of the formulation K126:ITX:DAI=96:2.5:1.5 ; (b) free radical photo-polymerization of the formulation DPEPA:BDMK=95:5. UV light of 365 nm wavelength is from UVP lamp (Blak-Ray). Exposure time intervals are 2 min for (a) and 30 sec for (b).

Fig. 8.
Fig. 8.

Increase of initiator’s concentration z allows the reduction of the threshold peak intensity J2th of cationically induced two-photon photopolymerization of the formulation K126:ITX:DAI=x:2.5:z, where x+2.5+z=100%, 0.5%<z<1.5%.

Fig. 9.
Fig. 9.

Threshold peak intensity J2th of two-photon free radical polymerization reduces as the concentration z of the initiator increases in the formulation DPEPA:BDMK=x:z, where x+z=100%, 1%<z<5%.

Equations (20)

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

R = dN dt
N = n 0 n ( N ) n 0 n sat = Δ n ( N ) Δ n sat
R ( N ) = k d [ Δ n ( N ) ] dt = k d [ n ( N ) ] dt ,
ϕ 1 = ( L λ ) ( n 0 + Δ n )
ϕ 2 = ( L λ ) n 0
Φ = Δ ϕ = ϕ 1 ϕ 2 = ( L λ ) Δ n
d ( Δ ϕ ) dt = ( L λ ) d ( Δ n ) dt .
I = 2 I 1 ( 1 + cos Δ ϕ ) = 2 I 1 ( 1 + cos Φ ) .
dI dt = 2 I 1 d dt ( cos Δ ϕ ) = 2 I 1 sin Φ d Φ dt .
dI dt = 2 I 1 d Φ dt ; ( Φ = π 2 ) ,
dI dt = 2 I 1 ( L λ ) d ( Δ n ) dt = 0.5 I max ( L λ ) ( R k ) ; ( Φ = π 2 )
R ( N ) K = ( dI dt ) I max ; ( Φ = π 2 )
R = C J 1 2
R = C ( J J 2 th )
R = ( C J ) m 2
R = [ C ( J J 2 th ) ] m
R ( 1 ) = [ C ( J ( 1 ) J 2 th ) ] m
R ( 2 ) = [ C ( J ( 2 ) J 2 th ) ] m
m = [ ln ( R ( 1 ) ) ln ( R ( 2 ) ) ] [ ln ( J ( 1 ) J 2 th ) ln ( J ( 2 ) J 2 th ) ] =
= Δ 12 [ ln ( R ) ] Δ 12 [ ln ( J J 2 th ) ]

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