Abstract

A novel approach for measuring the diffusion coefficients in photopolymerisable materials is proposed. The method is based on studying the evolution of the surface relief profile in a single illuminated spot using an interferometric surface profiler. It is shown that the observed post-exposure swelling in the illuminated spot is due to mass-transport of monomer from the unexposed to the exposed area driven by a monomer concentration gradient set up by the monomer polymerization in the exposed area. Appropriate choice of the thickness of the studied layers ensures both lateral movement of monomer and negligible contribution from the depth. The diffusion coefficient is retrieved from the standard one-dimensional diffusion equation where the height of the profile in the center of the illuminated spot is used instead of the monomer concentration. In contrast to other techniques for measuring the diffusion in photopolymerisable materials, no assumptions or preliminary information about the polymerization rates are required. It is shown how the method can be used for studying the intensity and polymer density dependence of diffusion coefficient.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, "Optical photopolymers: Design and applications," Adv. Mater. 10, 1219-1224 (1998).
    [CrossRef]
  2. A. Sullivan, M. Grabowski, and R. McLeod, "Three-dimensional direct-write lithography into photopolymer," Appl. Opt. 46, 295-301 (2007).
    [CrossRef] [PubMed]
  3. S. Guntaka, V. Toal, and S. Martin, "Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern Interferometry," Appl. Opt. 41, 7475-7479 (2002).
    [CrossRef] [PubMed]
  4. H. J. Zhou, V. Morozov, and J. Neff, "Characterization of DuPont photopolymers in infrared light for free-space optical interconnects," Appl. Opt. 34, 7457-7459 (1995).
    [CrossRef] [PubMed]
  5. H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, "Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing," J. Opt. A:Pure&Appl. Opt. 7, 255-261 (2005).
    [CrossRef]
  6. http://www.inphase-technologies.com/
  7. http://www.aprilisinc.com/
  8. G. Zhao and P. Mouroulis, "Diffusion model of hologram formation in dry photopolymer materials," J. Mod. Opt. 41, 1929-1939 (1994).
    [CrossRef]
  9. V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997).
    [CrossRef]
  10. V. Moreau, Y. Renotte, and Y. Lion, "Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model," Appl. Opt. 41, 3427-3435 (2002).
    [CrossRef] [PubMed]
  11. S. Piazzola and B. Jenkins, "First-harmonic diffusion model for holographic grating formation in photopolymers," J. Opt. Soc. Am. B 17, 1147-1157 (2000).
    [CrossRef]
  12. 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, 2900-2905 (2004).
    [CrossRef] [PubMed]
  13. S. Martin, I. Naydenova, R. Jallapuram, R. Howard, and V. Toal, "Two-way diffusion model for the recording mechanism in a self developing dry acrylamide photopolymer," Proc. SPIE 6252, 62525-625217 (2006).
  14. S. Martin, C. A. Feely, and V. Toal, "Holographic recording characteristics of an acrylamide-based photopolymer," Appl. Opt. 36, 5757-5768 (1997).
    [CrossRef] [PubMed]
  15. A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).
  16. C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996).
    [CrossRef]
  17. J. Neumann, K. S. Wieking, and D. Kip, "Direct laser writing of surface reliefs in dry, self-developing photopolymer films," Appl. Opt. 38, 5418-5421 (1999).
    [CrossRef]
  18. I. Naydenova, E. Mihaylova, S. Martin, and V. Toal, "Holographic patterning of acrylamide-based photopolymer surface," Opt. Express 13, 4878-4889 (2005).
    [CrossRef] [PubMed]
  19. K. Pavani, I. Naydenova, S. Martin, and V. Toal, "Photoinduced surface relief studies in an acrylamide-based photopolymer," J. Opt. A: Pure Appl. Opt. 9, 43-48 (2007).
    [CrossRef]
  20. W. J. Roff and J. R. Scott, Fibers, films, plastics and rubbers, a handbook of common polymers (Butterworths, London, 1971).
  21. A. Veniaminov and E. Bartsch, "Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate," J. Opt. A: Pure Appl. Opt. 4, 387-392 (2002).
    [CrossRef]
  22. R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, "Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer," Appl. Opt. 47, 206-212 (2008).
    [CrossRef] [PubMed]
  23. S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, "3 Dimensional analysis of holographic photopolymers based memories," Opt. Express 13, 3543-3557 (2005).
    [CrossRef] [PubMed]
  24. S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
    [CrossRef]
  25. P. Munk and T. M. Aminabhavi, "Introduction to macromolecular science," (Jonh Wiley & Sons, Inc., New York, 2002).
  26. M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008).
    [CrossRef]

2008

2007

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

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).

K. Pavani, I. Naydenova, S. Martin, and V. Toal, "Photoinduced surface relief studies in an acrylamide-based photopolymer," J. Opt. A: Pure Appl. Opt. 9, 43-48 (2007).
[CrossRef]

2006

S. Martin, I. Naydenova, R. Jallapuram, R. Howard, and V. Toal, "Two-way diffusion model for the recording mechanism in a self developing dry acrylamide photopolymer," Proc. SPIE 6252, 62525-625217 (2006).

2005

2004

2002

2000

1999

1998

T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, "Optical photopolymers: Design and applications," Adv. Mater. 10, 1219-1224 (1998).
[CrossRef]

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, 5913-5923 (1997).
[CrossRef]

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

1996

C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996).
[CrossRef]

1995

1994

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

Bartsch, E.

A. Veniaminov and E. Bartsch, "Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate," J. Opt. A: Pure Appl. Opt. 4, 387-392 (2002).
[CrossRef]

Belendez, A.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

Beléndez, A.

Byrne, H. J.

Colvin, V. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997).
[CrossRef]

Croutxe-Barghorn, C.

C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996).
[CrossRef]

Feely, C. A.

Fernandez, E.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

Gallego, S.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, "3 Dimensional analysis of holographic photopolymers based memories," Opt. Express 13, 3543-3557 (2005).
[CrossRef] [PubMed]

Grabowski, M.

Guntaka, S.

Harris, A. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997).
[CrossRef]

Havranek, A.

A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).

Havrankova, J.

A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).

Howard, R.

Jallapuram, R.

Jenkins, B.

Kelly, J. V.

Kip, D.

Kveton, M.

A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).

Larson, R. G.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997).
[CrossRef]

Lion, Y.

Lougnot, D. J.

C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996).
[CrossRef]

Márquez, A.

Martin, S.

McLeod, R.

Mihaylova, E.

Moreau, V.

Morozov, V.

Mouroulis, P.

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

Naydenova, I.

Neff, J.

Neipp, C.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, "3 Dimensional analysis of holographic photopolymers based memories," Opt. Express 13, 3543-3557 (2005).
[CrossRef] [PubMed]

Neumann, J.

Ortuno, M.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

Ortuño, M.

Pascual, I.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, "3 Dimensional analysis of holographic photopolymers based memories," Opt. Express 13, 3543-3557 (2005).
[CrossRef] [PubMed]

Pavani, K.

K. Pavani, I. Naydenova, S. Martin, and V. Toal, "Photoinduced surface relief studies in an acrylamide-based photopolymer," J. Opt. A: Pure Appl. Opt. 9, 43-48 (2007).
[CrossRef]

Piazzola, S.

Renotte, Y.

Schilling, M. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997).
[CrossRef]

Sheridan, J.

Sherif, H.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, "Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing," J. Opt. A:Pure&Appl. Opt. 7, 255-261 (2005).
[CrossRef]

Sullivan, A.

Tanaka, T.

M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008).
[CrossRef]

Toal, V.

Toishi, M.

M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008).
[CrossRef]

Veniaminov, A.

A. Veniaminov and E. Bartsch, "Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate," J. Opt. A: Pure Appl. Opt. 4, 387-392 (2002).
[CrossRef]

Watanabe, K.

M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008).
[CrossRef]

Wieking, K. S.

Zhao, G.

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

Zhou, H. J.

Adv. Mat.

T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, "Optical photopolymers: Design and applications," Adv. Mater. 10, 1219-1224 (1998).
[CrossRef]

Appl. Opt.

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

J. Neumann, K. S. Wieking, and D. Kip, "Direct laser writing of surface reliefs in dry, self-developing photopolymer films," Appl. Opt. 38, 5418-5421 (1999).
[CrossRef]

H. J. Zhou, V. Morozov, and J. Neff, "Characterization of DuPont photopolymers in infrared light for free-space optical interconnects," Appl. Opt. 34, 7457-7459 (1995).
[CrossRef] [PubMed]

V. Moreau, Y. Renotte, and Y. Lion, "Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model," Appl. Opt. 41, 3427-3435 (2002).
[CrossRef] [PubMed]

S. Guntaka, V. Toal, and S. Martin, "Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern Interferometry," Appl. Opt. 41, 7475-7479 (2002).
[CrossRef] [PubMed]

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, 2900-2905 (2004).
[CrossRef] [PubMed]

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

R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, "Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer," Appl. Opt. 47, 206-212 (2008).
[CrossRef] [PubMed]

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, 5913-5923 (1997).
[CrossRef]

J. Mod. Opt.

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

J. Opt. A: Pure Appl. Opt.

K. Pavani, I. Naydenova, S. Martin, and V. Toal, "Photoinduced surface relief studies in an acrylamide-based photopolymer," J. Opt. A: Pure Appl. Opt. 9, 43-48 (2007).
[CrossRef]

A. Veniaminov and E. Bartsch, "Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate," J. Opt. A: Pure Appl. Opt. 4, 387-392 (2002).
[CrossRef]

J. Opt. A:Pure&Appl. Opt.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, "Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing," J. Opt. A:Pure&Appl. Opt. 7, 255-261 (2005).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007).
[CrossRef]

Opt. Express

Opt. Rev.

M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008).
[CrossRef]

Polymer Bulletin

A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).

Proc. SPIE

S. Martin, I. Naydenova, R. Jallapuram, R. Howard, and V. Toal, "Two-way diffusion model for the recording mechanism in a self developing dry acrylamide photopolymer," Proc. SPIE 6252, 62525-625217 (2006).

Pure Appl. Opt.

C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996).
[CrossRef]

Other

http://www.inphase-technologies.com/

http://www.aprilisinc.com/

P. Munk and T. M. Aminabhavi, "Introduction to macromolecular science," (Jonh Wiley & Sons, Inc., New York, 2002).

W. J. Roff and J. R. Scott, Fibers, films, plastics and rubbers, a handbook of common polymers (Butterworths, London, 1971).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

(Color online) Typical images of the aperture (a) and the surface relief profile-perspective (b) and top view (c) collected by WLI.

Fig. 2.
Fig. 2.

(Color online) a) Cross-sections of the post-exposure time evolution of the surface relief profile. The unexposed sample surface is indicated by horizontal dashed line. Vertical solid lines mark the illuminated spot; b) Time dependence of the profile center height (t=0 is the time when exposure was stopped) (initial exposure of 30s with intensity of 10 mW/cm2)

Fig. 3.
Fig. 3.

(Color online) Exponential fit of the post-exposure time dependence of the profile height at the center of the spots with different diameters: 50µm (squares), 75µm (circles) and 100µm (triangles). Inset: the calculated time constant τ1 (Eq. (4)) as a function of squared spot radius. (Initial illumination for 30s with 10mW/cm2)

Fig. 4.
Fig. 4.

Thickness dependence of diffusion coefficient and intensity dependence on depth (inset) for photopolymer layer;

Fig. 5.
Fig. 5.

Intensity dependence of diffusion coefficient for the first (open circles) and second (solid squares) diffusion processes. Some of the error bars are within the symbols. (initial time of illumination is 30s).

Fig. 6.
Fig. 6.

Dependence of diffusion coefficient on the illumination time for the first and second (inset) process. (Intensity is 10 mW/cm2)

Equations (8)

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

Δ φ = Δ φ n + Δ φ h = φ n Δ n + φ h Δ h = 2 π λ ( h Δ n + n Δ h ) ,
Δ φ h Δ φ n = n Δ h h Δ n = Δ h h Δ n n .
r 2 = 2 D τ .
h = A 1 exp ( ( t τ 1 ) β 1 ) + A 2 exp ( ( t τ 2 ) β 2 ) .
m ( x , t ) t = x [ D ( x , t ) m ( x , t ) x ] ,
h ( x , t ) A ( m ( x , t ) m 0 ) ,
h ( x , t ) t = D ( t ) 2 h ( x , t ) x 2 ,
D ( t = t i ) = ( h t t = t i , x = x c ) ( 2 h x 2 t = t i , x = x c ) ,

Metrics