Abstract

The temporal behavior of beams diffracted by volume gratings in photopolymer thin films are measured and analyzed by solution of the diffusion equation for the monomer concentration inside the thin films. Two contributors to the refractive-index change that forms the volume gratings are assumed: One is the phase grating formed by modulation of the monomer concentration, and the other is the phase grating formed by modulation of the density of the polymeric materials. The phase grating that is due to monomer modulation is responsible for the initial fast rise and decay of the diffracted signal, and the phase grating that is due to modulation of density of the polymeric materials is responsible for the slowly rising and then steady signal. The temporal behavior of the diffracted beams is determined by the ratio of magnitudes of the incident beam intensity and the diffusion coefficient.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Curtis and D. Psaltis, “Characterization of the DuPont photopolymer for three-dimensional holographic storage,” Appl. Opt. 33, 5396–5399 (1994).
    [CrossRef] [PubMed]
  2. W. S. Colburn and K. A. Haines, “Volume hologram formation in photopolymer materials,” Appl. Opt. 10, 1636–1641 (1971).
    [CrossRef] [PubMed]
  3. D. J. Lougnot and C. Turck, “Photopolymers for holographic recording. III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269–279 (1992).
    [CrossRef]
  4. U. S. Rhee, H. J. Caulfield, C. S. Virkam, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
    [CrossRef] [PubMed]
  5. R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
    [CrossRef]
  6. S. Piazzolla and B. K. Jenkins, “Holographic grating formation in photopolymers,” Opt. Lett. 21, 1075–1077 (1996).
    [CrossRef] [PubMed]
  7. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
    [CrossRef]
  8. 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]
  9. R. H. Wopschall and T. R. Pampalone, “Dry photopolymer film for recording holograms,” Appl. Opt. 11, 2096–2097 (1972).
    [CrossRef] [PubMed]
  10. G. Odian, Principles of Polymerization (McGraw-Hill, New York, 1970), Chap. 3.
  11. G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
    [CrossRef]
  12. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975).
  13. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  14. U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
    [CrossRef]
  15. S. Calixto, “Dry polymer for holographic recording,” Appl. Opt. 26, 3904–3910 (1987).
    [CrossRef] [PubMed]
  16. T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
    [CrossRef]

1997 (1)

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]

1996 (1)

1995 (1)

1994 (2)

K. Curtis and D. Psaltis, “Characterization of the DuPont photopolymer for three-dimensional holographic storage,” Appl. Opt. 33, 5396–5399 (1994).
[CrossRef] [PubMed]

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

1993 (1)

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

1992 (1)

D. J. Lougnot and C. Turck, “Photopolymers for holographic recording. III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269–279 (1992).
[CrossRef]

1991 (1)

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[CrossRef]

1987 (1)

1984 (1)

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

1980 (1)

G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[CrossRef]

1972 (1)

1971 (1)

1969 (1)

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

Adhami, R. R.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[CrossRef]

Alvarez, D. C.

G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[CrossRef]

Burland, D. M.

G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[CrossRef]

Calixto, S.

Caufield, H. J.

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Caulfield, H. J.

Colburn, W. S.

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]

Curtis, K.

Dragostinova, V.

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Gregory, D. A.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[CrossRef]

Haines, K. A.

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]

Jenkins, B. K.

Kogelnik, H.

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

Lanteigne, D. J.

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[CrossRef]

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]

Lougnot, D. J.

D. J. Lougnot and C. Turck, “Photopolymers for holographic recording. III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269–279 (1992).
[CrossRef]

Markovski, P.

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Mirsalehi, M. M.

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Mouroulis, P.

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

Pampalone, T. R.

Piazzolla, S.

Psaltis, D.

Rhee, U. S.

Rhee, U.-S.

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

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]

Shamir, J.

U. S. Rhee, H. J. Caulfield, C. S. Virkam, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Stotanova, K.

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Todorov, T.

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Tomova, N.

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Turck, C.

D. J. Lougnot and C. Turck, “Photopolymers for holographic recording. III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269–279 (1992).
[CrossRef]

Urkam, C. S.

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Virkam, C. S.

Wopschall, R. H.

Zhao, G.

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

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

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

J. Appl. Phys. (1)

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. Chem. Phys. (1)

G. C. Bjorklund, D. M. Burland, and D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[CrossRef]

J. Mod. Opt. (1)

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

Microwave Opt. Technol. Lett. (1)

R. R. Adhami, D. J. Lanteigne, and D. A. Gregory, “Photopolymer hologram formation theory,” Microwave Opt. Technol. Lett. 4, 106–109 (1991).
[CrossRef]

Opt. Eng. (1)

U.-S. Rhee, H. J. Caufield, J. Shamir, C. S. Urkam, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

T. Todorov, P. Markovski, N. Tomova, V. Dragostinova, and K. Stotanova, “Photopolymers—holographic investigations, mechanism of recording and applications,” Opt. Quantum Electron. 16, 471–476 (1984).
[CrossRef]

Pure Appl. Opt. (1)

D. J. Lougnot and C. Turck, “Photopolymers for holographic recording. III. Time modulated illumination and thermal post-effect,” Pure Appl. Opt. 1, 269–279 (1992).
[CrossRef]

Other (2)

G. Odian, Principles of Polymerization (McGraw-Hill, New York, 1970), Chap. 3.

J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975).

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 (7)

Fig. 1
Fig. 1

Spatial distribution of monomers and density of polymeric materials as a photopolymer thin film is illuminated by a modulated beam. (a) The average monomer concentration decreases at intervals of 8 s from top to bottom, and the modulation vanishes finally. (b) The polymer grating appears from the bottom and it is cumulative with time.

Fig. 2
Fig. 2

Temporal changes of the monomer grating, the polymer grating, and the combined grating. A, The monomer modulation Δnm rises fast and finally decays to zero. B, The index modulation that is due to the density of the polymeric material rises more slowly but is cumulative with time, forming a permanent stable volume grating. C, D, Combined refractive-index modulation Δn for phase differences of 0 and π, respectively, between the monomer grating and the polymer grating.

Fig. 3
Fig. 3

Temporal behavior of diffraction efficiency obtained by the numerical analysis. (a) Temporal behavior of diffraction efficiency for beam intensities I1=40, 10, 2 mW/cm2 for the diffusion coefficient D=0.5×10-3 cm2/s. (b) Temporal behavior of diffraction efficiency for diffusion coefficients D=0.5×10-3, 1.0×10-3, and 2.0×10-3 cm2/s for a given value of the beam intensity, I1=20 mW/cm2.

Fig. 4
Fig. 4

Experimental setup for observing the temporal behavior of the diffraction efficiencies. Reference beam A1 and object beam A3 interfere to form the volume grating in the photopolymer thin film (PP), and read beam A2 is diffracted by the volume grating to generate signal beam A4. Another He–Ne laser measured the diffraction efficiency at the 633-nm wavelength. D1, D2, photoelectric detectors; M1, M2, mirrors; A5, A6, incident He–Ne laser beam, diffracted He–Ne laser beam; other abbreviations defined in text.

Fig. 5
Fig. 5

Temporal change in transmittance of the photopolymer thin film DuPont HRF150-38 for various beam intensities at a wavelength of 488 nm. We obtained the data by sending a single beam into the photopolymer film and measuring the transmitted intensity.

Fig. 6
Fig. 6

Temporal behavior of signal beam A4 for low-intensity exposure, I1=I3=4 mW/cm2. The assumed photochemical parameters that fit the experimental data are as shown, with ϕ=0.8 and T=0.65. Symbols represent results obtained from the experimental data. Because the incident beam is of low intensity, it increases monotonically and saturates to a relatively higher diffraction efficiency.

Fig. 7
Fig. 7

Temporal behavior of signal beam A4 for high-intensity exposure I1=I3=14 32mW/cm2. The assumed photochemical parameters that fit the experimental data are the same as for the low-intensity case of Fig. 6. Symbols represent the experimental data. For the intensity of I1=I3=14 mW/cm2, both the theory and the experimental data show that the diffraction ef ficiency reaches a flat value in 5 s. This means that the monomer grating becomes more significant to the diffraction efficien- cy at this intensity. As the intensity is increased I1=I3=32 mW/cm2, a fast-rising peak is observed, and then the final steady state with a relatively lower diffraction efficiency is reached.

Equations (29)

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

I2R.
R+MkiM1,
M1+MkpM2,
M2+MkpM3,
M3+MkpM4,
Mn+MkpMn+1,
Mn+Mmktdeadpolymer,
-Ct=Ri+Rp,
-Ct=Rp.
Rp=kpCCr,
Ri=2ktCr2.
Rp=kpC(Ri/2kt)1/2Ri1/2.
Ri=2ΦIa,
Ia(x)=I(x)[1-exp(-Zd)]=I(x)(1-T),
Cr=ΦI(x)(1-T)kt1/2,
Rp=kpCΦI(x)(1-T)kt1/2.
-Ct=kpCΦI(x)(1-T)kt1/2.
I(x)=I0[1+V cos(Kx)],
I0=I1+I3,
V=2I1I3I1+I3,
-Ct=D2Cx2+Q[1+V cos(Kx)]1/2C,
Q=kpΦI0(1-T)kt1/2,
St=Q[1+V cos(Kx)]1/2C,
Δnm=K1ΔCC0,
Δnp=K2ΔSC0,
Δn=Δnp+Δnm exp(iϕ).
η=exp(-2αd/cos θ)sin2πΔndλ cos θ,
Ci,j+1=Ci,j+δtδx2D(Ci+1,j-2Ci,j+Ci-1,j)-Qδt(1+V cos Kxi)1/2Ci,j,
Si,j+1=Si,j+Qδt(1+V cos Kxi)1/2Ci,j,

Metrics