Abstract

We demonstrate theoretically and experimentally that optical beams are self-focused and self-trapped upon initiating photopolymerization. This unique nonlinear optical phenomenon is dependent on the optical exposure and produces permanent index-of-refraction changes larger than 0.04. The resulting nonlinear wave equation is shown to be nonlocal in time and displays self-trapped solutions only for sufficiently low average optical intensities.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
    [CrossRef]
  2. G. Odian, Principles of Polymerization (Wiley, New York, 1981).
  3. W. J. Tomlinson, E. A. Chandross, in Advances in Photochemistry, J. J. N. Pitts, G. S. Hammond, K. Gollnick, eds. (Wiley, New York, 1985), Vol. 12, pp. 201–281.
  4. Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
    [CrossRef]
  5. L. Sun, G. L. Yip, Opt. Lett. 18, 1229 (1993).
    [CrossRef] [PubMed]
  6. G. R. Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
    [CrossRef]
  7. J. H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
    [CrossRef]

1993

1992

G. R. Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[CrossRef]

1990

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

1968

J. H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

1964

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
[CrossRef]

Chandross, E. A.

W. J. Tomlinson, E. A. Chandross, in Advances in Photochemistry, J. J. N. Pitts, G. S. Hammond, K. Gollnick, eds. (Wiley, New York, 1985), Vol. 12, pp. 201–281.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
[CrossRef]

Chung, Y.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Dagli, N.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Dawes, E.

J. H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
[CrossRef]

Hadley, G. R.

G. R. Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[CrossRef]

Marburger, J. H.

J. H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Odian, G.

G. Odian, Principles of Polymerization (Wiley, New York, 1981).

Sun, L.

Tomlinson, W. J.

W. J. Tomlinson, E. A. Chandross, in Advances in Photochemistry, J. J. N. Pitts, G. S. Hammond, K. Gollnick, eds. (Wiley, New York, 1985), Vol. 12, pp. 201–281.

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
[CrossRef]

Yip, G. L.

IEEE J. Quantum Electron

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

G. R. Hadley, IEEE J. Quantum Electron. 28, 363 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

J. H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479(1964).
[CrossRef]

Other

G. Odian, Principles of Polymerization (Wiley, New York, 1981).

W. J. Tomlinson, E. A. Chandross, in Advances in Photochemistry, J. J. N. Pitts, G. S. Hammond, K. Gollnick, eds. (Wiley, New York, 1985), Vol. 12, pp. 201–281.

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 (5)

Fig. 1
Fig. 1

Measured change in index of refraction (at 589.3 nm) of the diacrylate photopolymer under UV exposure at 325 nm. The fitted curve is given by Eq. (2) with Uo (in energy units) equal to 2.68 mJ cm−2.

Fig. 2
Fig. 2

Numerical simulations of beam propagation in photopolymer in time steps equal to 5tc. Left-most simulation, t = 0; right-most simulation, t = 15tc. The vertical scale is 103 wavelengths; the horizontal scale is 10 wavelengths.

Fig. 3
Fig. 3

Experimental setup for self-focusing and self-trapping of optical beams. The input power is approximately 5 mW at 325 nm.

Fig. 4
Fig. 4

Experimental demonstration of self-focusing upon photopolymerization. Left-most simulation, photopolymer at t = 0; right-most simulation, photopolymer at t = 30 s. The horizontal scale is 300 μm; the vertical scale is 1 mm.

Fig. 5
Fig. 5

(a) Series of fibers grown by self-trapping of the UV beam; the nominal diameter is 10 μm. (b) Three-dimensional fiber lattice with 50-μm-diameter filaments of 5-mm length, fabricated within a photopolymer-filled cuvette. (c) Array of fibers of 200-μm diameter and 10-mm length.

Equations (2)

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

Δ n ( x , y , z , t ) = Δ n o { 1 exp [ 1 U o 0 t τ | E ( t ) | 2 d t ] } ,
Δ n ( x , y , z , t ) = Δ n o exp [ 1 U o 0 t | E ( t ) | 2 d t ] .

Metrics