Abstract

We present numerical simulations of propagation of ultraviolet pulses through fused silica using a model that allows for the accumulative action of compaction back on the light. Compaction-induced self-focusing causes the light field to develop into a pattern of hot spots around the incident aperture that correlates with the damage patterns observed during marathon experiments designed to determine the onset of microchannel formation.

© 1999 Optical Society of America

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References

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  1. R. E. Schenker, W. G. Oldham, “Ultraviolet-induced densification in fused silica,” J. Appl. Phys. 82, 1065–1071 (1997).
    [CrossRef]
  2. V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
    [CrossRef]
  3. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).
  4. D. C. Allan, C. Smith, N. F. Borrelli, T. P. Seward, “193-nm excimer-laser-induced densification of fused silica,” Opt. Lett. 21, 1960–1962 (1996).
    [CrossRef] [PubMed]
  5. N. F. Borrelli, C. Smith, D. C. Allan, T. P. Seward, “Densification of fused silica under 193-nm excitation,” J. Opt. Soc. Am. B 14, 1606–1615 (1997).
    [CrossRef]
  6. The simulations reported in this article were performed by diffract, a software product of MM Research, Inc., Tucson, Ariz.
  7. A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
    [CrossRef]
  8. A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
    [CrossRef]
  9. A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 8.

1999 (1)

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

1997 (2)

R. E. Schenker, W. G. Oldham, “Ultraviolet-induced densification in fused silica,” J. Appl. Phys. 82, 1065–1071 (1997).
[CrossRef]

N. F. Borrelli, C. Smith, D. C. Allan, T. P. Seward, “Densification of fused silica under 193-nm excitation,” J. Opt. Soc. Am. B 14, 1606–1615 (1997).
[CrossRef]

1996 (1)

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).

1974 (1)

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
[CrossRef]

1973 (2)

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
[CrossRef]

Allan, D. C.

Borrelli, N. F.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 8.

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
[CrossRef]

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).

Grenville, A.

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

Liberman, V.

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).

Oldham, W. G.

R. E. Schenker, W. G. Oldham, “Ultraviolet-induced densification in fused silica,” J. Appl. Phys. 82, 1065–1071 (1997).
[CrossRef]

Pearson, J. E.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Rothschild, M.

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

Schenker, R. E.

R. E. Schenker, W. G. Oldham, “Ultraviolet-induced densification in fused silica,” J. Appl. Phys. 82, 1065–1071 (1997).
[CrossRef]

Sedlacek, J. H. C.

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

Seward, T. P.

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
[CrossRef]

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
[CrossRef]

Smith, C.

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
[CrossRef]

Terrell, N. J.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Uttaro, R. S.

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

Appl. Opt. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Opt. 10, 129–160 (1976).

Appl. Phys. Lett. (3)

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel diffraction effects in the design of high-power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–631 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178–181 (1974).
[CrossRef]

J. Appl. Phys. (1)

R. E. Schenker, W. G. Oldham, “Ultraviolet-induced densification in fused silica,” J. Appl. Phys. 82, 1065–1071 (1997).
[CrossRef]

J. NonCryst. Solids (1)

V. Liberman, M. Rothschild, J. H. C. Sedlacek, R. S. Uttaro, A. Grenville, “Excimer-laser-induced densification of fused silica: laser-fluence and material-grade effects on the scaling law,” J. NonCryst. Solids 244, 159–171 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 8.

The simulations reported in this article were performed by diffract, a software product of MM Research, Inc., Tucson, Ariz.

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Figures (2)

Fig. 1
Fig. 1

Output beam profile I(x, y, z = L, T) for (a) T = 0 showing Fresnel diffraction rings before the onset of compaction, (b) T = 20T c or N = 5.8 million pulses, (c) T = 30T c or N = 13 million pulses, (d) T = 60T c or N = 52.2 million pulses.

Fig. 2
Fig. 2

Photograph of microchannel formation on the back surface of a fused-silica sample irradiated from the front side with 5 × 107 pulses of a 193-nm excimer laser at a laser energy of 50 mJ/cm2/pulse incident through a hard aperture of 0.35-mm diameter.

Equations (7)

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

z=i2k2x2+2y2+ik0Δn,
Δρρ0=κNI2τc,
ddT Δnr, T=γI2cr, T,
z=i2k T2+ik0γ TdT|r, T|4cr, T.
lz=i2k T2l+ik0Δnlrl
Δnlr=Δnl-1r+γTc|l-1r|4c,
lx, y, z=0=inx, y,

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