Abstract

Computer models are used to simulate the nonlinear formation of images of obscurations in laser beams. The predictions of the model are found to be in good agreement with measurements conducted in the nonlinear regime corresponding to a typical solid-state laser operation. In this regime, peak-to-mean fluence ratios large enough to induce damage in optical components are observed. The amplitude of the images and their location along the propagation axis are accurately predicted by the simulations. This indicates that the model is a reliable design tool for specifying component staging and optical specifications to avoid optical damage by this mechanism.

© 1997 Optical Society of America

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References

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  1. J. A. Paisner, E. M. Campbell, W. J. Hogan, “The National Ignition Facility Project,” , June1994 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  2. N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
    [CrossRef]
  3. J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
    [CrossRef] [PubMed]
  4. V. I. Bespalov, V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–312 (1966).
  5. J. B. Trenholme, “Theory of irregularity growth on laser beams,” , 1975 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  6. D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
    [CrossRef]
  7. J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
    [PubMed]
  8. J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
    [CrossRef] [PubMed]
  9. K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
    [CrossRef]
  10. W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
    [CrossRef]
  11. M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
    [CrossRef]
  12. W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  13. D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1, 108–113, , 1991 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  14. R. G. Nelson, “PROP92, a family of laser beam propagation codes,” , 1992 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  15. R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).
  16. M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
    [CrossRef]
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), 48–54.

1993 (1)

J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

1984 (1)

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

1982 (1)

M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[CrossRef]

1980 (1)

K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
[CrossRef]

1978 (1)

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

1977 (1)

J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
[PubMed]

1975 (2)

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

1966 (1)

V. I. Bespalov, V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–312 (1966).

1948 (1)

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Baranova, N. B.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov, V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–312 (1966).

Boyd, R.

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1, 108–113, , 1991 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Bykovskii, N. E.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

Campbell, E. M.

J. A. Paisner, E. M. Campbell, W. J. Hogan, “The National Ignition Facility Project,” , June1994 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Carman, R. L.

M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Eimerl, D.

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1, 108–113, , 1991 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Feit, M. J.

M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[CrossRef]

Fleck, J. A.

M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[CrossRef]

Gabor, D.

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Galanti, M.

K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
[CrossRef]

Glaze, J. A.

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), 48–54.

Haney, S. W.

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Henesian, M. A.

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Hogan, W. J.

J. A. Paisner, E. M. Campbell, W. J. Hogan, “The National Ignition Facility Project,” , June1994 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Hunt, J. T.

J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
[PubMed]

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Manes, K. R.

J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Milam, D.

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1, 108–113, , 1991 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Moran, M. J.

M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Nelson, R. G.

R. G. Nelson, “PROP92, a family of laser beam propagation codes,” , 1992 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Paisner, J. A.

J. A. Paisner, E. M. Campbell, W. J. Hogan, “The National Ignition Facility Project,” , June1994 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Renard, P. A.

J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
[PubMed]

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Sacks, R. A.

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Senatskii, Yu. V.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

She, C.

M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Simmons, W. W.

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
[PubMed]

Soileau, M. J.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Steiger, A.

M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[CrossRef]

Talanov, V. I.

V. I. Bespalov, V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–312 (1966).

Trenholme, J. B.

J. B. Trenholme, “Theory of irregularity growth on laser beams,” , 1975 (Lawrence Livermore National Laboratory, Livermore, Calif.).

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Van Stryland, E. W.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Volk, R.

K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Williams, W. H.

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

Witte, K. J.

K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
[CrossRef]

Zel’dovich, B. Ya.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

Appl. Opt. (3)

J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977).
[PubMed]

J. T. Hunt, J. A. Glaze, W. W. Simmons, P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

M. J. Moran, C. She, R. L. Carman, “Interferometric measurements of the nonlinear refractive index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

J. Comput. Phys. (1)

M. J. Feit, J. A. Fleck, A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[CrossRef]

JETP Lett. (1)

V. I. Bespalov, V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–312 (1966).

Nature (London) (1)

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Opt. Commun. (2)

K. J. Witte, M. Galanti, R. Volk, “n2 -measurements at 1.32 µm of some organic compounds usable as solvents in a saturable absorber for an atomic iodine laser,” Opt. Commun. 34, 278–282 (1980).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Sov. J. Quantum Electron. (1)

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel’dovich, Yu. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362–1366 (1975).
[CrossRef]

Other (7)

J. A. Paisner, E. M. Campbell, W. J. Hogan, “The National Ignition Facility Project,” , June1994 (Lawrence Livermore National Laboratory, Livermore, Calif.).

J. B. Trenholme, “Theory of irregularity growth on laser beams,” , 1975 (Lawrence Livermore National Laboratory, Livermore, Calif.).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), 48–54.

W. H. Williams, K. R. Manes, J. T. Hunt, P. A. Renard, D. Milam, D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes,” ICF Quart. Rep.6, 7–14, , 1995 (Lawrence Livermore National Laboratory, Livermore, Calif.).

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1, 108–113, , 1991 (Lawrence Livermore National Laboratory, Livermore, Calif.).

R. G. Nelson, “PROP92, a family of laser beam propagation codes,” , 1992 (Lawrence Livermore National Laboratory, Livermore, Calif.).

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, 207–213, , 1997 (Lawrence Livermore National Laboratory, Livermore, Calif.).

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Figures (8)

Fig. 1
Fig. 1

Nonlinear image formation. An incident wave scatters from an obscuration and interferes with the main beam to produce an interference pattern. A phase screen is applied by the nonlinear (intensity-dependent) index of refraction of a second component downstream. The phase screen works like a Fresnel zone plate to focus light from the main beam on axis.

Fig. 2
Fig. 2

Experimental arrangement for recording high-intensity images formed by nonlinear refraction.

Fig. 3
Fig. 3

CCD image of a high-intensity image formed by nonlinear refraction. The nonlinear phase pushback, B, for this shot is 1.08 rad.

Fig. 4
Fig. 4

Vertical line-outs through fluence distribution for calculated (dashed curve) and measured (solid curve) high-intensity images. The nonlinear phase pushback was 1.08 rad.

Fig. 5
Fig. 5

Vertical line-outs through fluence distribution for calculated (dashed curve) and measured (solid curve) high-intensity images. The nonlinear phase pushback was 1.74 rad.

Fig. 6
Fig. 6

Calculated variation of the peak fluence of a nonlinear image with propagation distance from the rear of the nonlinear sample. The location of CCD camera in the experimental measurement is indicated.

Fig. 7
Fig. 7

Vertical line-out through the calculated fluence distribution of a high-intensity image in an image plane where object and image distances are equal.

Fig. 8
Fig. 8

Variation of the peak fluence of a nonlinear image with respect to the nonlinear phase pushback B. Points represent experimental data and the solid curve is the result of a numerical calculation.

Equations (2)

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n=n0+γI+.
B=2πλγIt,

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