Abstract

Experimental measurements and computer simulations of nonlinear holographic imaging of phase errors in laser beams are presented. The computer models are found to accurately predict the results of the experiments. Comparison with similar results by use of amplitude scatterers reveals that the image location (along the propagation path) is the same for phase and amplitude scatterers. However, the intensity and fluence of the image of a phase scatterer are significantly larger, indicating that phase objects pose a larger damage threat to optical components.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. T. Hunt, K. R. Manes, P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
    [CrossRef] [PubMed]
  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. 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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).
  4. C. C. Widmayer, D. Milam, S. P. deSzoeke, “Nonlinear formation of holographic images of obscurations in laser beams,” Appl. Opt. 36, 9342–9347 (1997).
    [CrossRef]
  5. R. G. Nelson, “PROP92, a family of laser beam propagation codes,” internal memorandum (unnumbered) (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).
  6. R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).
  7. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 735.
  8. D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1(3), 108–113, (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).
  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(2), 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(2), 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(6), 259–263 (1975).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, U.K., 1970).
  13. A. Sommerfeld, Optics (Academic, New York, 1954).
  14. A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54, 931–937 (1938).
    [CrossRef]

1997

1993

1984

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50(2), 256–260 (1984).
[CrossRef]

1980

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(2), 278–282 (1980).
[CrossRef]

1975

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(6), 259–263 (1975).
[CrossRef]

1938

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54, 931–937 (1938).
[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]

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, U.K., 1970).

Boyd, R.

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1(3), 108–113, (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

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]

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(6), 259–263 (1975).
[CrossRef]

deSzoeke, S. P.

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1(3), 108–113, (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

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(2), 278–282 (1980).
[CrossRef]

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, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).

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, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).

Hunt, J. T.

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

Milam, D.

C. C. Widmayer, D. Milam, S. P. deSzoeke, “Nonlinear formation of holographic images of obscurations in laser beams,” Appl. Opt. 36, 9342–9347 (1997).
[CrossRef]

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1(3), 108–113, (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

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(6), 259–263 (1975).
[CrossRef]

Nelson, R. G.

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

Renard, P. A.

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

Rubinowicz, A.

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54, 931–937 (1938).
[CrossRef]

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, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).

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(6), 259–263 (1975).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 735.

Soileau, M. J.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50(2), 256–260 (1984).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1954).

Trenholme, J. B.

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).

Van Stryland, E. W.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50(2), 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(2), 278–282 (1980).
[CrossRef]

Widmayer, C. C.

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50(2), 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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

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(2), 278–282 (1980).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, U.K., 1970).

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.

IEEE J. Quantum Electron.

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(6), 259–263 (1975).
[CrossRef]

Opt. Commun.

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(2), 278–282 (1980).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50(2), 256–260 (1984).
[CrossRef]

Phys. Rev.

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54, 931–937 (1938).
[CrossRef]

Sov. J. Quantum Electron.

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

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, (1), 7–14, (Lawrence Livermore National Laboratory, Livermore, Calif., 1995).

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

R. A. Sacks, M. A. Henesian, S. W. Haney, J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Quart. Rep.6, (4), 207–213, (Lawrence Livermore National Laboratory, Livermore, Calif., 1997).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 735.

D. Eimerl, R. Boyd, D. Milam, “The OSL: a new facility for laser research,” ICF Quart. Rep.1(3), 108–113, (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, U.K., 1970).

A. Sommerfeld, Optics (Academic, New York, 1954).

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 (9)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Phase shift applied to the numerically calculated beam in the region containing the phase dot.

Fig. 3
Fig. 3

Measured (solid curve) and calculated (dotted curve) spatial profiles of nonlinear image in plane 88.6 cm behind the nonlinear element. Nonlinear phase pushback B was 1.00 rad.

Fig. 4
Fig. 4

Measured (solid curve) and calculated (dotted curve) spatial profiles of nonlinear image in plane 88.6 cm behind the nonlinear element. Nonlinear phase pushback B was 0.56 rad.

Fig. 5
Fig. 5

Calculated spatial profile showing a sharp image of the phase dot in the plane 94.6 cm behind the nonlinear element. Nonlinear phase pushback B was 1.00 rad.

Fig. 6
Fig. 6

Calculated evolution of peak fluence along a section of the propagation path for B = 1.00 rad. Measured points are experimental shot data with 0.97 < B < 1.06. The dashed line represents the linear case with no nonlinear refraction in the optical element.

Fig. 7
Fig. 7

Peak fluence as a function of the B integral with the imaging plane at the first peak 88.6 cm from the back of the CS2.

Fig. 8
Fig. 8

Comparative peak fluence evolution that is due to phase and amplitude scatterers; B = 1.00 rad.

Fig. 9
Fig. 9

Comparison of peak fluence for phase and amplitude scatterers at the second peak along the propagation path.

Equations (2)

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

n = n 0 + γ I + ,
B = 2 π λ   γ It ,

Metrics