Abstract

High-performance phase plates are of vital concern for controlling the far-field irradiance of laser-fusion systems. Several designs for solving this difficult problem have been reported in Optics Letters [e. g., S. N. Dixit et al., Opt. Lett. 19, 417 (1994)]. We report a surface-based form of simulated annealing that significantly improves the irradiance control while eliminating the high-scatter problems that have plagued other methods.

© 1996 Optical Society of America

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References

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  1. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, K. A. Nugent, Opt. Lett. 19, 417 (1994).
    [PubMed]
  2. Y. Lin, T. J. Kessler, G. N. Lawrence, Opt. Lett. 20, 764 (1995).
    [CrossRef] [PubMed]
  3. N. Yoshikawa, T. Yatagai, Appl. Opt. 33, 863 (1994).
    [CrossRef] [PubMed]
  4. S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef]
  5. S. Kirkpatrick, J. Stat. Phys. 34, 975 (1984).
    [CrossRef]
  6. S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, Opt. Lett. 20, 1409 (1995).
    [CrossRef] [PubMed]
  7. H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
    [CrossRef]
  8. K. Ergenzinger, K. H. Hoffman, P. Salamon, J. Appl. Phys. 77, 5501 (1995).
    [CrossRef]

1995 (3)

1994 (2)

1987 (1)

H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
[CrossRef]

1984 (1)

S. Kirkpatrick, J. Stat. Phys. 34, 975 (1984).
[CrossRef]

1983 (1)

S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Chen, C.

Dixit, S. N.

Ergenzinger, K.

K. Ergenzinger, K. H. Hoffman, P. Salamon, J. Appl. Phys. 77, 5501 (1995).
[CrossRef]

Gelatt, C. D.

S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Hartley, R.

H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
[CrossRef]

Hoffman, K. H.

K. Ergenzinger, K. H. Hoffman, P. Salamon, J. Appl. Phys. 77, 5501 (1995).
[CrossRef]

Hudson, T. D.

Kessler, T. J.

Kirkpartrick, S.

S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, J. Stat. Phys. 34, 975 (1984).
[CrossRef]

Lawrence, G. N.

Lawson, J. K.

Lin, Y.

Lu, M.

Manes, K. R.

McMillen, D. K.

Nugent, K. A.

Powell, H. T.

Salamon, P.

K. Ergenzinger, K. H. Hoffman, P. Salamon, J. Appl. Phys. 77, 5501 (1995).
[CrossRef]

Szu, H.

H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
[CrossRef]

Vecchi, M. P.

S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Yatagai, T.

Yin, S.

Yoshikawa, N.

Yu, F. T. S.

Appl. Opt. (1)

J. Appl. Phys. (1)

K. Ergenzinger, K. H. Hoffman, P. Salamon, J. Appl. Phys. 77, 5501 (1995).
[CrossRef]

J. Stat. Phys. (1)

S. Kirkpatrick, J. Stat. Phys. 34, 975 (1984).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

H. Szu, R. Hartley, Phys. Lett. A 122, 157 (1987).
[CrossRef]

Science (1)

S. Kirkpartrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Azimuthal average of far-field irradiance owing to a phase plate designed by phase retrieval, with the parameters defined in the text. The ideal eighth-order super-Gaussian curve is shown by the smooth solid curve. The azimuthal average provides considerable smoothing of the data, particularly at the larger radius values. The phase-retrieval solution shows shoulder droop and rather slow decay to zero at large radius values because of wide-angle scattering from steep surface slopes. The effect of 2π line discontinuities does not appear in the numerical calculation because the width of the discontinuities is effectively zero but will exist in the manufactured part because, in practice, there must always be some finite width to the discontinuities.

Fig. 2
Fig. 2

Azimuthal average of far-field irradiance owing to a phase plate designed by simulated annealing. The conditions are the same as for Fig. 1. The shoulder of the curve is considerably more square than for phase retrieval, and the decay to zero is more rapid, indicating little wide-angle scattering because there are no steep surface slopes.

Equations (3)

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target shape = t ( r ) = exp [ 2 ( r / r 0 ) M ] ,
cos t function = S = 0 [ f ( r ) t ( r ) ] 2 2 πr d r ,
p = exp ( Δ S / T ) ,

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