Abstract

A versatile, rapidly convergent, iterative algorithm is presented for the construction of kinoform phase plates for tailoring the far-field intensity distribution of laser beams. The method consists of repeated Fourier transforming between the near-field and the far-field planes with constraints imposed in each plane. For application to inertial confinement fusion, the converged far-field pattern contains more than 95% of the incident energy inside a desired region and is relatively insensitive to beam aberrations.

© 1994 Optical Society of America

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References

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  1. J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
    [CrossRef]
  2. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
    [CrossRef]
  3. S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
    [CrossRef] [PubMed]
  4. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8, p. 393.
  5. See, for example,J. R. Feinup, Appl. Opt. 21, 2758 (1982).
    [CrossRef]
  6. A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).
  7. X. Deng, X. Liang, Z. Chen, W. Yu, R. Ma, Appl. Opt. 25, 377 (1986); T. Jitsuno, N. Nishi, K. Tsubakimoto, M. Nakatsuka, K. Nishihara, S. Nakai in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper CThI2; C. N. Danson, Rutherford Appleton Laboratory, Didcot, Oxon. OX11 0QX, UK (personal communication, 1993).
    [CrossRef]
  8. H. T. Powell, S. N. Dixit, M. A. Henesian, LLNL ICF Quarterly Rep. UCRL-LR-105821-91-1 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990), pp. 28–38; S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, J. Appl. Phys. 66, 3456 (1989).
    [CrossRef]
  9. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5, p. 225.

1993

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

1992

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
[CrossRef]

1986

1984

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

1982

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8, p. 393.

Campbell, E. M.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
[CrossRef]

Chen, Z.

Deng, X.

Dixit, S. N.

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

H. T. Powell, S. N. Dixit, M. A. Henesian, LLNL ICF Quarterly Rep. UCRL-LR-105821-91-1 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990), pp. 28–38; S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, J. Appl. Phys. 66, 3456 (1989).
[CrossRef]

Eimerl, D.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Feinup, J. R.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5, p. 225.

Henesian, M. A.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

H. T. Powell, S. N. Dixit, M. A. Henesian, LLNL ICF Quarterly Rep. UCRL-LR-105821-91-1 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990), pp. 28–38; S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, J. Appl. Phys. 66, 3456 (1989).
[CrossRef]

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Lawson, J. K.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Liang, X.

Lindl, J. D.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
[CrossRef]

Ma, R.

Manes, K. R.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

McCrory, R. L.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
[CrossRef]

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Morgan, A. J.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Powell, H. T.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

H. T. Powell, S. N. Dixit, M. A. Henesian, LLNL ICF Quarterly Rep. UCRL-LR-105821-91-1 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990), pp. 28–38; S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, J. Appl. Phys. 66, 3456 (1989).
[CrossRef]

Thomas, I. M.

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Trenholme, J. B.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Wegner, P. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8, p. 393.

Woods, B. W.

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, Appl. Opt. 32, 2543 (1993), and references therein.
[CrossRef] [PubMed]

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Yu, W.

Appl. Opt.

Phys. Rev. Lett.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Phys. Today

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45 (9), 32 (1992).
[CrossRef]

Proc. Soc. Photo Opt. Instrum. Eng.

A preliminary account of this research was reported byJ. K. Lawson, S. N. Dixit, D. Eimerl, M. A. Henesian, K. R. Manes, A. J. Morgan, H. T. Powell, I. M. Thomas, J. B. Trenholme, B. W. Woods, Proc. Soc. Photo Opt. Instrum. Eng. 1870, 88 (1993).

Other

H. T. Powell, S. N. Dixit, M. A. Henesian, LLNL ICF Quarterly Rep. UCRL-LR-105821-91-1 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990), pp. 28–38; S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, J. M. Soures, J. Appl. Phys. 66, 3456 (1989).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5, p. 225.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8, p. 393.

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Figures (3)

Fig. 1
Fig. 1

Example of a complex FF intensity profile that can be produced by a suitably generated phase screen by use of the iterative algorithm described in this Letter.

Fig. 2
Fig. 2

(a) FF intensity distribution obtained after 50 iterations. The spatial extent of the image is 800 μm × 800 μm. (b) A portion of the NF kinoform phase screen. The gray scale spans from −π (black) to π (white). The spatial extent of the image is 15 cm × 15 cm. (c) The same as (a) but including the input beam phase aberrations.

Fig. 3
Fig. 3

FF energy content as a function of the FF radius (see text for a description of the various curves).

Equations (2)

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E FF ( ν x , ν y ) = - i λ f input aperture d x d y × exp [ - i 2 π λ f ( x x + y y ) ] E NF ( x , y ) exp [ i ϕ ( x , y ) ] ,
I NF ( x , y ) = E NF 2 = exp { - [ ( x 2 + y 2 ) / r 0 2 ] 4 } ,

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