Abstract

The design of phase plates based on a phase-retrieval algorithm has been shown to be successful in achieving high-order super-Gaussian distributions in the far field; however, these phase plates exhibit wide-angle scattering losses due to phase discontinuities. We report that, by starting with a distributed phase plate that is a strictly continuous surface and using only a few cycles of a phase-retrieval algorithm, we have obtained good fourth-order super-Gaussian fit and lower scattering loss.

© 1995 Optical Society of America

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References

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  1. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
    [CrossRef]
  2. Laboratory for Laser Energetics LLE Review 33, NTIS document DOE/DP40200-65 (Laboratory for Laser Energetics, Rochester, N.Y., 1987), p. 1.
  3. X. Deng, X. Liang, Z. Chen, W. Yu, R. Ma, Appl. Opt. 25, 377 (1986).
    [CrossRef] [PubMed]
  4. T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).
  5. J. W. Goodman, in Laser Speckle and Related Phenomena, Vol. 9 of Springer Series in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 2, p. 9.
    [CrossRef]
  6. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, K. A. Nugent, Opt. Lett. 19, 417 (1994).
    [PubMed]
  7. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  8. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  9. J. M. Huntley, Appl. Opt. 28, 3268 (1989).
    [CrossRef] [PubMed]
  10. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.
  11. GLAD is a general-purpose laser system and physical-optics computer program. It is a proprietary product of Applied Optics Research, Tucson, Arizona.

1994 (1)

1993 (1)

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).

1989 (1)

1986 (1)

1984 (1)

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

1982 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Arinaga, S.

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

Armstrong, J. J.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).

Chen, Z.

Deng, X.

Dixit, S. N.

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, Vol. 9 of Springer Series in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 2, p. 9.
[CrossRef]

Huntley, J. M.

Kato, Y.

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

Kessler, T. J.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).

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.

Liang, X.

Lin, Y.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).

Ma, R.

Manes, K. R.

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]

Nakatsuka, M.

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

Nugent, K. A.

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Powell, H. T.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Velazquez, B.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(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.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Appl. Opt. (3)

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Phys. Rev. Lett. (1)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. Soc. Photo-Opt. Instrum. Eng. 1870, 95(1993).

Other (4)

J. W. Goodman, in Laser Speckle and Related Phenomena, Vol. 9 of Springer Series in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 2, p. 9.
[CrossRef]

Laboratory for Laser Energetics LLE Review 33, NTIS document DOE/DP40200-65 (Laboratory for Laser Energetics, Rochester, N.Y., 1987), p. 1.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

GLAD is a general-purpose laser system and physical-optics computer program. It is a proprietary product of Applied Optics Research, Tucson, Arizona.

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Figures (3)

Fig. 1
Fig. 1

Example of a horizontally oriented pair of positive (right) and negative (left) phase poles with a branch cut between the poles. The wave-front slope in the immediate region of each pole is approximately λ/2πr, causing wide-angle vortex scattering. Theoretically the branch cut is a perfectly sharp discontinuity of λ height; however, manufacturing can result in a finite slope to the branch cut, causing scattering loss.

Fig. 2
Fig. 2

Azimuthally averaged profiles of the fourth-order super-Gaussian function (curve 1), the hybrid DPP (curve 2), the PRRS (curve 3), and the PRHD (curve 4). The curves represent an ensemble average of 100 calculations done with different random seeds. Light that falls outside 500 μm is considered wide-angle scattering. The PRHD has a wider flat region in the center than does the PRRS.

Fig. 3
Fig. 3

(a) Phase plot of PRHD kinoform showing a 1.2 cm × 1.2 cm section of the 28-cm-diameter beam. Islands and plateaus of height λ result in discontinuities of net length of ∼140 pixel lengths. (b) Conventional phase unwrapping, which ignores branch cuts, reduces the net length of the discontinuities. The phase-unwrapping algorithm fails at the branch cut between the vertically oriented pole pair near the center of the display, creating a spurious horizontal plateau of 28 pixel lengths. (c) Loci of real (solid lines) and imaginary (dashed lines) zeros. The two primary poles are marked. (d) Phase unwrapping with branch-cut recognition reduces the net discontinuity length to the length of the branch cut (approximately two pixel lengths).

Tables (1)

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Table 1 Pole Counts and Wide-Angle Scattering Losses for the Three Design Typesa

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