Abstract

We report on the theory and development of a diffractive element composed of a binary phase zone-plate array. This component conditions the intensity distribution in the focal plane of a conventional refractive lens to generate efficiently (82%) a flattop intensity envelope on target. Analysis of the design indicates that manufacturing tolerances are not critical. Experimental performances on target from x-ray emission and shock-breakout measurements are also presented.

© 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, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
    [CrossRef]
  2. M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
    [CrossRef] [PubMed]
  3. R. Epstein, S. Skupsky, “Anticipated improvement in laser beam uniformity using distributed phase plates with quasi-random patterns,” J. Appl. Phys. 68, 924–931 (1990).
    [CrossRef]
  4. S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, “Random phase plates for beam smoothing on the Nova laser,” Appl. Opt. 32, 2543–2544 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, “Kinoform phase plates for focal irradiance profile control,” Opt. Lett. 19, 417–419 (1994).
    [PubMed]
  7. R. M. Stevenson, M. J. Norman, T. H. Bett, D. A. Pepler, C. N. Danson, I. N. Ross, “Binary-phase zone plate arrays for the generation of uniform focal profiles,” Opt. Lett. 19, 363–365 (1994).
    [PubMed]
  8. O. E. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
    [CrossRef]
  9. D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).
  10. I. N. Ross, D. A. Pepler, C. N. Danson, “Binary phase plate designs using calculations of far-field distributions,” Opt. Commun. (to be published).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. M. H. Horman, “Efficiencies of zone plates and phase zone plates,” Appl. Opt. 6, 2011–2013 (1967).
    [CrossRef] [PubMed]
  13. P. Kirkpatrick, U. Baez, “Formation of optical images by x-rays,” J. Opt. Soc. Am. 38, 766–774 (1948).
    [CrossRef] [PubMed]
  14. Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
    [CrossRef]

1994 (2)

1993 (2)

S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, “Random phase plates for beam smoothing on the Nova laser,” Appl. Opt. 32, 2543–2544 (1993).
[CrossRef] [PubMed]

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

1992 (1)

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

1990 (1)

R. Epstein, S. Skupsky, “Anticipated improvement in laser beam uniformity using distributed phase plates with quasi-random patterns,” J. Appl. Phys. 68, 924–931 (1990).
[CrossRef]

1986 (1)

1984 (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

1967 (1)

1951 (1)

O. E. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

1948 (1)

Afshar-Rad, T.

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Baez, U.

Bann, R.

D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).

Bett, T. H.

Chen, Z.

Danson, C. N.

R. M. Stevenson, M. J. Norman, T. H. Bett, D. A. Pepler, C. N. Danson, I. N. Ross, “Binary-phase zone plate arrays for the generation of uniform focal profiles,” Opt. Lett. 19, 363–365 (1994).
[PubMed]

D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).

I. N. Ross, D. A. Pepler, C. N. Danson, “Binary phase plate designs using calculations of far-field distributions,” Opt. Commun. (to be published).

Deng, X.

Desselberger, M.

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Dixit, S. N.

Epstein, R.

R. Epstein, S. Skupsky, “Anticipated improvement in laser beam uniformity using distributed phase plates with quasi-random patterns,” J. Appl. Phys. 68, 924–931 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Henesian, M. A.

Horman, M. H.

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Khattak, F.

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Kirkpatrick, P.

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Kolodziejczyk, A.

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

Lawson, J. K.

Liang, X.

Ma, R.

Manes, K. R.

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Morgan, A. J.

Mouriz, D.

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

Myers, O. E.

O. E. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Norman, M. J.

Pepler, D. A.

R. M. Stevenson, M. J. Norman, T. H. Bett, D. A. Pepler, C. N. Danson, I. N. Ross, “Binary-phase zone plate arrays for the generation of uniform focal profiles,” Opt. Lett. 19, 363–365 (1994).
[PubMed]

D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).

I. N. Ross, D. A. Pepler, C. N. Danson, “Binary phase plate designs using calculations of far-field distributions,” Opt. Commun. (to be published).

Powell, H. T.

Ross, I. N.

R. M. Stevenson, M. J. Norman, T. H. Bett, D. A. Pepler, C. N. Danson, I. N. Ross, “Binary-phase zone plate arrays for the generation of uniform focal profiles,” Opt. Lett. 19, 363–365 (1994).
[PubMed]

D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).

I. N. Ross, D. A. Pepler, C. N. Danson, “Binary phase plate designs using calculations of far-field distributions,” Opt. Commun. (to be published).

Skupsky, S.

R. Epstein, S. Skupsky, “Anticipated improvement in laser beam uniformity using distributed phase plates with quasi-random patterns,” J. Appl. Phys. 68, 924–931 (1990).
[CrossRef]

Sochacki, J.

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

Stevenson, R. M.

Thomas, I. M.

Viana, S.

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Wegner, P. J.

Willi, O.

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Woods, B. W.

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Yu, W.

Am. J. Phys. (1)

O. E. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

R. Epstein, S. Skupsky, “Anticipated improvement in laser beam uniformity using distributed phase plates with quasi-random patterns,” J. Appl. Phys. 68, 924–931 (1990).
[CrossRef]

J. Mod. Opt. (1)

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, J. Sochacki, “Generalized zone plates focusing light into arbitrary line segments,” J. Mod. Opt. 40, 601–612 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

M. Desselberger, T. Afshar-Rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Other (3)

D. A. Pepler, C. N. Danson, R. Bann, I. N. Ross, “Focal spot smoothing and tailoring for high-power laser applications,” in Laser Coherence Control: Technology and Applications, T. J. Kessler, H. T. Powell, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1870, 76–87 (1993).

I. N. Ross, D. A. Pepler, C. N. Danson, “Binary phase plate designs using calculations of far-field distributions,” Opt. Commun. (to be published).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (14)

Fig. 1
Fig. 1

PZP focusing scheme showing the geometric formation of the image.

Fig. 2
Fig. 2

(a) Schematic of the PZP focusing system showing the intermediate focal planes for the positive–negative first orders and (b) focal-spot sizes in the principal plane of the overlapping orders.

Fig. 3
Fig. 3

Plots of Bessel-function data: (a) logarithmic for an 11-zone PZP, (b) linear for an 11-zone PZP, (c) linear for a 10-zone PZP, and (d) linear for a 10½-zone PZP.

Fig. 4
Fig. 4

Computer simulations of PZP images using GLAD: 2-D focal spot and associated 1-D line scan (a) in the principal plane, (b) in the optimum plane 130 mm beyond the principal plane), and (c) 50 mm beyond the principal plane.

Fig. 5
Fig. 5

Modified square wave of period 2π showing the phase step δ, the transition point ϕ, and the transition width 2γ.

Fig. 6
Fig. 6

Graph showing intensity of zeroth order produced from fabrication errors.

Fig. 7
Fig. 7

Example of PZP mask structure; π phase areas are black, and 0 phase areas are white.

Fig. 8
Fig. 8

Radial integration curves for the Bessel-function data and for the experimental data from a single cell and from the PZP array.

Fig. 9
Fig. 9

Radial line scans of principal-plane focal-spot intensity-distribution data: (a) experimental data and (b) theoretical (Bessel) data.

Fig. 10
Fig. 10

PZP focal-spot distributions and associated line scans at (a) the principal focal plane (PFP), (b) the optimum plane 6.75 mm beyond the PFP, and (c) 13.5 mm beyond the PFP.

Fig. 11
Fig. 11

PZP focal-spot distribution and associated line scan with a reduced-coherence input beam.

Fig. 12
Fig. 12

X-ray emission produced from PZP illumination of a gold-foil target (a) in the principal plane, (b) in the optimum plane, and (c) beyond the optimum plane.

Fig. 13
Fig. 13

Circular burn through produced from PZP illumination of a gold-foil target.

Fig. 14
Fig. 14

Time-resolved streak record of a shock breakout using (a) a defocused beam and (b) a PZP to generate a large focal spot.

Tables (1)

Tables Icon

Table 1 Theoretical Efficiency of Binary Phase Zone-Plate Array Diffraction Orders, in Target Plane, Calculated Using Fourier Analysis

Equations (14)

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F C = F Z ( F P Δ ) F Z + F P Δ + Δ
W S = W Z F P F Z ,
W S = W Z ( F P Δ F Z ) .
F Z = ± 1 n ( R m 2 m λ m λ 4 ) ,
U ( P ) = 2 π i C [ 0 a J 0 ( k w ρ ) ρδρ + a 2 a J 0 ( k w ρ ) ρδρ + ( 1 ) 2 a 3 a J 0 ( k w ρ ) ρδρ + ( 1 ) N N 1 a N a J 0 ( k w ρ ) ρδρ ] ,
U ( P ) = 2 π a 2 C i [ N 2 J 1 ( k w N a ) k w N a + 2 n = 1 N 1 ( 1 ) n n 2 J 1 ( k w n a ) k w n a ]
t ( r ) = exp { i ( δ / 2 ) sgn [ cos ( α r 2 ) ] } ,
θ = α r 2 ,
F t ( θ ) = { exp ( i δ / 2 ) π θ < π / 2 exp ( i δ / 2 ) π / 2 θ < π / 2 . exp ( i δ / 2 ) π / 2 θ < π
F t ( θ ) = i π n = exp ( i n θ ) [ 2 sin ( n π / 2 ) n sin ( n π ) n ] .
F t ( θ ) = i 2 π { [ exp ( i θ ) + exp ( i θ ) ] 1 3 [ exp ( i 3 θ ) + exp ( i θ ) ] + 1 5 [ exp ( i 5 θ ) + exp ( i 5 θ ) ] + .
F t ( θ ) = cos δ 2 + i 2 π sin δ 2 n = exp ( i n θ ) sin ( n π / 2 ) n .
F t ( θ ) = i 2 π ( ϕ π 2 ) + i 2 π n = exp ( i n θ ) sin ( n ϕ ) n .
F t ( θ ) = 4 γ π 2 + 2 i π n = exp ( i n θ ) sin ( n π / 2 ) n cos ( n γ ) 1 4 ( γ n / π ) 2 .

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