Abstract

A continuous-phase plate (CPP) is a key element for beam smoothing in a high-power laser system. For the beam-smoothing effect, the surface shape of a CPP is one of the most important facts. In this paper, the change law of the transmission direction of light rays has been analyzed according to the geometrical optical principle. It is discovered that the 2-dimensional histogram of a surface gradient can be used to show the far-field distribution of a CPP. Drawing on the experience of histogram modification technology in digital image processing, a novel method is proposed to design a CPP. The design steps of a 1-dimensional CPP are introduced in detail. The far-field distribution and spatial frequency spectrum of this CPP are calculated. The results show that this method is efficient and can reflect the relationship between the surface figure and the far-field distribution of a CPP directly.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
    [CrossRef]
  2. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express11(19), 2278–2288 (2003).
    [CrossRef] [PubMed]
  3. C. J. Zapata-Rodríguez and M. T. Caballero, “Isotropic compensation of diffraction-driven angular dispersion,” Opt. Lett.32(17), 2472–2474 (2007).
    [CrossRef] [PubMed]
  4. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
    [CrossRef]
  5. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, and K. A. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Opt. Lett.19(6), 417–419 (1994).
    [PubMed]
  6. K. L. Wlodarczyk, E. Mendez, H. J. Baker, R. McBride, and D. R. Hall, “Laser smoothing of binary gratings and multilevel etched structures in fused silica,” Appl. Opt.49(11), 1997–2005 (2010).
    [CrossRef] [PubMed]
  7. J. A. Marozas, “Fourier transform-based continuous phase-plate design technique: a high-pass phase-plate design as an application for OMEGA and the National Ignition Facility,” J. Opt. Soc. Am. A24(1), 74–83 (2007).
    [CrossRef] [PubMed]
  8. C. Yang, R. Zhang, Q. Xu, and P. Ma, “Continuous phase plate for laser beam smoothing,” Appl. Opt.47(10), 1465–1469 (2008).
    [CrossRef] [PubMed]
  9. N. Jérôme, R. Xavier, D. Jérôme, V. Denis, L. Martine, B. Vincent, and V. Laurent, “Design and optical characterization of a large continuous-phase plate for laser integration line and laser mega joule facilities,” Appl. Opt.42(13), 2377–2382 (2007).
  10. Y. Arieli, “Continuous-phase plate for non-uniform illumination beam shaping using the inverse phase contrast method,” Opt. Commun.180(4–6), 239–245 (2000).
    [CrossRef]
  11. D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
    [CrossRef]
  12. M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).
  13. W. Williams, J. Auerbach, J. Hunt, L. Lawson, K. Manes, C. Orth, R. Sacks, J. Trenholme, and P. Wegner, “NIF optics phase gradient specification” LLNL Technical Report UCRL-ZD_127297, (1997).
  14. M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Tsinghua University Press, 2011).

2012 (1)

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

2010 (1)

2008 (1)

2007 (3)

2005 (1)

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

2003 (1)

2000 (1)

Y. Arieli, “Continuous-phase plate for non-uniform illumination beam shaping using the inverse phase contrast method,” Opt. Commun.180(4–6), 239–245 (2000).
[CrossRef]

1994 (1)

1988 (1)

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

1984 (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Arieli, Y.

Y. Arieli, “Continuous-phase plate for non-uniform illumination beam shaping using the inverse phase contrast method,” Opt. Commun.180(4–6), 239–245 (2000).
[CrossRef]

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Ayral, H.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Baker, H. J.

Caballero, M. T.

Cabrini, S.

Cojoc, D.

Denis, V.

Di Fabrizio, E.

Dixit, S. N.

Facci, P.

Gouedard, C.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Hall, D. R.

Husson, D.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Jérôme, D.

Jérôme, N.

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Kaulich, B.

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Laurent, V.

Lauriou, J.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Lawson, J. K.

Liliana, P.

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

Lin, Z.

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

Ma, P.

Manes, K. R.

Marozas, J. A.

Martin, O.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Martine, L.

McBride, R.

Mendez, E.

Meyer, B.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Mona, M.

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Nugent, K. A.

Powell, H. T.

Preda, A. M.

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

Rostaing, M.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Sauteret, C.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Scarlat, E. I.

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

Susini, J.

Véron, D.

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Vincent, B.

Wan, Y.

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

Wilhein, T.

Wlodarczyk, K. L.

Xavier, R.

Xu, Q.

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

Yang, C.

Zapata-Rodríguez, C. J.

Zhang, D.

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

Zhang, R.

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

C. Yang, R. Zhang, Q. Xu, and P. Ma, “Continuous phase plate for laser beam smoothing,” Appl. Opt.47(10), 1465–1469 (2008).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

Y. Arieli, “Continuous-phase plate for non-uniform illumination beam shaping using the inverse phase contrast method,” Opt. Commun.180(4–6), 239–245 (2000).
[CrossRef]

D. Véron, H. Ayral, C. Gouedard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical spatial smoothing of Nd-Glass laser beam,” Opt. Commun.65(1), 42–46 (1988).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (Stuttg.) (1)

D. Zhang, Y. Wan, R. Zhang, and Z. Lin, “Surface statistical characteristics and smoothing analysis of continuous-phase plate,” Optik (Stuttg.)123(22), 2062–2067 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random Phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett.53(11), 1057–1060 (1984).
[CrossRef]

UPB Sci. Bull. Series A (1)

M. Mona, P. Liliana, A. M. Preda, and E. I. Scarlat, “Modified Gerchberg–Saxton algorithm for diffractive optical element image retrieval” UPB Sci. Bull. Series A67(4), 65–76 (2005).

Other (2)

W. Williams, J. Auerbach, J. Hunt, L. Lawson, K. Manes, C. Orth, R. Sacks, J. Trenholme, and P. Wegner, “NIF optics phase gradient specification” LLNL Technical Report UCRL-ZD_127297, (1997).

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Tsinghua University Press, 2011).

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 (10)

Fig. 1
Fig. 1

Typical application scheme of continuous-phase plate.

Fig. 2
Fig. 2

CPP and the light rays in the incidence plane.

Fig. 3
Fig. 3

Surface shape of a CPP that calculated by Eq. (5) (a) and the far-field distribution of the CPP that obtained by ray tracing (b).

Fig. 4
Fig. 4

2-dimensional histogram (a) and the focal spot calculated by traditional Fourier transform method (b) of the CPP.

Fig. 5
Fig. 5

Original surface (dotted line) and the optimized surface (solid line) of a 1-dimensional CPP.

Fig. 6
Fig. 6

Spatial frequency spectrum of the original surface (a) and the optimized surface (b).

Fig. 7
Fig. 7

Calculation results by Fourier transform. Far-field distribution of the original surface (a) and the optimized surface (b).

Fig. 8
Fig. 8

Histograms of the original surface (a) and the optimized surface (b).

Fig. 9
Fig. 9

Design result of a two-dimensional CPP.

Fig. 10
Fig. 10

Far-field distribution of the 2-dimensional CPP before filtering (a) and after filtering by a low-passing filter (b).

Equations (14)

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

δ= θ o θ i =(n1) θ i .
OB =[ tan θ i cosα tan θ i sinα 1 ],
OP =[ tanδcosα tanδsinα 1 ],
OP (n1) OB +[ 0 0 2n ]=(n1)ϕ+[ 0 0 2n ].
ϕ(x,y)=ARand(x,y)*exp[ ( x s ) 2 ( y s ) 2 ],
p hist(p)dp= q hist(q)dq ,
hist(p)={ const,p[ a,b ] 0,other .
p hist(p)dp ={ 0,p<a (pa)const,p[ a,b ] (ba)const,p>b ,
pa= 1 const q hist(q)dq .
hist(p)Δp=hist(q)Δq,
p i p 1 = p N p 1 N q 1 q i hist(q) ,
p x p y = 1 const q x , q y hist( q x , q y ) d q x d q y .
p x y = p y x .
p= p x dx + p y dy p x y dxdy.

Metrics