Abstract

The chromatic properties of binary beam shapers inducing a spatially dependent transmission on the near field of an optical source after far-field filtering and imaging are derived. Beam shapers using pixels with two transmission states are highly versatile and have been experimentally realized with distributions of amplitude pixels, phase pixels, or polarization pixels that can be designed using a half-toning algorithm. The amplitude of the shaped beam in an image plane has a precisely controlled continuous profile given by the local density of the two pixel types in the object plane. The wavelength dependence of the field transmission corresponding to the full range of design transmission between 0 and 1 is studied analytically to assess the general performance of the corresponding beam shapers for broadband sources, with an example of a specific 2D transmission profile relevant to laser engineering. Amplitude beam shapers have no significant chromaticity, but have low damage threshold. The high-damage-threshold twisted nematic liquid crystal and phase shapers induce a wavelength-dependent transmission and phase on the shaped beam.

© 2013 Optical Society of America

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2012 (1)

2011 (6)

S. J. Thomas, R. Soummer, D. Dillon, B. Macintosh, D. Gavel, and A. Sivaramakrishnan, “Testing the apodized pupil Lyot coronagraph on the laboratory for adaptive optics extreme adaptive optics testbed,” Astron. J. 142, 119 (2011).
[CrossRef]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

M. J. Guardalben and L. J. Waxer, “Improvements to long-pulse system performance and operational efficiency on OMEGA EP,” Proc. SPIE 7916, 79160G (2011).
[CrossRef]

S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Experimental demonstration of generalized phase contrast based Gaussian beam-shaper,” Opt. Express 19, 7106–7111(2011).
[CrossRef]

C. Dorrer, S. K. H. Wei, P. Leung, M. Vargas, K. Wegman, J. Boulé, Z. Zhao, K. L. Marshall, and S. H. Chen, “High-damage-threshold static laser beam shaping using optically patterned liquid-crystal devices,” Opt. Lett. 36, 4035–4037 (2011).
[CrossRef]

A. V. Korzhimanov, A. A. Gonoskov, E. A. Khazanov, and A. M. Sergeev, “Horizons of petawatt laser technology,” Phys.-Usp. 54, 9–28 (2011).
[CrossRef]

2010 (1)

2009 (4)

C. Dorrer, “High-damage-threshold beam shaping using binary phase plates,” Opt. Lett. 34, 2330–2332 (2009).
[CrossRef]

J.-C. Liang, N. Kohn, M. F. Becker, and D. J. Heinzen, “1.5% root-mean-square flat-intensity laser beam formed using a binary-amplitude spatial light modulator,” Appl. Opt. 48, 1955–1962 (2009).
[CrossRef]

A. Laskin, “Achromatic refractive beam shaping optics for broad spectrum laser applications,” Proc. SPIE 7430, 743003 (2009).
[CrossRef]

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[CrossRef]

2008 (1)

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

2007 (3)

2005 (2)

J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

A. B. Kostinski and W. Yang, “Pupil phase apodization for imaging of faint companions in prescribed regions,” J. Mod. Opt. 52, 2467–2474 (2005).
[CrossRef]

2003 (1)

D. L. Lau, R. Ulichney, and G. R. Arce, “Blue- and green-noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
[CrossRef]

2000 (1)

F. M. Dickey, L. S. Weichman, and R. N. Shagam, “Laser beam shaping techniques,” Proc. SPIE 4065, 338–348 (2000).
[CrossRef]

1998 (1)

M. A. Golub and I. Grossinger, “Diffractive optical elements for biomedical applications,” Proc. SPIE 3199, 220–231(1998).
[CrossRef]

1997 (1)

1988 (1)

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

1985 (1)

1978 (1)

1976 (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

1975 (1)

C. H. Gooch, and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90°,” J. Phys. D 8, 1575–1584 (1975).
[CrossRef]

Agresti, J.

Arce, G. R.

D. L. Lau, R. Ulichney, and G. R. Arce, “Blue- and green-noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
[CrossRef]

Auerbach, J. M.

Bahk, S.-W.

Bañas, A.

Barker, C. E.

Becker, M. F.

Begishev, I. A.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Behrendt, W. C.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Bor, Z.

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

Boulé, J.

Bowers, M. W.

Bromage, J.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Browning, D. F.

Brugioni, S.

J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Campbell, J. H.

Chen, S. H.

D’Ambrosio, E.

DeGama, M.

DeSalvo, R.

Dickey, F.

Dickey, F. M.

F. M. Dickey, L. S. Weichman, and R. N. Shagam, “Laser beam shaping techniques,” Proc. SPIE 4065, 338–348 (2000).
[CrossRef]

Dillon, D.

S. J. Thomas, R. Soummer, D. Dillon, B. Macintosh, D. Gavel, and A. Sivaramakrishnan, “Testing the apodized pupil Lyot coronagraph on the laboratory for adaptive optics extreme adaptive optics testbed,” Astron. J. 142, 119 (2011).
[CrossRef]

Dixit, S. N.

Dorrer, C.

C. Dorrer, S. K. H. Wei, P. Leung, M. Vargas, K. Wegman, J. Boulé, Z. Zhao, K. L. Marshall, and S. H. Chen, “High-damage-threshold static laser beam shaping using optically patterned liquid-crystal devices,” Opt. Lett. 36, 4035–4037 (2011).
[CrossRef]

C. Dorrer, “High-damage-threshold beam shaping using binary phase plates,” Opt. Lett. 34, 2330–2332 (2009).
[CrossRef]

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

C. Dorrer and J. D. Zuegel, “Design and analysis of binary beam shapers using error diffusion,” J. Opt. Soc. Am. B 24, 1268–1275 (2007).
[CrossRef]

du Plessis, A.

Edwards, J. L.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Efron, U.

U. Efron, Spatial Light Modulator Technology: Materials, Devices, and Applications, Vol. 47 of Optical Engineering (Marcel Dekker, 1995).

Erbert, G. V.

Faetti, S.

J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
[CrossRef]

Fess, E.

Feurer, T.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[CrossRef]

Floyd, R. W.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

Folnsbee, L.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Forbes, A.

Forest, D.

Frei, F.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[CrossRef]

Galler, A.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[CrossRef]

Gavel, D.

S. J. Thomas, R. Soummer, D. Dillon, B. Macintosh, D. Gavel, and A. Sivaramakrishnan, “Testing the apodized pupil Lyot coronagraph on the laboratory for adaptive optics extreme adaptive optics testbed,” Astron. J. 142, 119 (2011).
[CrossRef]

Glückstad, J.

S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Experimental demonstration of generalized phase contrast based Gaussian beam-shaper,” Opt. Express 19, 7106–7111(2011).
[CrossRef]

J. Glückstad and D. Palima, Generalized Phase Contrast: Applications in Optics and Photonics, Springer Series in Optical Sciences (Springer, 2009), Vol. 146, p. 310.

Golub, M. A.

M. A. Golub and I. Grossinger, “Diffractive optical elements for biomedical applications,” Proc. SPIE 3199, 220–231(1998).
[CrossRef]

Gonoskov, A. A.

A. V. Korzhimanov, A. A. Gonoskov, E. A. Khazanov, and A. M. Sergeev, “Horizons of petawatt laser technology,” Phys.-Usp. 54, 9–28 (2011).
[CrossRef]

Gooch, C. H.

C. H. Gooch, and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90°,” J. Phys. D 8, 1575–1584 (1975).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., Mcgraw-Hill Series in Electrical and Computing Engineering (McGraw-Hill, 1996).

Grossinger, I.

M. A. Golub and I. Grossinger, “Diffractive optical elements for biomedical applications,” Proc. SPIE 3199, 220–231(1998).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays, Wiley Series in Pure and Applied Optics (Wiley, 1999).

Guardalben, M. J.

M. J. Guardalben and L. J. Waxer, “Improvements to long-pulse system performance and operational efficiency on OMEGA EP,” Proc. SPIE 7916, 79160G (2011).
[CrossRef]

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Haynam, C. A.

Heestand, G. M.

Heinzen, D. J.

Henesian, M. A.

Hermann, M. R.

Jacobs, S. D.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Jancaitis, K. S.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Jungquist, R.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Kawaguchi, K.

Kelly, J. H.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

Kessler, T. J.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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A. B. Kostinski and W. Yang, “Pupil phase apodization for imaging of faint companions in prescribed regions,” J. Mod. Opt. 52, 2467–2474 (2005).
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S.-W. Bahk, E. Fess, B. E. Kruschwitz, and J. D. Zuegel, “A high-resolution, adaptive beam-shaping system for high-power lasers,” Opt. Express 18, 9151–9163 (2010).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. L. Lau, R. Ulichney, and G. R. Arce, “Blue- and green-noise halftoning models,” IEEE Signal Process. Mag. 20(4), 28–38 (2003).
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J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
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Loucks, S. J.

D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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S. J. Thomas, R. Soummer, D. Dillon, B. Macintosh, D. Gavel, and A. Sivaramakrishnan, “Testing the apodized pupil Lyot coronagraph on the laboratory for adaptive optics extreme adaptive optics testbed,” Astron. J. 142, 119 (2011).
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Manes, K. R.

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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
[CrossRef]

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J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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D. N. Maywar, J. H. Kelly, L. J. Waxer, S. F. B. Morse, I. A. Begishev, J. Bromage, C. Dorrer, J. L. Edwards, L. Folnsbee, M. J. Guardalben, S. D. Jacobs, R. Jungquist, T. J. Kessler, R. W. Kidder, B. E. Kruschwitz, S. J. Loucks, J. R. Marciante, R. L. McCrory, D. D. Meyerhofer, A. V. Okishev, J. B. Oliver, G. Pien, J. Qiao, J. Puth, A. L. Rigatti, A. W. Schmid, M. J. Shoup, C. Stoeckl, K. A. Thorp, and J. D. Zuegel, “OMEGA EP high-energy petawatt laser: progress and prospects,” J. Phys. 112, 032007 (2008).
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Figures (7)

Fig. 1.
Fig. 1.

Principle of binary pixelated near-field beam shapers using (a) amplitude pixels, (b) polarization pixels, and (c) phase pixels. These pixel distributions provide beam shaping in an image plane of the device after low-pass filtering in the far field.

Fig. 2.
Fig. 2.

Setup and notations for the 4f line used for imaging and far-field filtering of a binary beam shaper. For all simulations, f=1m, and the diameter of the round aperture at the conjugate plane is 5.5 mm for the amplitude and polarization shapers and 4.5 mm for the phase shapers.

Fig. 3.
Fig. 3.

(a) Design transmission, corresponding to a 40th-order super-Gaussian beam in the x and y directions for apodization combined with a sixth-order polynomial modulation in the x direction. (b) Lineout of the modulus of the design field transmission (dashed line), of the pixel transmission (shaded gray zone), and the smoothing function a˜[(xαH)/λf,(yβH)/λf] for λ=800nm and f=1m (continuous line). These three quantities have been normalized to 1 to facilitate comparison. (c) Lineouts of the design transmission (dashed line) and obtained transmission at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=0mm in the inset. (d) Lineouts corresponding to zero phase (dashed line) and obtained phase at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=0mm in the inset.

Fig. 4.
Fig. 4.

Axes definition for twisted nematic LC devices with binary pixels of rotation (a) 0, (b) π/2, (c) π/4, and (d) π/4.

Fig. 5.
Fig. 5.

(a) Transmission and (b) phase errors for a binary LC shaper in the first configuration with h=11.38μm. (c) Lineouts of the design transmission (dashed line) and obtained transmission at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=4.5mm in the inset. (d) Lineouts corresponding to zero phase (dashed line) and obtained phase at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=4.5mm in the inset.

Fig. 6.
Fig. 6.

(a) Transmission and (b) phase errors for a binary LC shaper in the second configuration with h=11.38μm. (c) Lineouts of the design transmission (dashed line) and obtained transmission at 740.5 nm (light gray line), 800 nm (dark gray line), and 858.3 nm (black line), with a close-up around x=0mm in the inset. (d) Lineouts corresponding to zero phase (dashed line) and obtained phase at 740.5 nm (light gray line), 800 nm (dark gray line), and 858.3 nm (black line), with a close-up around x=0mm in the inset.

Fig. 7.
Fig. 7.

(a) Transmission and (b) phase errors for a fused-silica binary phase shaper with L=0.88μm. (c) Lineouts of the design transmission (dashed line) and obtained transmission at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=0mm in the inset. (d) Lineouts corresponding to zero phase (dashed line) and obtained phase at 700 nm (light gray line), 800 nm (dark gray line), and 900 nm (black line), with a close-up around x=0mm in the inset.

Equations (46)

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m(x,y,λ)=α,βmα,β(λ)P(xαH,yβH),
M(u,v,λ)=P˜(uλf,vλf)α,βmα,β(λ)exp[i2πHλf(αu+βv)],
M(u,v,λ)=P˜(uλf,vλf)a(u,v)α,βmα,β(λ)exp[i2πHλf(αu+βv)].
M(u,v,λ)=H2a(u,v)α,βmα,β(λ)exp[i2πHλf(αu+βv)].
t(x,y,λ)=H2α,βmα,β(λ)a˜(xαHλf,yβHλf).
t(x,y,λ)=H2[mA(λ)(α,β)Aa˜(xαHλf,yβHλf)+mB(λ)(α,β)Ba˜(xαHλf,yβHλf)].
dA(x,y)=H2a˜(xλf,yλf)dxdy(λf)2(α,β)Aa˜(xαHλf,yβHλf).
t(x,y,λ)=mA(λ)dA(x,y)+mB(λ)dB(x,y).
t(x,y,λ)=T(x,y,λ)exp[iψ(x,y,λ)].
t(x,y,λ)=0×dt=0(x,y)+1×dt=1(x,y)=dt=1(x,y).
2πΔn(λ)ξλ.
E(h)=Ax(h)x(h)+Ay(h)y(h).
Ax(h)={Ax(0)cos(τ)+F[iAx(0)X+Ay(0)]sin(τ)}exp(iβsh),
Ay(h)={Ay(0)cos(τ)F[iAy(0)X+Ax(0)]sin(τ)}exp(iβsh),
Ax(h)=exp(iβxh),
Ay(h)=0.
Ai(h)=exp(iβxh),
Aj(h)=0.
Ax(h)=[cos(τ)+iFXsin(τ)]exp(iβsh),
Ay(h)=Fsin(τ)exp(iβsh).
Ai(h)=Fsin(τ)exp(iβsh),
Aj(h)=[cos(τ)+iFXsin(τ)]exp(iβsh),
t=d1[cos(τ)+iFXsin(τ)]exp(iβsh).
t=d1[cos(τ)+iFXsin(τ)]exp(iπX/2)exp(iβxh).
TT0=η2T0,
ψ=arg[cos(τ)+iFXsin(τ)]πX/2,
t=d1exp(iβxh)+d0Fsin(τ)exp(iβsh),
t=exp(iβxh)[d1+d0ηexp(iπX/2)].
TT0=2T0(1T0)ηcos(πX/2)+(1T0)2η2,
ψ=atan[(1T0)ηsin(πX/2)T0+(1T0)ηcos(πX/2)].
Ax(h)=[cos(τ)+iFXsin(τ)]exp(iβsh),
Ay(h)=Fsin(τ)exp(iβsh)
Ax(h)=[cos(τ)+iFXsin(τ)]exp(iβsh),
Ay(h)=Fsin(τ)exp(iβsh)
t={[cos(τ)+iFXsin(τ)]d1+Fsin(τ)d0}exp(iβsh),
t={[cos(τ)+iFXsin(τ)]d1+Fsin(τ)d0}exp(iπx/4)exp(iβxh).
t(x,y)=dφ=0(x,y)+exp(i×Δφ)×dφ=Δφ(x,y).
t(x,y)=dφ=0(x,y)dφ=π(x,y).
t(x,y)=2dφ=0(x,y)1=12dφ=π(x,y).
t(x,y)=dφ=0(x,y)exp(iε)×dφ=π(x,y).
t=1+t02+t012exp(iε),
t=t0+(1t0)ε24+it012ε.
TT0=ε2(1T0)/4,
ψ=atan{ε(T01)2[T0+(1T0)ε2/4]}.
Δφ(λ)=2πλL[nFS(λ)nair(λ)].
T0=TTε2/41ε2/4,

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