Abstract

We fabricate computer generated holograms for the generation of phase singularities at extreme ultraviolet (EUV) wavelengths using electron beam lithography and demonstrate their ability to generate optical vortices in the nonzero diffraction orders. To this end, we observe the characteristic intensity distribution of the vortex beam and verify the helical phase structure interferometrically. The presented method forms the basis for further studies on singular light fields in the EUV frequency range, i.e., in EUV interference lithography. Since the method is purely achromatic, it may also find applications in various fields of x ray optics.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
    [CrossRef]
  2. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005).
  3. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef] [PubMed]
  4. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
    [CrossRef] [PubMed]
  5. G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  6. S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch Marte, Opt. Lett. 30, 1953 (2005).
    [CrossRef] [PubMed]
  7. T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
    [CrossRef] [PubMed]
  8. A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, Opt. Lett. 27, 1752 (2002).
    [CrossRef]
  9. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef] [PubMed]
  10. Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
    [CrossRef]
  11. E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
    [CrossRef]
  12. H. H. Solak, J. Phys. D 39, R171 (2006).
    [CrossRef]
  13. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  14. A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
    [CrossRef] [PubMed]
  15. M. van Veeneendaal and I. McNulty, Phys. Rev. Lett. 98, 157401 (2007).
    [CrossRef]
  16. J. Becker, P. Rose, M. Boguslawski, and C. Denz, Opt. Express 19, 9848 (2011).
    [CrossRef] [PubMed]
  17. S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
    [CrossRef]
  18. J. B. Pendry, Science 306, 1353 (2004).
    [CrossRef] [PubMed]
  19. E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
    [CrossRef]

2011 (1)

2010 (1)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

2009 (2)

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

2007 (3)

M. van Veeneendaal and I. McNulty, Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef]

G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
[CrossRef]

2006 (2)

H. H. Solak, J. Phys. D 39, R171 (2006).
[CrossRef]

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef] [PubMed]

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

1996 (1)

S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
[CrossRef]

Alexandrescu, A.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Becker, J.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
[CrossRef]

Boguslawski, M.

Bowman, C. N.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

Chavez-Cerda, S.

S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Cojoc, D.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Denz, C.

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005).

Di Fabrizio, E.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Dong, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Fedotov, V. A.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Furhapter, S.

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Guo, Z.

Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
[CrossRef]

Harvey, E.

Hayes, J. P.

Heckenberg, N. R.

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Jesacher, A.

Kivshar, Y. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Kivshar, Yu. S.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005).

Koschny, T.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Kowalski, B. A.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

Krolikowski, W.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Lai, B.

Liu, S.

Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
[CrossRef]

Mancuso, A. P.

Marte, M. Ritsch

McDonald, G. S.

S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

McDuff, R.

McLeod, R. R.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

McMahon, P. J.

McNulty, I.

New, G. H. C.

S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Nugent, K. A.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
[CrossRef]

Paterson, D.

Peele, A. G.

Pendry, J. B.

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef] [PubMed]

Plum, E.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Qu, S.

Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
[CrossRef]

Rode, A. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Rose, P.

Scott, T. F.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Shvedov, V. G.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Smith, C. P.

Solak, H. H.

H. H. Solak, J. Phys. D 39, R171 (2006).
[CrossRef]

Soukoulis, C. M.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Sullivan, A. C.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

Terriza, G. Molina

G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torner, L.

G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005).

Torres, J. P.

G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Tran, C. Q.

van Veeneendaal, M.

M. van Veeneendaal and I. McNulty, Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef]

White, A. G.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Zheludev, N. I.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Zhou, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

J. Phys. D (1)

H. H. Solak, J. Phys. D 39, R171 (2006).
[CrossRef]

Nat. Phys. (1)

G. Molina Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

Z. Guo, S. Qu, and S. Liu, Opt. Commun. 273, 286 (2007).
[CrossRef]

S. Chavez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (1)

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407(2009).
[CrossRef]

Phys. Rev. Lett. (3)

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

M. van Veeneendaal and I. McNulty, Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
[CrossRef]

Rev. Sci. Instrum. (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, and S. A. Sheets, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Science (2)

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef] [PubMed]

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, Science 324, 913 (2009).
[CrossRef] [PubMed]

Other (1)

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005).

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 (3)

Fig. 1
Fig. 1

(a),(b) Numerical simulation of an ideal Gaussian vortex beam with topological charge M = 1 . (a) Normalized doughnut-shaped intensity distribution. (b) Phase profile. (c),(d) Computer generated hologram. (c) Ideal pattern corresponding to the interference of an optical vortex with a tilted reference wave (normalized intensity). (d) Binary pattern.

Fig. 2
Fig. 2

Generation of EUV vortex beams. (a) Scanning electron micrograph of the computer generated hologram. (b) Experimentally observed intensity distribution in the first diffraction order. (c) Numerically calculated Fraunhofer diffraction pattern using the experimental parameters and taking into account the finite-size aperture of the grating. Scale bars correspond to 1 μm in (a) and 500 μm in (b), respectively.

Fig. 3
Fig. 3

Interferometric phase analysis. (a) Schematic experimental setup. VG: vortex grating, LG: linear grating, BST: beam stop, Int: calculated intensity distribution of the interference pattern in the first diffraction orders. (b) Scanning electron micrograph of the mask containing the computer generated hologram plus the additional linear grating. (c),(d) Experimentally observed intensity distribution in the positive and negative first diffraction order, respectively. Scale bars correspond to 1 μm in (b) and 500 μm in (c), respectively.

Metrics