Abstract

Spatial shaping of light beams has led to numerous new applications in fields such as imaging, optical communication, and micromanipulation. However, structured radiation is less well explored beyond visible optics, where methods for shaping fields are more limited. Binary amplitude filters are often used in these regimes and one such example is a photon sieve consisting of an arrangement of pinholes, the positioning of which can tightly focus incident radiation. Here, we describe a method to design generalized photon sieves: arrays of pinholes that generate arbitrary structured complex fields at their foci. We experimentally demonstrate this approach by the production of Airy and Bessel beams, and Laguerre–Gaussian and Hermite–Gaussian modes. We quantify the beam fidelity and photon sieve efficiency, and also demonstrate control over additional unwanted diffraction orders and the incorporation of aberration correction. The fact that these photon sieves are robust and simple to construct will be useful for the shaping of short- or long-wavelength radiation and eases the fabrication challenges set by more intricately patterned binary amplitude masks.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Focusing analysis of the pinhole photon sieve: individual far-field model

Qing Cao and Jürgen Jahns
J. Opt. Soc. Am. A 19(12) 2387-2393 (2002)

Individual far-field model for photon sieves composed of square pinholes

Junyong Zhang, Qing Cao, Xingqiang Lu, and Zunqi Lin
J. Opt. Soc. Am. A 27(6) 1342-1346 (2010)

Generalized Fibonacci photon sieves

Jie Ke and Junyong Zhang
Appl. Opt. 54(24) 7278-7283 (2015)

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref]
  2. G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
    [Crossref]
  3. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
    [Crossref]
  4. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [Crossref]
  5. G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [Crossref]
  6. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
    [Crossref]
  7. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
    [Crossref]
  8. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
    [Crossref]
  9. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
    [Crossref]
  10. S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
    [Crossref]
  11. K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
    [Crossref]
  12. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [Crossref]
  13. N. Simpson, K. Dholakia, L. Allen, and M. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
    [Crossref]
  14. M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
    [Crossref]
  15. D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
    [Crossref]
  16. L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
    [Crossref]
  17. B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
    [Crossref]
  18. J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
    [Crossref]
  19. J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
    [Crossref]
  20. J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
    [Crossref]
  21. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36, 1517–1524 (1997).
    [Crossref]
  22. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [Crossref]
  23. B. R. Brown and A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
    [Crossref]
  24. W.-H. Lee, “Binary computer-generated holograms,” Appl. Opt. 18, 3661–3669 (1979).
    [Crossref]
  25. C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
    [Crossref]
  26. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
    [Crossref]
  27. M. Mirhosseini, O. S. Magana-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21, 30196–30203 (2013).
    [Crossref]
  28. J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
    [Crossref]
  29. N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
    [Crossref]
  30. V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
  31. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
    [Crossref]
  32. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
    [Crossref]
  33. Q. Cao and J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20, 1576–1581 (2003).
    [Crossref]
  34. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [Crossref]
  35. Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
    [Crossref]
  36. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  37. Z. Li, M. Zhang, G. Liang, X. Li, X. Chen, and C. Cheng, “Generation of high-order optical vortices with asymmetrical pinhole plates under plane wave illumination,” Opt. Express 21, 15755–15764 (2013).
    [Crossref]
  38. R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
    [Crossref]
  39. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009).
    [Crossref]
  40. J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
    [Crossref]
  41. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007).
    [Crossref]
  42. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
    [Crossref]
  43. K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
  44. R. F. Egerton, P. Lee, and M. Malac, “Radiation damage in TEM and SEM,” Micron 35, 399–409 (2004).
    [Crossref]
  45. T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
    [Crossref]

2015 (2)

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

2014 (6)

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

2013 (5)

J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Z. Li, M. Zhang, G. Liang, X. Li, X. Chen, and C. Cheng, “Generation of high-order optical vortices with asymmetrical pinhole plates under plane wave illumination,” Opt. Express 21, 15755–15764 (2013).
[Crossref]

M. Mirhosseini, O. S. Magana-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21, 30196–30203 (2013).
[Crossref]

2011 (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

2010 (2)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
[Crossref]

2009 (1)

2007 (4)

2006 (2)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
[Crossref]

2005 (1)

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

2004 (2)

2003 (2)

Q. Cao and J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20, 1576–1581 (2003).
[Crossref]

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

2001 (1)

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

1999 (1)

1998 (1)

J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
[Crossref]

1997 (2)

1996 (1)

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

1995 (1)

1992 (1)

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

1989 (1)

1987 (1)

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

1979 (1)

1966 (1)

Adelung, R.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Agrawal, A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Agrawal, A. K.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Allen, L.

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Anderson, I. M.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Andrews, D.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

Arrizón, V.

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Babiker, M.

J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
[Crossref]

Barnett, S.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Barnett, S. M.

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Béché, A.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Berndt, R.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Bernet, S.

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Boyd, R. W.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

M. Mirhosseini, O. S. Magana-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21, 30196–30203 (2013).
[Crossref]

Broky, J.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Brown, B. R.

Campos, J.

Cao, Q.

Carrada, R.

Cartwright, A. N.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Cathey, W. T.

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Chen, C.

Chen, X.

Cheng, C.

Christodoulides, D.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Clark, L.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Cottrell, D. M.

Courtial, J.

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Davis, J. A.

Dennis, M. R.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

N. Simpson, K. Dholakia, L. Allen, and M. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
[Crossref]

Dogariu, A.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Dowski, E. R.

Dudley, A.

Durnin, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref]

Eberly, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Egerton, R. F.

R. F. Egerton, P. Lee, and M. Malac, “Radiation damage in TEM and SEM,” Micron 35, 399–409 (2004).
[Crossref]

Ercius, P.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Forbes, A.

Frabboni, S.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Franke-Arnold, S.

Friberg, A. T.

Fürhapter, S.

Furlan, W. D.

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

Garcia-Vidal, F. J.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Gazzadi, G. C.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref]

Gibson, G.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Giménez, F.

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Grillo, V.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Guzzinati, G.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Harm, S.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Harvey, T. R.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Hell, S. W.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Herzing, A. A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Hong, M.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Huang, K.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Jacobsen, C.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

Jahn, R.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Jahns, J.

Jesacher, A.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Johnson, R.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Juchtmans, R.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Karimi, E.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Khilo, N.

Kipp, L.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Kudyshev, Z. A.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Lavery, M.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

Lavery, M. P.

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Lee, M.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

Lee, P.

R. F. Egerton, P. Lee, and M. Malac, “Radiation damage in TEM and SEM,” Micron 35, 399–409 (2004).
[Crossref]

Lee, W.-H.

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Lezec, H. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Li, F.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

Li, X.

Li, Z.

Liang, G.

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Linck, M.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Litchinitser, N. M.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Liu, H.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Liu, R.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

Lloyd, S. M.

J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
[Crossref]

Lohmann, A. W.

Love, G. D.

Lubk, A.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Luk’yanchuk, B.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Magana-Loaiza, O. S.

Malac, M.

R. F. Egerton, P. Lee, and M. Malac, “Radiation damage in TEM and SEM,” Micron 35, 399–409 (2004).
[Crossref]

Malik, M.

Maurer, C.

McArdle, N.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

McClelland, J. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

McMorran, B. J.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

Miceli, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Milkie, D. E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Mirhosseini, M.

Monsoriu, J. A.

Moreno, I.

Padgett, M.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

N. Simpson, K. Dholakia, L. Allen, and M. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
[Crossref]

Padgett, M. J.

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Pas’ko, V.

Paterson, C.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Phillips, D.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

Pierce, J. S.

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Pons, A.

Qiu, C. W.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Ritsch-Marte, M.

Rizzoli, S. O.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Rodenburg, B.

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Ruiz, U.

Schattschneider, P.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
[Crossref]

Schwaighofer, A.

Scott, G.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Seemann, R.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Simpson, N.

Simpson, S.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

Siviloglou, G.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Skibowski, M.

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

Smith, R.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Speirits, F.

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

Speirits, F. C.

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Sun, J.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Teng, J.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Tian, H.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
[Crossref]

Turunen, J.

Unguris, J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Van Boxem, R.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Van Tendeloo, G.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

Vasara, A.

Vasilyeu, R.

Vasnetsov, M.

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Verbeeck, J.

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
[Crossref]

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Wang, X.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Wang, Y.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

Westphal, V.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Williams, M.

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

Willig, K. I.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Xu, T.

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Yuan, J.

J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
[Crossref]

Yun, W.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

Yzuel, M. J.

Zhang, M.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Appl. Opt. (5)

C. R. Phys. (1)

J. Verbeeck, G. Guzzinati, L. Clark, R. Juchtmans, R. Van Boxem, H. Tian, A. Béché, A. Lubk, and G. Van Tendeloo, “Shaping electron beams for the generation of innovative measurements in the (S)TEM,” C. R. Phys. 15, 190–199 (2014).
[Crossref]

J. Opt. (1)

R. Liu, D. Phillips, F. Li, M. Williams, D. Andrews, and M. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 045608 (2015).
[Crossref]

J. Opt. Soc. Am. A (3)

Micron (1)

R. F. Egerton, P. Lee, and M. Malac, “Radiation damage in TEM and SEM,” Micron 35, 399–409 (2004).
[Crossref]

Nano Lett. (1)

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning light on the nanoscale,” Nano Lett. 14, 2726–2729 (2014).
[Crossref]

Nat. Commun. (1)

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C. W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).

Nat. Methods (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Nat. Photonics (3)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Nature (8)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

L. Kipp, M. Skibowski, R. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[Crossref]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467, 301–304 (2010).
[Crossref]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
[Crossref]

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

New J. Phys. (1)

T. R. Harvey, J. S. Pierce, A. K. Agrawal, P. Ercius, M. Linck, and B. J. McMorran, “Efficient diffractive phase optics for electrons,” New J. Phys. 16, 093039 (2014).
[Crossref]

Opt. Commun. (3)

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[Crossref]

Opt. Eng. (1)

G. Scott and N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. A (2)

D. Phillips, M. Lee, F. Speirits, S. Barnett, S. Simpson, M. Lavery, M. Padgett, and G. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90, 011801 (2014).
[Crossref]

J. Yuan, S. M. Lloyd, and M. Babiker, “Chiral-specific electron-vortex-beam spectroscopy,” Phys. Rev. A 88, 031801 (2013).
[Crossref]

Phys. Rev. Lett. (2)

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Phys. Rev. X (1)

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).

Science (2)

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331, 192–195 (2011).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts, 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 (6)

Fig. 1.
Fig. 1.

Design of a Fresnel zone plate to generate an Airy beam at its focus. (a) Gaussian amplitude (upper panel) and cubic phase (lower panel) of Airy(x,y). Upper scale bar denotes relative amplitude. Lower scale bar denotes phase as color over a 2π range and relative amplitude as brightness. These scale bars are also used throughout the other figures in this paper. (b) Amplitude and phase of CAiry(x,y), resulting from the propagation of Airy(x,y) a distance f in free space. (c) Phase of the field CAiryexpiϕlens. (d) Binary transmittance function of an on-axis Airy Fresnel zone plate calculated directly from (c) without the incorporation of a phase tilt. (e) Simulation of the intensity at the focal plane of (d). Relative intensity is indicated using the same color map as (a). In this case, the on-axis Airy beam interferes with other on-axis diffraction orders, reducing its fidelity. Scale bars in (d) and (e) represent 1 mm. (f)–(h) Amplitude, phase, and intensity of the target field: an Airy beam generated with parameters ω0=0.01m, ζ=3.5×109rad/m3, f=0.25m. (i) Phase of the field CAiryexpi(ϕlens+ϕtilt). (j) TAiryZP, an off-axis Airy Fresnel zone plate, calculated from (i) using Eqs. (1)–(3). (k) Simulated intensity at the focal plane of (j). The Airy beam is now well separated from other diffraction orders, therefore maintaining a high fidelity. The border plot highlights the relative intensity along the dashed horizontal line through the center of the diffraction pattern. The simulated amplitude and phase of the generated beam (at a plane tilted normal to its propagation direction) is shown as insets for comparison with the target field in (f) and (g).

Fig. 2.
Fig. 2.

Design of a photon sieve to generate an Airy beam. (a) Schematic showing two beams (primary and secondary) incident on a plane with orthogonal tilts, at angles θ1 and θ2. (b) Field created by the interference of the primary and secondary beams shown in (a), DAiryCross(x,y). Inset shows the amplitude of the field. (c) Binary transmittance function of a dual beam Fresnel zone plate, calculated from the field in (b) using Eqs. (1)–(3). The choice of the tilt angles of the primary and secondary beams affects both the position and the shape of the apertures in (c). Keeping the tilt angle of the secondary beam the same magnitude as the tilt angle of the primary beam (i.e., θ1=θ2) results in apertures that can be well approximated by circular pinholes. (d) Binary transmittance function of an off-axis Airy beam photon sieve, TAiryPS(x,y), formed by replacing each aperture in (c) with a pinhole of equivalent area. Apertures below a threshold area have been removed, and the smallest aperture is 5.5μm in diameter. (e) Simulation of the intensity at the focal plane of the photon sieve shown in (d). As required, the Airy beam is the brightest part of the field. Plots at the edge show a cross-section of the relative intensity along the dashed lines. (f)–(h) Comparisons of the simulated phase of the target field (f) with the beam created by the dual-beam Fresnel zone plate (g) and the Airy photon sieve (h). (i)–(l) Comparison of the simulated propagation characteristics of the beams. (i) shows the propagation of the target field shown in (f). (j) shows the propagation of the beam shown in (g) created by the dual-beam Fresnel zone plate. (k) shows the propagation of the beam shown in (h) generated with the Airy photon sieve. (l) shows the propagation of a Gaussian beam of equivalent far-field beam waist to that of the Airy beam, for comparison. The phase scale is the same as used in Fig 1(a).

Fig. 3.
Fig. 3.

Control of additional diffraction orders. (a)–(c) show three different photon sieve designs (once again, the smallest pinhole diameter in these arrays is 5.5μm), and (d)–(f) show the corresponding simulated diffraction patterns at the focal plane. Relative intensity cross-sections along the dashed lines are plotted at the border of each figure. The primary beam used to design each photon sieve is the same: CAiryeiϕpri, where ϕpri is given by Eq. (11), resulting in the same primary first diffraction order in each case. The phase of the secondary beams varies (CAiryeiϕsec), thus changing the nature of the other diffraction orders. In (a), ϕsec=ϕpri, resulting in twin copies of the Airy beam produced in the primary and secondary first orders. In (b), the cubic phase term is dropped: ϕsec=2πu0y+ϕlens(x,y,f1), so while the secondary order is still focused to the same plane, it no longer exhibits the pseudo-diffraction-free properties of an Airy beam. In (c), ϕsec=2πu0y, the secondary beam is no longer focused, and the pinholes are positioned in regularly spaced rows, resulting in regularly spaced copies of the Airy beam. Scale bars represent 1 mm.

Fig. 4.
Fig. 4.

Experimental verification of an Airy beam photon sieve. (a) Schematic of the experimental setup. An Airy photon sieve, TAiryPS(x,y) [shown in (d)] is displayed on a DMD (Texas Instruments DLP3000, 684×608 micromirrors, active area of 3.70×6.57mm). We note that the use of a DMD introduces an additional lateral phase tilt due to the offset of the DMD pixels which each pivot about their own axis. We compensate for this by laterally stretching the displayed pattern. The degree of stretch is dependent upon the incident angle of the illuminating beam. This would be unnecessary if fabricating a planar photon sieve. A 633 nm wavelength laser beam was guided through a single-mode fiber to produce a TEM 00 output mode, which is then expanded to overfill the DMD. (b) The intensity of the diffraction pattern from light incident at positions inside the pinholes is observed with a CMOS camera (Hamamatsu ORCA-Flash 4.0) at the focal plane of the photon sieve at distance f from the DMD. Mirrors corresponding to the positions outside the pinholes transmit light into a rejected order away from the camera. Inset shows the interference of the Airy beam with a plane wave (formed from light scattered from around the active area of the DMD, which was blocked in the main image). (c) Top row: simulated propagation of the required Airy beam showing the intensity at (i) the focal plane, (ii) 5 cm beyond, and (iii) 10 cm beyond the focal plane. Bottom row: experimentally measured intensity of the Airy beam as it propagates the same distances. (d) and (e) Pinhole configurations (the smallest pinhole diameter in these arrays is 5.5μm) and corresponding first-order intensity distributions at the focal plane for two different focal lengths of Airy beam photon sieve. Focal length=20cm in (d) and 25 cm in (e). As expected, the beam in (e) is enlarged due to the lower NA of the photon sieve. Scale bars in (d) and (e) represent 1 mm.

Fig. 5.
Fig. 5.

Experimental demonstration of photon sieves to create a range of different spatial modes. The focal length of the photon sieves is 20 cm and the smallest pinhole diameter in these arrays is once again 5.5μm. In each case, the insets show the target intensity and phase (top left and right, respectively) and the experimentally measured intensity and plane wave interference pattern (bottom left and right, respectively). In each case, the measured intensity pattern is zoomed out to show the separation of the target beam from other diffraction orders. (a) Laguerre–Gaussian beam carrying a vortex charge of =5 and radial mode p=4. (b) Bessel beam of vortex charge =0. To create this, the Fourier transform of a pseudo-diffraction-free Bessel beam was approximated by an annular slit [39]. (c) Hermite–Gaussian beam of mode order m=7, n=5. (d) Superposition state of two LG beams of opposite vortex charge =±5, p=0. Scale bars represent 1 mm. The phase scale is the same as used in Fig 1(a).

Fig. 6.
Fig. 6.

Experimental demonstration of aberration correction of a nonplanar illuminating wave. (a) Estimate of the phase front of the beam incident on the photon sieve. (b) Uncorrected photon sieve to generate a LG beam varying a vortex charge of =2 and radial mode of p=0. Inset shows the resultant distorted first-order beam. (c) Aberration-corrected photon sieve, where the positions of the apertures have been adjusted to accommodate the aberrations in the illuminating beam. Inset shows that distortions in the first-order beam are now corrected. Scale bars in (b) and (c) represent 1 mm, and 0.5 mm in the insets. The phase scale is the same as used in Fig. 1(a).

Equations (15)

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

T(x,y)=12+12sgn[cos(p(x,y))+cos(q(x,y))],
p(x,y)=ϕA(x,y)+ϕtilt(x,y),
q(x,y)=arcsin(A(x,y)/Amax),
Airy(x,y)=B0ex2+y2/ω0eiζ(x3+y3),
ϕlens(x,y,f)=2πλ[f(f2+x2+y2)12],
p(x,y)=ϕC(x,y)+ϕtilt(x,y)+ϕlens(x,y),
q(x,y)=arcsin[C(x,y)/Cmax],
F=|1NFU(x,y)V*(x,y)dxdy|2,
NF=[|U(x,y)|2dxdy×|V(x,y)|2dxdy]12,
DAiryCross=CAiry[eiϕpri+eiϕsec],
ϕpri=ϕcub+2πu0x+ϕlens(x,y,f1),
ϕsec=2πu0y+ϕlens(x,y,f2),
E=|1NET(x,y)[C(x,y)ei(ϕtilt+ϕlens)]*dxdy|2,
NE=[|T(x,y)|2dxdy×|C(x,y)|2dxdy]12,
p(x,y)=ϕC+ϕtilt+ϕlensϕabb.

Metrics