Abstract

We present a design method for diffractive fan-out elements generating an array of subdiffraction spots in a predetermined area using propagating light. A specific constraint is introduced to the Gerchberg-Saxton algorithm to control the dispersion of light energy and the phase of spots. In our demonstration, an element generating a 3 × 3 spot array achieves the spot size reduced to 70% comparing to the diffraction limited spot in simulation and about 80% in the experiment. Various layouts of subdiffraction spots can be made with a high signal to noise ratio using our design method. The relationship between the spot size and the power efficiency is also shown based on the simulation.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Diffractive fan-out elements for wavelength-multiplexing subdiffraction-limit spot generation in three dimensions

Yusuke Ogura, Masahiko Aino, and Jun Tanida
Appl. Opt. 55(23) 6371-6380 (2016)

Efficient optical elements to generate intensity weighted spot arrays: design and fabrication

Mark P. Dames, Robert J. Dowling, Paul McKee, and David Wood
Appl. Opt. 30(19) 2685-2691 (1991)

References

  • View by:
  • |
  • |
  • |

  1. D. Prongué, H. P. Herzig, R. Döndliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31(26), 5706–5711 (1992).
    [Crossref] [PubMed]
  2. A. Hermerschmidt, S Krüger, and G. Wernicke, “Binary diffractive beam splitters with arbitrary diffraction angles,” Opt. Lett. 32(5), 448–450 (2007).
    [Crossref] [PubMed]
  3. J. Amako, K. Nagasaka, and N. Kazuhiro, “Chromatic-distortion compensation in splitting and focusing of femtosecond pulses by use of a pair of diffractive optical elements,” Opt. Lett. 27(11), 969–971 (2002).
    [Crossref]
  4. G. Milewski, D. Engström, and J. Bengtsson, “Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators,” Appl. Opt. 46(1), 95–105 (2007).
    [Crossref]
  5. M. Karlsson and F. Nikolajeff, “Fabrication and evaluation of a diamond diffractive fan-out element for high power lasers,” Opt. Express 11(3), 191–198 (2003).
    [Crossref] [PubMed]
  6. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
    [Crossref]
  7. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
    [Crossref]
  8. S. Torres-Peiró, J. González-Ausejo, O. Mendoza-Yero, G. Mínguez-Vega, P. Andrés, and J. Lancis, “Parallel laser micromachining based on diffractive optical elements with dispersion compensated femtosecond pulses,” Opt. Express 21(26), 31830–31836 (2013).
    [Crossref]
  9. H. Blom, M. Johansson, A. Hedman, L. Lundberg, A. Hanning, S. Hard, and R. Rigler, “Parallel fluorescence detection of single biomolecules in microarrays by a diffractive-optical-designed 2 × 2 fan-out element,” Appl. Opt. 41(16), 3336–3342 (2002).
    [Crossref] [PubMed]
  10. S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
    [Crossref]
  11. H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
    [Crossref]
  12. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34(26), 5961–5969 (1995).
    [Crossref] [PubMed]
  13. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” OPTIK 35(2), 237–246 (1972).
  14. V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).
  15. H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
    [Crossref]
  16. J. Bengtsson, “Kinoform design with an optimal-rotation-angle method,” Appl. Opt. 33(29), 6879–6884 (1994).
    [Crossref] [PubMed]
  17. Y. Ogura, N. Shirai, J. Tanida, and Y. Ichioka, “Wavelength-multiplexing diffractive phase elements: design, fabrication, and performance evaluation,” J. Opt. Soc. Am. A 18(5), 1082–1092 (2001).
    [Crossref]
  18. M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33(24), 2976–2978 (2008).
    [Crossref] [PubMed]
  19. E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
    [Crossref]
  20. M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22) 6965–6977 (2006).
    [Crossref]
  21. T. R. M. Sales and G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14(7), 1637–1646 (1997).
    [Crossref]
  22. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
    [Crossref]
  23. A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3, 1715 (2013).
    [Crossref] [PubMed]
  24. L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
    [Crossref]
  25. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  26. E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
    [Crossref]
  27. K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
    [Crossref]

2014 (1)

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

2013 (5)

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3, 1715 (2013).
[Crossref] [PubMed]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
[Crossref]

S. Torres-Peiró, J. González-Ausejo, O. Mendoza-Yero, G. Mínguez-Vega, P. Andrés, and J. Lancis, “Parallel laser micromachining based on diffractive optical elements with dispersion compensated femtosecond pulses,” Opt. Express 21(26), 31830–31836 (2013).
[Crossref]

2012 (1)

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

2008 (2)

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33(24), 2976–2978 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22) 6965–6977 (2006).
[Crossref]

2005 (1)

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

2004 (1)

H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
[Crossref]

2003 (1)

2002 (3)

2001 (1)

1997 (1)

1995 (1)

1994 (1)

1992 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” OPTIK 35(2), 237–246 (1972).

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Abrahamsson, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Amako, J.

Andrés, P.

Bargmann, C. I.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Bengtsson, J.

Berry, M. V.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22) 6965–6977 (2006).
[Crossref]

Blom, H.

Boissel, Y.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

Chad, J. E.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Chen, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Courtial, J.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33(24), 2976–2978 (2008).
[Crossref] [PubMed]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Dahan, M.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Darzacq, C. D.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Darzacq, X.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Dennis, M. R.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33(24), 2976–2978 (2008).
[Crossref] [PubMed]

Döndliker, R.

Doskolovich, L.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Eleftheriades, G. V.

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3, 1715 (2013).
[Crossref] [PubMed]

Engström, D.

Gale, M. T.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” OPTIK 35(2), 237–246 (1972).

González-Ausejo, J.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Gustafsson, M. G. L.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Hajj, B.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Hamilton, A. C.

Hanning, A.

Hard, S.

Hayasaki, Y.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Hedman, A.

Hermerschmidt, A.

Herzig, H. P.

Huang, K.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Ichioka, Y.

Johansson, M.

Karlsson, M.

Katsov, A. Y.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Kazuhiro, N.

Kim, H.

H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
[Crossref]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Kotlyar, V. V.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Krüger, S

Lancis, J.

Lee, B.

H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
[Crossref]

Lindberg, J.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Liu, L.

Luk’yanchuk, B.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Lundberg, L.

Mendoza-Yero, O.

Milewski, G.

Mínguez-Vega, G.

Mizuguchi, G.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Morris, G. M.

Mueller, F.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Nagasaka, K.

Nikolajeff, F.

Nishida, N.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Ogura, Y.

Popescu, S.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22) 6965–6977 (2006).
[Crossref]

Prongué, D.

Qiu, C.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Rigler, R.

Rogers, E. T. F.

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
[Crossref]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Roy, T.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Sales, T. R. M.

Savo, S.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” OPTIK 35(2), 237–246 (1972).

Shirai, N.

Soifer, V. A.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Soule, P.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Stallinga, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Sugimoto, T.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Takita, A.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Tanida, J.

Teng, J.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Thomson, L. C.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

Torres-Peiró, S.

Wernicke, G.

Whyte, G.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

Wisniewski, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Wong, A. M. H.

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3, 1715 (2013).
[Crossref] [PubMed]

Wu, C.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

Yang, B.

H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
[Crossref]

Yao, E.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

Ye, H.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Yeo, S. P.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Zheludev, N. I.

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
[Crossref]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Zhou, C.

Appl. Opt. (5)

Appl. Phys. Lett. (2)

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

J. Opt. (1)

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
[Crossref]

J. Opt. Soc. Am. A (2)

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

H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A, 21(12) 2353–2365 (2004).
[Crossref]

J. Phys. A: Math. Gen. (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22) 6965–6977 (2006).
[Crossref]

Laser Photon. Rev. (1)

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photon. Rev. 8(1), 152–157 (2014).
[Crossref]

Nat. Mat. (1)

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mat. 11(5), 432–435 (2012).
[Crossref]

Nature Methods (1)

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multi-color 3D imaging using aberration-corrected multifocus microscopy,” Nature Methods 10(1) 60–63 (2013).
[Crossref]

New J. Phys. (1)

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10(2), 023015 (2008).
[Crossref]

Opt. Commun. (2)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

OPTIK (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” OPTIK 35(2), 237–246 (1972).

Sci. Rep. (1)

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3, 1715 (2013).
[Crossref] [PubMed]

Other (2)

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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 (8)

Fig. 1
Fig. 1

The model of an optical system using a fan-out element and its coordinate system.

Fig. 2
Fig. 2

The configuration of the output plane in design. One of operations (I)–(III) is applied to each cell in the spot-area. Operation (IV) is applied to the pixels in the surrounding area.

Fig. 3
Fig. 3

Experimental setup. L: Lens, OL: Objective lens, BS: Beam splitter.

Fig. 4
Fig. 4

A design result for a fan-out element generating 3 × 3 spots. (a) The position of the spot-area. (b) The designed phase distribution of the element. (c) The intensity and phase distributions on the output plane within the area indicated by the red rectangle in (a) (left), and within the spot-area (right). (d) Comparison between the diffraction limited spot and the subdiffraction spots placed around the center of the spot-area.

Fig. 5
Fig. 5

(a) The intensity distributions obtained using the fan-out element generating 3 × 3 spots with the focusing system 1 (upper) and the focusing system 2 (lower), within the area indicated by the red rectangle in Fig. 4(a) (left) and within the spot-area (right). (b) Comparison between the diffraction limited spot and the subdiffraction spots placed around the center of the spot-area.

Fig. 6
Fig. 6

Size of the generated spots measured in the design and the experiment.

Fig. 7
Fig. 7

Output images obtained using a fan-out element to generate spots arranged in the shape of ”DH2014”. (a) The design result, (b) the experimental result using the focusing system 1, and (c) using the focusing system 2. Upper: the images within the spot-area, Lower: comparison between the diffraction limited spot and the subdiffraction spots placed around the area indicated by a red triangle.

Fig. 8
Fig. 8

The relationship between the averaged spot-size and the power efficiency. The inset is an enlarged view of a lower left part of the main graph. The values of C used are as follows: C = 0.05, 0.075, 0.10, 0.20, 0.30 for Lc = 0.9Ld.l.; C = 0.04, 0.05, 0.10, 0.20, 0.30 for Lc = 0.8Ld.l.; C = 0.055, 0.07, 0.09, 0.10, 0.30 for Lc = 0.7Ld.l.; C = 0.10, 0.20, 0.30 for Lc = 0.6Ld.l.; C = 0.20, 0.25, 0.30 for Lc = 0.5Ld.l..

Equations (11)

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

I ( x , y ) | t ( ξ , η ) exp [ j 2 π λ f ( x ξ + y η ) ] d ξ d η | 2 ,
A out = α k A out ,
ϕ out = { ϕ out ( 0 ϕ out < π 2 ) π ϕ out ( π 2 ϕ out < π ) ϕ out π ( π ϕ out < 3 π 2 ) 2 π ϕ out ( 3 π 2 < ϕ out < 2 π ) .
A out = α k A out ,
ϕ out = { ϕ out + π ( 0 ϕ out < π 2 ) 2 π ϕ out ( π 2 ϕ out < π ) ϕ out ( π ϕ out < 3 π 2 ) 3 π ϕ out ( 3 π 2 < ϕ out < 2 π ) .
A out = 0 .
α k = I s . a . ( ave ) I ( ave ) ( k ) ,
I s . a . ( ave ) = l = 1 K I ( ave ) ( l ) K ,
A out = C × I s . a . ( ave ) × A out ,
ϕ out = ϕ out ,
SNR = The minimum peak intensity among spots The maximum noise intensity .

Metrics