Abstract

Sub-diffraction-limit optical needle can be created by a binary amplitude mask through tailoring the interference of diffraction beams. In this paper, a controllable design of super-oscillatory planar lenses to create sub-diffraction-limit optical needles with the tunable focal length and depth of focus (DOF) is presented. As a high-quality optical needle is influenced by various factors, we first propose a multi-objective and multi-constraint optimization model compromising all the main factors to achieve a needle with the prescribed characteristics. The optimizing procedure is self-designed using the Matlab programming language based on the genetic algorithm (GA) and fast Hankel transform algorithm. Numerical simulations show that the optical needles’ properties can be controlled accurately. The optimized results are further validated by the theoretical calculation with the Rayleigh-Sommerfeld integral. The sub-diffraction-limit optical needles can be used in wide fields such as optical nanofabrication, super-resolution imaging, particle acceleration and high-density optical data storage.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Vectorial design of super-oscillatory lens

Tao Liu, Jiubin Tan, Jian Liu, and Hongting Wang
Opt. Express 21(13) 15090-15101 (2013)

Visible achromatic super-oscillatory metasurfaces for sub-diffraction focusing

Dongliang Tang, Long Chen, and Jianjun Liu
Opt. Express 27(9) 12308-12316 (2019)

Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50nm resolution

Guanghui Yuan, Edward T. F. Rogers, Tapashree Roy, Zexiang Shen, and Nikolay I. Zheludev
Opt. Express 22(6) 6428-6437 (2014)

References

  • View by:
  • |
  • |
  • |

  1. Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
    [Crossref] [PubMed]
  2. E. T. 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. Mater. 11(5), 432–435 (2012).
    [Crossref] [PubMed]
  3. S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
    [Crossref]
  4. H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
    [Crossref]
  5. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
    [Crossref]
  6. K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
    [Crossref] [PubMed]
  7. D. Panneton, G. St-Onge, M. Piché, and S. Thibault, “Needles of light produced with a spherical mirror,” Opt. Lett. 40(3), 419–422 (2015).
    [Crossref] [PubMed]
  8. H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
    [Crossref] [PubMed]
  9. Y. Yu and Q. Zhan, “Optimization-free optical focal field engineering through reversing the radiation pattern from a uniform line source,” Opt. Express 23(6), 7527–7534 (2015).
    [Crossref] [PubMed]
  10. E. T. 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]
  11. G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
    [Crossref] [PubMed]
  12. F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
    [Crossref] [PubMed]
  13. M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
    [Crossref]
  14. F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
    [Crossref] [PubMed]
  15. V. V. Kotlyar, S. S. Stafeev, Y. Liu, L. O’Faolain, and A. A. Kovalev, “Analysis of the shape of a subwavelength focal spot for the linearly polarized light,” Appl. Opt. 52(3), 330–339 (2013).
    [Crossref] [PubMed]
  16. T. Liu, J. Tan, J. Liu, and H. Wang, “Vectorial design of super-oscillatory lens,” Opt. Express 21(13), 15090–15101 (2013).
    [Crossref] [PubMed]
  17. T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046611 (2003).
    [Crossref] [PubMed]
  18. A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
    [Crossref]
  19. C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example,” IEEE Trans. Syst. Man Cy. A 28(1), 38–47 (1998).
    [Crossref]
  20. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1(1), 13–15 (1977).
    [Crossref] [PubMed]
  21. H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
    [Crossref]
  22. J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
    [Crossref]

2015 (3)

2014 (1)

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

2013 (5)

V. V. Kotlyar, S. S. Stafeev, Y. Liu, L. O’Faolain, and A. A. Kovalev, “Analysis of the shape of a subwavelength focal spot for the linearly polarized light,” Appl. Opt. 52(3), 330–339 (2013).
[Crossref] [PubMed]

T. Liu, J. Tan, J. Liu, and H. Wang, “Vectorial design of super-oscillatory lens,” Opt. Express 21(13), 15090–15101 (2013).
[Crossref] [PubMed]

E. T. 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]

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

2012 (3)

E. T. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
[Crossref] [PubMed]

2010 (1)

2009 (2)

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
[Crossref]

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2007 (1)

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

2006 (2)

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

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

2003 (1)

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046611 (2003).
[Crossref] [PubMed]

1998 (1)

C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example,” IEEE Trans. Syst. Man Cy. A 28(1), 38–47 (1998).
[Crossref]

1977 (1)

Adamo, G.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

April, A.

Berry, M. V.

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

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Chad, J. E.

E. T. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Chong, T.

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Coit, D. W.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

Courjon, D.

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046611 (2003).
[Crossref] [PubMed]

Dehez, H.

Dennis, M. R.

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Fleming, P. J.

C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example,” IEEE Trans. Syst. Man Cy. A 28(1), 38–47 (1998).
[Crossref]

Fonseca, C. M.

C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example,” IEEE Trans. Syst. Man Cy. A 28(1), 38–47 (1998).
[Crossref]

Fourmaux, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Grosjean, T.

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046611 (2003).
[Crossref] [PubMed]

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Hong, M.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

Huang, F. M.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

Huang, K.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
[Crossref] [PubMed]

Jiao, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

Kang, X. L.

Kieffer, J. C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Konak, A.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

Kotlyar, V. V.

Kovalev, A. A.

Légaré, F.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Li, J.

J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
[Crossref]

Li, Y. P.

Lindberg, J.

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Liu, J.

Liu, T.

Liu, Y.

Lu, B.

J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
[Crossref]

Luk’yanchuk, B.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Luo, X.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

MacLean, J. P.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

O’Faolain, L.

Panneton, D.

Payeur, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Piché, M.

D. Panneton, G. St-Onge, M. Piché, and S. Thibault, “Needles of light produced with a spherical mirror,” Opt. Lett. 40(3), 419–422 (2015).
[Crossref] [PubMed]

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
[Crossref] [PubMed]

Popescu, S.

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

Qin, F.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

Qiu, C.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

Qiu, C. W.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Rogers, E. T.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Roy, T.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Savo, S.

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Schmidt, B. E.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Shen, Z.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Shi, P.

Siegman, A. E.

Smith, A. E.

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

Stafeev, S. S.

St-Onge, G.

Tan, J.

Tan, W.

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Teng, J.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Thibault, S.

Wang, H.

T. Liu, J. Tan, J. Liu, and H. Wang, “Vectorial design of super-oscillatory lens,” Opt. Express 21(13), 15090–15101 (2013).
[Crossref] [PubMed]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Wu, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

Ye, H.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Yeo, S. P.

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Yu, Y.

Yuan, G.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Zhan, Q.

Zhang, X.

Zheludev, N. I.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

E. T. 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. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

Zhu, S.

J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

E. T. 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. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

IEEE Trans. Syst. Man Cy. A (1)

C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example,” IEEE Trans. Syst. Man Cy. A 28(1), 38–47 (1998).
[Crossref]

J. Phys. Math. Gen. (1)

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

Laser Phys. Lett. (1)

H. Ye, C. W. Qiu, K. Huang, J. Teng, B. Luk’yanchuk, and S. P. Yeo, “Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh–Sommerfeld method,” Laser Phys. Lett. 10(6), 065004 (2013).
[Crossref]

Nano Lett. (1)

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

Nat. Commun. (1)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Nat. Mater. (1)

E. T. 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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Opt. Commun. (1)

J. Li, S. Zhu, and B. Lu, “The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture,” Opt. Commun. 282(23), 4475–4480 (2009).
[Crossref]

Opt. Eng. (1)

H. Wang, G. Yuan, W. Tan, L. Shi, and T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46(6), 065201 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046611 (2003).
[Crossref] [PubMed]

Reliab. Eng. Syst. Saf. (1)

A. Konak, D. W. Coit, and A. E. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).
[Crossref]

Sci. Rep. (2)

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4, 6333 (2014).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[Crossref] [PubMed]

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 Schematic diagram of sub-diffraction-limit focusing by a super-oscillatory lens.
Fig. 2
Fig. 2 The strategy to construct a controllable sub-diffraction-limit optical needle.
Fig. 3
Fig. 3 The optimization procedure of designing super-oscillatory lenses for sub-diffraction-limit optical needles.
Fig. 4
Fig. 4 Optimization results of sub-diffraction-limit optical needles with different focal lengths and DOFs. (a), (b), (c) and (d) are the simulated intensity of the diffraction patterns along the propagation direction (left) with the corresponding intensity distributions at the focal plane (center) and line-scan profiles across the focal spot (right), for SOL1, SOL2, SOL3 and SOL4, respectively.
Fig. 5
Fig. 5 (a)-(d) are the axial intensity distributions for SOL1, SOL2, SOL3 and SOL4, respectively. (e)-(h) are the FWHMs of the focal spot along the propagation direction for SOL1, SOL2, SOL3 and SOL4, respectively, and the upper red lines denote the calculated diffraction limit of λ/2NA at the focal plane along the DOF of the optical needles, and the lower blue lines represent the value of λ/4.
Fig. 6
Fig. 6 Comparison of the (a) axial and (b) transverse intensity distributions of the optical needle for SOL2 calculated using the angular spectrum theory (black solid line) and Rayleigh-Sommerfeld diffraction integral (red dot), respectively.

Tables (1)

Tables Icon

Table 1 Targeted parameters and transmittance functions of the optimized binary amplitude SOLs.

Equations (7)

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

{ E x ( r , z ) = 0 A 0 ( l ) exp [ j 2 π q ( l ) z ] J 0 ( 2 π l r ) 2 π l d l E y ( r , z ) = 0 E z ( r , φ , z ) = j cos φ 0 l q ( l ) A 0 ( l ) exp [ j 2 π q ( l ) z ] J 1 ( 2 π l r ) 2 π l d l
q ( l ) = { ( 1 / λ 2 l 2 ) 1 / 2 , l 1 / λ j ( l 2 1 / λ 2 ) 1 / 2 , l > 1 / λ
A 0 ( l ) = 0 t ( r ) g ( r ) J 0 ( 2 π l r ) 2 π r d r
M i n i m i z e { I 1 = max [ I ( 0 , z 0 ; t i ) ] min [ I ( 0 , z 0 ; t i ) ] I 2 = max { max [ I ( 0 , z 1 ; t i ) ] max [ I ( 0 , z 2 ; t i ) ] } I 3 = max [ I ( F W H M 2 , z 0 ; t i ) ] min [ I ( F W H M 2 , z 0 ; t i ) ]
S u b j e c t t o { 0.9 I ( 0 , z 0 ; t i ) 1.1 , f D f 2 z 0 f + D f 2 I ( 0 , z 1 ; t i ) 0.3 & I ( 0 , z 2 ; t i ) 0.3 , 0 < z 1 < f D f 2 , f + D f 2 < z 2 z 0.4 I ( F W H M 2 , z 0 ; t i ) 0.5 , f D f 2 z 0 f + D f 2 I ( r , z 0 ; t i ) 0.3 , F W H M r κ F W H M , f D f 2 z 0 f + D f 2 t i { 0 , 1 } i = 1 , 2 , , N
min ( I ) = min { Σ j = 1 3 [ ω j I j ( r , φ ; t i ) ] }
{ E x ( r , φ , z ) = 1 2 π R 2 t ( ρ ) g ( ρ ) [ z exp ( j k n R ) R 2 ( j k n 1 R ) ] ρ d ρ d θ E y ( r , φ , z ) = 0 E z ( r , φ , z ) = 1 2 π R 2 t ( ρ ) g ( ρ ) ( r cos φ ρ cos θ ) [ exp ( j k n R ) R 2 ( j k n 1 R ) ] ρ d ρ d θ

Metrics