Abstract

Due to its unique properties of nondiffracting propagation, highly-localized intensity distribution, small beam cross-section, and self-healing, a nondiffracting beam is attractive for materials processing, microscopy, and optical research. Various methods have been investigated to generate such beams with conventional optics. However, the transverse size of those nondiffracting beams is restricted by the diffraction-limit. To overcome the diffraction limit, we use the concepts of super-oscillation and the vectorial angular spectrum method to design a phase mask mirror with a focal length of 1 m, radius of 5 mm, and numerical aperture of about 0.005 for a wavelength of 632.8 nm. The phase mask mirror was created with a phase spatial light modulator. Under the illumination of a linearly polarized Gaussian wave, a nondiffracting beam was created with sub-diffraction transverse size. The maximum transverse size of the beam is smaller than the diffraction limit of 0.5λ/NA for a propagation distance greater than 43.3 mm. A nondiffracting beam with smaller transverse size can be realized by further increasing the NA value.

© 2017 Optical Society of America

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2016 (5)

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

2015 (1)

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

2014 (3)

2013 (4)

2012 (3)

J. Lindberg, “Mathematical concepts of optical superresolution,” J. Opt. 14(8), 083001 (2012).
[Crossref]

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

2011 (1)

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

2010 (2)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

2009 (1)

2008 (1)

H. F. Wang, L. P. Shi, B. Luk’yanchuk, 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 (3)

2004 (1)

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

1993 (1)

1991 (1)

1989 (1)

1988 (1)

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

1972 (1)

Adamo, G.

G. Yuan, E. T. F. 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]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Baumgartl, J.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

Burvall, A.

Carter, W. H.

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

Chen, G.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

Z. Wen, Y. He, Y. Li, L. Chen, and G. Chen, “Super-oscillation focusing lens based on continuous amplitude and binary phase modulation,” Opt. Express 22(18), 22163–22171 (2014).
[Crossref] [PubMed]

Chen, L.

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

Z. Wen, Y. He, Y. Li, L. Chen, and G. Chen, “Super-oscillation focusing lens based on continuous amplitude and binary phase modulation,” Opt. Express 22(18), 22163–22171 (2014).
[Crossref] [PubMed]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, 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]

Cottrell, D. M.

Dai, L.

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

Dai, L. R.

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Davis, J. A.

Deng, D.

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

Dholakia, K.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

Di Trapani, P.

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Friberg, A. T.

Gao, P.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Gong, L.

Greenfield, E.

Guertin, J.

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Guo, Q.

He, Y.

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

Z. Wen, Y. He, Y. Li, L. Chen, and G. Chen, “Super-oscillation focusing lens based on continuous amplitude and binary phase modulation,” Opt. Express 22(18), 22163–22171 (2014).
[Crossref] [PubMed]

Herman, R. M.

Hurwitz, I.

Jaroszewicz, Z.

Jarutis, V.

Jiang, S.

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

Jiang, S. L.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

Jin, N.

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antenn. Propag. 55(3), 556–567 (2007).
[Crossref]

Kivshar, Y. S.

Kolacz, K.

Kosmeier, S.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

Krolikowski, W.

Li, C.

Li, X.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Li, Y.

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

Z. Wen, Y. He, Y. Li, L. Chen, and G. Chen, “Super-oscillation focusing lens based on continuous amplitude and binary phase modulation,” Opt. Express 22(18), 22163–22171 (2014).
[Crossref] [PubMed]

Li, Y. M.

Li, Y. Y.

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Lin, F.

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

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

J. Lindberg, “Mathematical concepts of optical superresolution,” J. Opt. 14(8), 083001 (2012).
[Crossref]

Liu, S.

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

Luk’yanchuk, B.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, 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.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Luo, X. G.

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Makris, K. G.

Matijošius, A.

Mazilu, M.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
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J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
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Neshev, D.

Piskarskas, A.

Pu, M.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Rahmat-Samii, Y.

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antenn. Propag. 55(3), 556–567 (2007).
[Crossref]

Ren, Y. X.

Rogers, E. T. F.

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

G. Yuan, E. T. F. 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. 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 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, 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]

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
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F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
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Roy, T.

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

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

Saltiel, S.

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. Mater. 11(5), 432–435 (2012).
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Schley, R.

Segev, M.

Shen, Z.

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

G. Yuan, E. T. F. 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. F. Wang, L. P. Shi, B. Luk’yanchuk, 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. P.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, 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]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
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Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
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Tang, D.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
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Turunen, J.

Vasara, A.

Wang, C.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
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Wang, C. T.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

Wang, H. F.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, 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]

Wang, Q. C.

Wang, X.

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

Wang, Y.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Wang, Z. Q.

Wen, Z.

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

Z. Wen, Y. He, Y. Li, L. Chen, and G. Chen, “Super-oscillation focusing lens based on continuous amplitude and binary phase modulation,” Opt. Express 22(18), 22163–22171 (2014).
[Crossref] [PubMed]

Wen, Z. Q.

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Wiggins, T. A.

Wu, Z. X.

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Xue, G. S.

Yu, A.

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

Yu, A. P.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

Yuan, G.

G. Yuan, E. T. F. 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]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

Zhang, K.

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

Zhang, Z.

G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016).
[Crossref] [PubMed]

G. Chen, Y. Li, A. Yu, Z. Wen, L. Dai, L. Chen, Z. Zhang, S. Jiang, K. Zhang, X. Wang, and F. Lin, “Super-oscillatory focusing of circularly polarized light by ultra-long focal length planar lens based on binary amplitude-phase modulation,” Sci. Rep. 6(1), 29068 (2016).
[Crossref] [PubMed]

Zhang, Z. H.

A. P. Yu, G. Chen, Z. H. Zhang, Z. Q. Wen, L. R. Dai, K. Zhang, S. L. Jiang, Z. X. Wu, Y. Y. Li, C. T. Wang, and X. G. Luo, “Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens,” Sci. Rep. 6, 38859 (2016).
[Crossref] [PubMed]

G. Chen, Z. X. Wu, A. P. Yu, Z. H. Zhang, Z. Q. Wen, K. Zhang, L. R. Dai, S. L. Jiang, Y. Y. Li, L. Chen, C. T. Wang, and X. G. Luo, “Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave,” Sci. Rep. 6(1), 37776 (2016).
[Crossref] [PubMed]

Zhao, Z.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Zheludev, N. I.

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

G. Yuan, E. T. F. 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. 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 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, 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]

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[Crossref]

Zhong, M. C.

Zhou, J. H.

Appl. Opt. (4)

Appl. Phys. Lett. (2)

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, “Far field subwavelength focusing using optical eigenmodes,” Appl. Phys. Lett. 98(18), 181109 (2011).
[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]

IEEE Photonics Technol. Lett. (1)

G. Chen, Y. Li, X. Wang, Z. Wen, F. Lin, L. Dai, L. Chen, Y. He, and S. Liu, “Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array,” IEEE Photonics Technol. Lett. 28(3), 335–338 (2016).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations,” IEEE Trans. Antenn. Propag. 55(3), 556–567 (2007).
[Crossref]

J. Opt. (2)

J. Lindberg, “Mathematical concepts of optical superresolution,” J. Opt. 14(8), 083001 (2012).
[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]

J. Opt. Soc. Am. (1)

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

Laser Photonics Rev. (3)

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Nat. Mater. (1)

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Figures (6)

Fig. 1
Fig. 1 The optimized mirror phase distribution. (a) The gray map of the optimized phase distribution of the mirror; (b)-(f) the phase distribution plotted against radius along the radial direction.

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Fig. 2
Fig. 2 The theoretically calculated total electric field intensity profiles in the XY plane. (a)-(f) the diffraction patterns obtained at the propagation distances of z = 974.4 mm, 985.6 mm, 996.8 mm, 1008.0 mm, 1019.2 mm, and 1030.4 mm, respectively, within the designed nondiffracting.

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Fig. 3
Fig. 3 (a) The theoretically calculated intensity of the diffraction pattern in the propagation plane, (b) the peak intensity, the transverse FWHM, and the side lobe ratio within propagation distance of 96 mm, (c) The phase distribution (blue) and the local spatial frequency (red) of electric field along the radial coordinate on the focal plane at z = 1000mm, where the black dashed line denotes the cut-off frequency corresponding diffraction limit of a conventional mirror with NA = 0.005, (d) the angular spectrum of the designed beam (blue), and the inset shows its zoom-in and the angular spectrum of a zero-order Bessel beam (red dashed line) respectively.

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Fig. 4
Fig. 4 The experimental setup.

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Fig. 5
Fig. 5 The experimentally obtained total electric field intensity profiles in the XY plane. (a)-(f) the diffraction patterns obtained at the propagation distances of z = 979.5 mm, 988.5 mm, 997.5 mm, 1006.5 mm, 1015.5 mm, and 1024.5 mm, respectively, within the designed nondiffracting beam.

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Fig. 6
Fig. 6 The experimentally obtained total electric field intensity profiles in the propagation plane. (a) and (b): the intensity of the diffraction pattern in XZ and YZ plane, respectively. (c) The peak intensity, the average FWHM of the spot in transverse direction, and the side lobe ratio within propagation distance of 64 mm.

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Equations (1)

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{ E p ^ ( r, z f )= ∫ 0 ∞ A( l ) exp[ j2πq( l ) z f ] J 0 ( 2πlr )2πldl, E z ( r,ϕ, z f )=−jcosϕ ∫ 0 ∞ l q( l ) A( l )exp[ j2πq( l ) z f ] J 1 ( 2πlr )2πld, A( l )= ∫ 0 ∞ t( r )g( r ) J 1 ( 2πlr )2πrdr,

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