Abstract

Sub-diffraction quasi-non-diffracting beams with sub-wavelength transverse size are attractive for applications such as optical nano-manipulation, optical nano-fabrication, optical high-density storage, and optical super-resolution microscopy. In this paper, we proposed an optimization-free design approach and demonstrated the possibility of generating sub-diffraction quasi-non-diffracting beams with sub-wavelength size for different polarizations by a binary-phase Fresnel planar lens. More importantly, the optimization-free method significantly simplifies the design procedure and the generation of sub-diffracting quasi-non-diffracting beams. Utilizing the concept of normalized angular spectrum compression, for wavelength λ0 = 632.8 nm, a binary-phase Fresnel planar lens was designed and fabricated. The experimental results show that the sub-diffraction transverse size and the non-diffracting propagation distances are 0.40λ0–0.54λ0 and 90λ0, 0.43λ0–0.54λ0 and 73λ0, and 0.34λ0–0.41λ0 and 80λ0 for the generated quasi-non-diffracting beams with circular, longitudinal, and azimuthal polarizations, respectively.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]

2017 (7)

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[Crossref] [PubMed]

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

H. Gao, M. Pu, X. Li, X. Ma, Z. Zhao, Y. Guo, and X. Luo, “Super-resolution imaging with a Bessel lens realized by a geometric metasurface,” Opt. Express 25(12), 13933–13943 (2017).
[Crossref] [PubMed]

V. V. Kotlyar, S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, L. O’Faolain, and E. S. Kozlova, “Tight focusing of laser light using a chromium Fresnel zone plate,” Opt. Express 25(17), 19662–19671 (2017).
[Crossref] [PubMed]

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[Crossref] [PubMed]

2016 (4)

Z. Man, C. Min, L. Du, Y. Zhang, S. Zhu, and X. Yuan, “Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes,” Opt. Express 24(2), 874–882 (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(1), 38859 (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, 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]

2015 (2)

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

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]

2014 (6)

M. Zhu, Q. Cao, and H. Gao, “Creation of a 50,000λ long needle-like field with 0.36λ width,” J. Opt. Soc. Am. A 31(3), 500–504 (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]

A. Sabatyan and B. Meshginqalam, “Generation of annular beam by a novel class of Fresnel zone plate,” Appl. Opt. 53(26), 5995–6000 (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(1), 6333 (2014).
[Crossref] [PubMed]

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

2013 (9)

S. S. Stafeev, V. V. Kotlyar, and L. O’Faolain, “Subwavelength focusing of laser light by microoptics,” J. Mod. Opt. 60(13), 1050–1059 (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]

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photonics News 24(6), 22–29 (2013).
[Crossref]

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]

H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express 21(5), 5363–5372 (2013).
[Crossref] [PubMed]

G. Thériault, Y. De Koninck, and N. McCarthy, “Extended depth of field microscopy for rapid volumetric two-photon imaging,” Opt. Express 21(8), 10095–10104 (2013).
[Crossref] [PubMed]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. G. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21(11), 13425–13435 (2013).
[Crossref] [PubMed]

L. Gong, Y. X. Ren, G. S. Xue, Q. C. Wang, J. H. Zhou, M. C. Zhong, Z. Q. Wang, and Y. M. Li, “Generation of nondiffracting Bessel beam using digital micromirror device,” Appl. Opt. 52(19), 4566–4575 (2013).
[Crossref] [PubMed]

G. Y. Chen, F. Song, and H. T. Wang, “Sharper focal spot generated by 4π tight focusing of higher-order Laguerre-Gaussian radially polarized beam,” Opt. Lett. 38(19), 3937–3940 (2013).
[Crossref] [PubMed]

2012 (7)

2011 (2)

2009 (2)

Y. Y. Yu, D. Z. Lin, L. S. Huang, and C. K. Lee, “Effect of subwavelength annular aperture diameter on the nondiffracting region of generated Bessel beams,” Opt. Express 17(4), 2707–2713 (2009).
[Crossref] [PubMed]

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

2008 (2)

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]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
[Crossref]

2007 (3)

F. Huang, Y. Chen, F. J. G. Abajo, and N. I. Zheludev, “Optical super-resolution through super-oscillations,” J. Opt. A, Pure Appl. Opt. 9(9), S285–S288 (2007).
[Crossref]

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]

Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

2006 (1)

A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
[Crossref]

1996 (1)

1992 (1)

1991 (2)

1954 (1)

Abajo, F. J. G.

F. Huang, Y. Chen, F. J. G. Abajo, and N. I. Zheludev, “Optical super-resolution through super-oscillations,” J. Opt. A, Pure Appl. Opt. 9(9), S285–S288 (2007).
[Crossref]

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(1), 6333 (2014).
[Crossref] [PubMed]

April, A.

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]

Bhattacharya, S.

Buchter, S. C.

A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
[Crossref]

Cao, Q.

Cerullo, G.

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, C.

J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Chen, G.

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[Crossref] [PubMed]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[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]

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(1), 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).
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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).
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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).
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F. Huang, Y. Chen, F. J. G. Abajo, and N. I. Zheludev, “Optical super-resolution through super-oscillations,” J. Opt. A, Pure Appl. Opt. 9(9), S285–S288 (2007).
[Crossref]

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K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

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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).
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Dai, L.

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
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S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[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).
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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).
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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(1), 38859 (2016).
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Davis, J. A.

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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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M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
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M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
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Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
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A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photonics News 24(6), 22–29 (2013).
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A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photonics News 24(6), 22–29 (2013).
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Fu, Y.

Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
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García-Martínez, P.

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Gong, L.

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J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
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Guo, H.

Guo, Y.

Hakola, A.

A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
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He, Y.

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G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
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Herman, R. M.

Herminghaus, S.

Hong, M.

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
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F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
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Huang, F.

F. Huang, Y. Chen, F. J. G. Abajo, and N. I. Zheludev, “Optical super-resolution through super-oscillations,” J. Opt. A, Pure Appl. Opt. 9(9), S285–S288 (2007).
[Crossref]

Huang, K.

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
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F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

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Hurwitz, I.

Jiang, M.

Jiang, S.

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[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(1), 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).
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Jiao, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
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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).
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J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

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A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
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Klewitz, S.

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H. Kurt and M. Turduev, “Generation of a two-dimensional limited-diffraction beam with self-healing ability by annular-type photonic crystals,” J. Opt. Soc. B 29(6), 1245–1256 (2012).
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A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photonics News 24(6), 22–29 (2013).
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Leiderer, P.

Li, X.

Li, X. F.

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

Li, Y.

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[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]

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(1), 38859 (2016).
[Crossref] [PubMed]

Lim, L. E. N.

Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Lin, D. Z.

Lin, F.

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]

Lin, J.

J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

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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]

Liu, Y.

Lukyanchuk, B.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

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).
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H. Gao, M. Pu, X. Li, X. Ma, Z. Zhao, Y. Guo, and X. Luo, “Super-resolution imaging with a Bessel lens realized by a geometric metasurface,” Opt. Express 25(12), 13933–13943 (2017).
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G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Luo, X. 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(1), 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]

Ma, X.

Ma, Y.

J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Magni, V.

Makris, K. G.

Man, Z.

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
[Crossref]

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McLeod, J. H.

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R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

Nalimov, A. G.

Nemirovsky, J.

O’Faolain, L.

Padgett, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photonics News 24(6), 22–29 (2013).
[Crossref]

Panneton, D.

Piché, M.

Psaltis, D.

Pu, M.

Qin, F.

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Qiu, C.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Qiu, C. W.

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

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.

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

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(1), 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]

Roy, T.

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(1), 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]

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[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. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Sabatyan, A.

Sánchez-López, M. M.

Sand, D.

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).
[Crossref] [PubMed]

Schley, R.

Segev, M.

Seifert, A.

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(1), 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]

Shevchenko, A.

A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
[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]

Silvestri, S. D.

Sogomonian, S.

Song, F.

Spether, D.

Stafeev, S. S.

St-Onge, G.

Sui, G.

Tabiryan, N. V.

A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, “Creation of a narrow Bessel-like laser beam using a nematic liquid crystal,” J. Opt. Soc. B 23(4), 637–641 (2006).
[Crossref]

Tan, J.

J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Teng, J.

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Thériault, G.

Thibault, S.

Turduev, M.

H. Kurt and M. Turduev, “Generation of a two-dimensional limited-diffraction beam with self-healing ability by annular-type photonic crystals,” J. Opt. Soc. B 29(6), 1245–1256 (2012).
[Crossref]

Vijayakumar, A.

Wang, A. L.

Wang, C.

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[Crossref] [PubMed]

Wang, C. T.

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(1), 38859 (2016).
[Crossref] [PubMed]

Wang, H.

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]

Wang, H. T.

Wang, Q. C.

Wang, X.

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.

Wang, Z. Q.

Weber, N.

Wen, Z.

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[Crossref] [PubMed]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[Crossref] [PubMed]

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[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]

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(1), 38859 (2016).
[Crossref] [PubMed]

Weng, X.

Wiggins, T. A.

Wu, J.

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Wu, Z.

Wu, Z. X.

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(1), 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]

Xue, G. S.

Ye, H.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yeo, S. P.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Lukyanchuk, and W. Cheng, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yu, A.

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[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.

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(1), 38859 (2016).
[Crossref] [PubMed]

Yu, S. F.

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
[Crossref]

Yu, Y. Y.

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(1), 6333 (2014).
[Crossref] [PubMed]

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

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]

Yuan, X.

Zappe, H.

Zhang, K.

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[Crossref] [PubMed]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[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, 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(1), 38859 (2016).
[Crossref] [PubMed]

Zhang, S.

Zhang, Y.

Zhang, Z.

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

S. Zhang, H. Chen, Z. Wu, K. Zhang, Y. Li, G. Chen, Z. Zhang, Z. Wen, L. Dai, and A. L. Wang, “Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression,” Opt. Express 25(22), 27104–27118 (2017).
[Crossref] [PubMed]

G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
[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(1), 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).
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Zhao, Z.

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T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

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).
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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(1), 6333 (2014).
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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).
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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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R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
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Adv. Mater. (1)

F. Qin, K. Huang, J. Wu, J. Teng, C. W. Qiu, and M. Hong, “A supercritical Lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance,” Adv. Mater. 29(8), 1602721 (2017).
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Appl. Opt. (4)

Appl. Phys. Lett. (4)

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

R. G. Mote, S. F. Yu, W. Zhou, and X. F. Li, “Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states,” Appl. Phys. Lett. 95(19), 191113 (2009).
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Y. Fu, W. Zhou, L. E. N. Lim, C. Du, and X. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
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IEEE Trans. Antenn. Propag. (1)

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F. Huang, Y. Chen, F. J. G. Abajo, and N. I. Zheludev, “Optical super-resolution through super-oscillations,” J. Opt. A, Pure Appl. Opt. 9(9), S285–S288 (2007).
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Nat. Mater. (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. Mater. 11(5), 432–435 (2012).
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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).
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J. Guan, J. Lin, C. Chen, Y. Ma, J. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
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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(1), 6333 (2014).
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F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a sub-wavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
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G. Chen, Z. Wu, A. Yu, K. Zhang, J. Wu, L. Dai, Z. Wen, Y. He, Z. Zhang, S. Jiang, C. Wang, and X. Luo, “Planar binary-phase lens for super-oscillatory optical hollow needles,” Sci. Rep. 7(1), 4697 (2017).
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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(1), 38859 (2016).
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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).
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Figures (10)

Fig. 1
Fig. 1 Numerical results of the single focal spot generated with different polarizations at the designing wavelength λ = 672.8 nm: intensity distribution in the xz propagation plane for incident waves with (a) circular, (b) radial, and (c) azimuthal polarizations; distributions of peak intensity (red, PI), FWHM (blue) and sidelobe ratio (green, SR) along the optical axis for incident waves with (a) circular, (b) radial, and (c) azimuthal polarizations, where the magenta-dashed line and black-dashed line are DL and SOC, respectively. For azimuthal polarization, FWHM refers to the inner full-width-at-half-maximum.

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Fig. 2
Fig. 2 Flowchart of the binary phase zone plate design process: (a) the optimization-free design method based on CFZP; (b) the previously reported design approach based on particle swarm algorithm and vectorial angular spectrum diffraction calculation.

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Fig. 3
Fig. 3 Numerical results of the QND beams generated by the binary-phase lens based on CFZP with incident different polarizations at the working wavelength of λ0 = 632.8 nm. intensity distribution in the xz propagation plane for incident waves with (a,b) circular, (c) radial, and (d) azimuthal polarizations; distributions of peak intensity (red, PI), FWHM (blue), and sidelobe ratio (green, SR) along the optical axis for incident waves with (a,b) circular, (c) radial, and (d) azimuthal polarizations, where the magenta-dashed line and black-dashed line are DL and SOC, respectively; (a,e) and (b,f) are the results for total optical field and transverse optical field, respectively. For azimuthal polarization, FWHM refers to the inner full-width-at-half-maximum.

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Fig. 4
Fig. 4 Comparison between QND beams generated by the binary-phased lens based on CFZP (red) and SDFL (blue) with circularly polarized incident wave: distributions of peak intensity (top), transverse size (FWHM, middle) and sidelobe ratio (bottom) for QND generated with (a) circularly, (b) radially and (c) azimuthally polarized light, respectively. For azimuthal polarization, FWHM refers to the inner full-width-at-half-maximum. The magenta-dashed line and black-dashed line are DL and SOC, respectively.

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Fig. 5
Fig. 5 Comparison of the phase distribution along the radial axis between CFZP (red) and SDFL (blue).

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Fig. 6
Fig. 6 SEM images of the binary phase lens (taken with an NOVA Nano SEM 430 + EDS): (a) a full-size image of the binay-phase lens based on CFZP, and (b) a zoom-in image of the lens central area.

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Fig. 7
Fig. 7 Experimental setup for QND beam measurement, including He-Ne laser, optical isolator, linear polarizer, S-wave plate/quarter-wave plate (WP), binary phase lens (FL) based on CFZP, and (1) high-NA objective lens, 1D nano-positioner (1D NP), tube lens, and CMOS camera for transverse polarization only; (2) tilted nano-fiber probe (TNFP), 3D nano-positioner (3D NP), and single-photon-counter (SPC) for total optical field.

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Fig. 8
Fig. 8 QND beams formed by circularly polarized incident wave: intensity of (a) the transverse optical field and (b) total optical field in the xz propagation plane; major parameters of the beam, i.e., (c,f) peak intensity, (d,g) FWHM, and (e,h) sidelobe ratio, respective to the propagation distance, for the two cases (a,b), respectively. Experimental (blue, Exp.) and theoretical (red, Theo.) data are plotted for comparison, and magenta-dashed line and black-dashed line are DL and SOC, respectively.

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Fig. 9
Fig. 9 Longitudinal polarized QND beam formed by radially polarized incident wave: intensity of (a) optical field in the xz propagation plane; major parameters of the beam, i.e., (b) peak intensity, (c) FWHM, and (d) sidelobe ratio, where experimental (blue, Exp.) and theoretical (red, Theo.) data are plotted for comparison, and magenta-dashed line and black-dashed line are DL and SOC, respectively.

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Fig. 10
Fig. 10 Azimuthally polarized sub-diffraction QND beams formed by azimuthally polarized incident wave: intensity of (a) the optical field in the xz propagation plane; major parameters of the beam, i.e., (b) peak intensity, (c) inner FWHM, and (d) sidelobe ratio, where experimental (blue, Exp.) and theoretical (red, Theo.) data are plotted for comparison, and magenta-dashed line and black-dashed line are DL and SOC, respectively.

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Equations (3)

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r n = nλf+ n 2 λ 2 4
z(r)= r⋅ {1− [ λ 0 /d(r)] 2 } 1/2 [ λ 0 /d(r)]
{ f=z(0) Z max =z(R)−z(0)