Abstract

A three-dimensional (3D) hollow spot is of great interest for a wide variety of applications such as microscopy, lithography, data storage, optical manipulation, and optical manufacturing. Based on conventional high-numerical-aperture objective lenses, various methods have been proposed for the generation of 3D hollow spots for different polarizations. However, conventional optics are bulky, costly, and difficult to integrate. More importantly, they are diffraction-limited in nature. Owing to their unique properties of small size, light weight, and ease of integration, planar lenses have become attractive as components in the development of novel optical devices. Utilizing the concept of super-oscillation, planar lenses have already shown great potential in the generation of sub-diffraction, or even of super-oscillatory features, in propagating optical waves. In this paper, we propose a binary-phase planar lens with an ultra-long focal length (300λ) for the generation of a 3D hollow spot with a cylindrical vector wave. In addition, we experimentally demonstrate the formation of such a hollow spot with a sub-diffraction transverse size of 0.546λ (smaller than the diffraction limit of 0.5λ/NA, where NA denotes the lens numerical aperture) and a longitudinal size of 1.585λ. The ratio of central minimum intensity to the central ring peak intensity is less than 3.7%. Such a planar lens provides a promising way to achieve tight 3D optical confinement for different uses that might find applications in super-resolution microscopy, nano-lithography, high-density data storage, nano-particle optical manipulation, and nano-optical manufacturing.

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

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References

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2018 (2)

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale 10(2), 666–671 (2018).
[Crossref] [PubMed]

Y. Zhou, H. Gao, J. Teng, X. Luo, and M. Hong, “Orbital angular momentum generation via a spiral phase microsphere,” Opt. Lett. 43(1), 34–37 (2018).
[Crossref] [PubMed]

2017 (6)

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]

X. Dong, A. M. H. Wong, M. Kim, and G. V. Eleftheriades, “Superresolution far-field imaging of complex objects using reduced superoscillating ripples,” Optica 4(9), 1126–1133 (2017).
[Crossref]

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]

Y. Li, X. Li, L. Che, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5(2), 1600502 (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]

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]

2016 (5)

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]

F. Zhang, H. Yu, J. Fang, M. Zhang, S. Chen, J. Wang, A. He, and J. Chen, “Efficient generation and tight focusing of radially polarized beam from linearly polarized beam with all-dielectric metasurface,” Opt. Express 24(6), 6656–6664 (2016).
[Crossref] [PubMed]

T. Liu, S. Yang, and Z. Jiang, “Electromagnetic exploration of far-field super-focusing nanostructured metasurfaces,” Opt. Express 24(15), 16297–16308 (2016).
[Crossref] [PubMed]

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
[Crossref]

2015 (2)

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 (2015).
[Crossref] [PubMed]

A. P. Porfirev and R. V. Skidanov, “Dark-hollow optical beams with a controllable shape for optical trapping in air,” Opt. Express 23(7), 8373–8382 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (5)

A. M. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
[Crossref] [PubMed]

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

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

Z. Gu, C. Kuang, X. Hao, Y. Xue, Z. Zheng, and X. Liu, “Methods for generating a dark spot using phase and polarization modulation light,” Optik (Stuttg.) 124(7), 650–654 (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]

2012 (3)

2011 (1)

Y. Xue, C. Kuang, X. Hao, Z. Gu, and X. Liu, “A method for generating a three-dimensional hollow spot using a radially polarized beam,” J.Opt.A 13(12), 125704 (2011).
[Crossref]

2010 (2)

2009 (3)

2008 (1)

2007 (3)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

N. Bokor and N. Davidson, “Tight parabolic hollow spot with high numerical aperture focusing with a circular π phase plate,” Opt. Commun. 270(2), 145–150 (2007).
[Crossref]

N. B. 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]

2006 (3)

2001 (1)

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow-beam optical trap for cold atoms,” J.Opt.B. Quantum Semiclass.Opt. 3(6), 353–357 (2001).
[Crossref]

2000 (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(1), 6333 (2015).
[Crossref] [PubMed]

Ahmed, M. A.

Aubin, S.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow-beam optical trap for cold atoms,” J.Opt.B. Quantum Semiclass.Opt. 3(6), 353–357 (2001).
[Crossref]

Benfenati, F.

Berry, M. V.

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

Bianchini, P.

Bokor, N.

N. Bokor and N. Davidson, “Tight parabolic hollow spot with high numerical aperture focusing with a circular π phase plate,” Opt. Commun. 270(2), 145–150 (2007).
[Crossref]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett. 31(2), 149–151 (2006).
[Crossref] [PubMed]

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. 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]

Chang, J.

H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
[Crossref]

Che, L.

Y. Li, X. Li, L. Che, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5(2), 1600502 (2017).
[Crossref]

Chen, G.

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]

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. 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]

Chen, H.

Chen, J.

Chen, L.

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale 10(2), 666–671 (2018).
[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]

Chen, S.

Christe, S.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow-beam optical trap for cold atoms,” J.Opt.B. Quantum Semiclass.Opt. 3(6), 353–357 (2001).
[Crossref]

Dai, L.

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]

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]

Dally, A.

Davidson, N.

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]

Diaspro, A.

Dong, D.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Dong, X.

Eleftheriades, G. V.

X. Dong, A. M. H. Wong, M. Kim, and G. V. Eleftheriades, “Superresolution far-field imaging of complex objects using reduced superoscillating ripples,” Optica 4(9), 1126–1133 (2017).
[Crossref]

A. M. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
[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]

Fang, J.

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

Friedman, N.

Galiani, S.

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]

Gao, F.

H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
[Crossref]

Gao, H.

Gao, P.

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale 10(2), 666–671 (2018).
[Crossref] [PubMed]

Gao, X.

Golub, I.

Gong, Q.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Graf, T.

Gu, M.

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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. 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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N. B. 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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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 (2015).
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S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow-beam optical trap for cold atoms,” J.Opt.B. Quantum Semiclass.Opt. 3(6), 353–357 (2001).
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M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
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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 (2015).
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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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W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
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W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
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Z. Gu, C. Kuang, X. Hao, Y. Xue, Z. Zheng, and X. Liu, “Methods for generating a dark spot using phase and polarization modulation light,” Optik (Stuttg.) 124(7), 650–654 (2013).
[Crossref]

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H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
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W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
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W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
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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 (2015).
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[Crossref] [PubMed]

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Zhang, M.

Zhang, S.

Zhang, Y.

H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
[Crossref]

Zhang, 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]

Zhang, Z. H.

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, W.

Zhao, Z.

Zheludev, N. I.

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 (2015).
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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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Zheng, Z.

Z. Gu, C. Kuang, X. Hao, Y. Xue, Z. Zheng, and X. Liu, “Methods for generating a dark spot using phase and polarization modulation light,” Optik (Stuttg.) 124(7), 650–654 (2013).
[Crossref]

Zhou, Y.

Zhuang, S.

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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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Y. Li, X. Li, L. Che, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5(2), 1600502 (2017).
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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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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).
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Optica (1)

Optik (Stuttg.) (2)

H. Yang, Y. Zhang, Y. Xiao, F. Gao, J. Chang, T. Wei, and S. Jiang, “Generation and comparison of donut-shaped depletion beams in STED microscopy,” Optik (Stuttg.) 127(8), 3735–3739 (2016).
[Crossref]

Z. Gu, C. Kuang, X. Hao, Y. Xue, Z. Zheng, and X. Liu, “Methods for generating a dark spot using phase and polarization modulation light,” Optik (Stuttg.) 124(7), 650–654 (2013).
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A. M. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
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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).
[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. 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 (2015).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Binary-phase-modulation-based planar lens for 3D hollow-spot generation. (a) Structure of the binary-phase planar lens. (b) Generation of 3D hollow spot by focusing a cylindrical vector wave with the planar lens.
Fig. 2
Fig. 2 Numerical simulation results obtained with COMSOL Multiphysics. 2D intensity distributions of the (a) transverse, (b) longitudinal, and (c) total electrical fields in the propagation plane in the range between z = 290λ and 310λ for ratio of 0 between the azimuthal and radial polarizations, respectively. The intensity distribution (d) along the optical axis and (e) on the focal plane at z = 300.28λ for different ratios of azimuthal and radial polarizations, i.e., 0 (black-solid line), 0.6 (red-dotted line), and 0.8 (blue-dashed line), where AP and RP represent azimuthal and radial polarizations.
Fig. 3
Fig. 3 SEM image of the binary-phase planar lens (taken with NOVA Nano SEM 430 + EDS).
Fig. 4
Fig. 4 Experimental setup for 3D hollow-spot characterization. The custom system consists of a linearly polarized He-Ne laser, optical isolator, linear polarizer, s-wave plate (SWP), mirror, binary-phase planar lens (BPPL), nano-fiber-probe, nano-positioner, and single-photon counter (SPC).
Fig. 5
Fig. 5 Comparison of the optical intensity distribution on the propagation plane between experimental and theoretical results. 2D optical intensity distribution obtained with (a) experiment and (b) numerical simulation, respectively. (c) Normalized experimental (blue) and theoretical (red) intensity distributions along the optical axis, which show a longitudinal FWHM of 1.585λ and a peak-to-peak distance of 2.845λ in the experimentally generated hollow spot.
Fig. 6
Fig. 6 Comparison of the optical intensity distribution on the focal plane between experimental and theoretical results. 2D optical intensity distribution obtained with (a) experiment and (b) numerical simulation, respectively, where the inset of (a) gives the intensity obtained by high-NA microscope within the same area. (c) Nano-fiber-probe obtained (blue-solid line), microscope obtained (green-solid line) and theoretical (red-dashed line) normalized intensity distributions with respect to the radial coordinate on the focal plane, which shows a peak-to-peak distance of 1.01λ and a transverse FWHM of 0.546λ in the experimentally generated 3D hollow spot. The transverse FWHM is smaller than the diffraction limit of 0.551λ (0.5λ/NA).

Tables (1)

Tables Icon

Table 1 Optimized phase distribution of the planar lens.

Equations (3)

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E( r,z )= E i w 0 w ( z ) 2 rexp[ r 2 w ( z ) 2 ]exp{ j[ kz+ k r 2 2R( z ) 2arctan( z z 0 ) ] }
E φ ( r, z f )= 0 A( r ) exp[ j2πq( ρ ) z f ] J 1 ( 2πρr )2πρdρ,
{ E r ( r, z f )= 0 A( ρ ) exp[ j2πq( ρ ) z f ] J 1 ( 2πρr )2πρdρ, E z ( r, z f )= 0 A( ρ ) exp[ j2πq( ρ ) z f ] J 0 ( 2πρr )2πρdρ,

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