Abstract

Quasi-non-diffracting beams are attractive for various applications, including optical manipulation, super-resolution microscopes, and materials processing. However, it is a great challenge to design and generate super-long quasi-non-diffracting beams with sub-diffraction and sub-wavelength size. In this paper, a method based on the idea of compressing a normalized angular spectrum is developed, which makes it possible and provides a practical tool for the design of a quasi-non-diffracting beam with super-oscillatory sub-wavelength transverse size. It also presents a clear physical picture of the formation of super-oscillatory quasi-non-diffracting beams. Based on concepts of a local grating and super-oscillation, a lens was designed and fabricated for a working wavelength of λ = 632.8 nm. The validity of the idea of normalized angular spectrum compression was confirmed by both numerical investigations and experimental studies. An optical hollow needle with a length of more than 100λ was experimentally demonstrated, in which an optical hollow needle was observed with a sub-diffraction and sub-wavelength transverse size within a non-diffracting propagation distance of 94λ. Longer non-diffracting propagation distance is expected for a lens with larger radius and shorter effective wavelength.

© 2017 Optical Society of America

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References

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2017 (5)

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).

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).
[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).
[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).
[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).
[PubMed]

2016 (7)

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).
[PubMed]

J. Diao, W. Yuan, Y. Yu, Y. Zhu, and Y. Wu, “Controllable design of super-oscillatory planar lenses for sub-diffraction-limit optical needles,” Opt. Express 24(3), 1924–1933 (2016).
[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).
[PubMed]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[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, 29068 (2016).
[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).
[PubMed]

G. Chen, Y. Y. Li, X. Y. Wang, Z. Q. Wen, F. Lin, L. R. Dai, L. Chen, Y. H. 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).

2015 (4)

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).
[PubMed]

T. Liu, T. Shen, S. M. Yang, and Z. D. Jiang, “Subwavelength focusing by binary multi-annular plates: design theory and experiment,” J. Opt. 17, 035610 (2015).

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

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).
[PubMed]

2014 (5)

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).
[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).
[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).
[PubMed]

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

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).
[PubMed]

2013 (5)

2012 (7)

2011 (2)

2009 (1)

2008 (2)

H. F. Wang, L. P. 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).

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

2007 (2)

F. M. Huang, Y. F. 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).

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).

2006 (3)

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

I. Golub, “Fresnel axicon,” Opt. Lett. 31(12), 1890–1892 (2006).
[PubMed]

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

2005 (2)

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).

2003 (1)

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[PubMed]

1996 (1)

1991 (2)

N. Davidson, A. A. Friesem, and E. Hasman, “Holographic axilens: high resolution and long focal depth,” Opt. Lett. 16(7), 523–525 (1991).
[PubMed]

R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. 8(6), 932–942 (1991).

1990 (1)

1987 (2)

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

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

1975 (1)

O. Bryngdahl, “Computer-Generated Holograms as Generalized Optical Components,” Opt. Eng. 14, 145426 (1975).

1954 (1)

Abajo, F. J. G.

F. M. Huang, Y. F. 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).

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).
[PubMed]

Ahluwalia, B. P. S.

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

Amano, A.

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).

Berry, M. V.

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

Bhattacharya, S.

Bryngdahl, O.

O. Bryngdahl, “Computer-Generated Holograms as Generalized Optical Components,” Opt. Eng. 14, 145426 (1975).

Buchter, S. C.

Cao, Q.

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).
[PubMed]

Chattrapiban, N.

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).

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).
[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).
[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).
[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, 29068 (2016).
[PubMed]

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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, 29068 (2016).
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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, 031108 (2013).

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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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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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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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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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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, 031108 (2013).

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).
[PubMed]

Schley, R.

Segev, M.

Seifert, A.

Shen, T.

T. Liu, T. Shen, S. M. Yang, and Z. D. Jiang, “Subwavelength focusing by binary multi-annular plates: design theory and experiment,” J. Opt. 17, 035610 (2015).

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).
[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).
[PubMed]

Sheppard, C.

H. F. Wang, L. P. 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).

Shevchenko, A.

Shi, L. P.

H. F. Wang, L. P. 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).

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[PubMed]

Sogomonian, S.

Song, S.

Spether, D.

Stafeev, S. S.

Stief, F.

St-Onge, G.

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).

Tang, D. L.

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

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).
[PubMed]

Terashima, K.

Thériault, G.

Thibault, S.

Turduev, M.

Ueda, K.

Uematsu, Y.

Vijayakumar, A.

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).
[PubMed]

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).
[PubMed]

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

Wang, H.

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

Wang, H. F.

H. F. Wang, L. P. 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).

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, 29068 (2016).
[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).
[PubMed]

Wang, X. Y.

G. Chen, Y. Y. Li, X. Y. Wang, Z. Q. Wen, F. Lin, L. R. Dai, L. Chen, Y. H. 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).

Wang, Y. Q.

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

Wang, Z. Q.

Weber, N.

Wen, Z.

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).
[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).
[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, 29068 (2016).
[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).
[PubMed]

Wen, Z. Q.

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).
[PubMed]

G. Chen, Y. Y. Li, X. Y. Wang, Z. Q. Wen, F. Lin, L. R. Dai, L. Chen, Y. H. 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).

Wiggins, T. A.

R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. 8(6), 932–942 (1991).

Wu, 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).
[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).
[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).
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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).
[PubMed]

Wu, Y.

Wu, 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).
[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).
[PubMed]

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, 38859 (2016).
[PubMed]

Xu, H.

Xue, G. S.

Yang, S. M.

T. Liu, T. Shen, S. M. Yang, and Z. D. Jiang, “Subwavelength focusing by binary multi-annular plates: design theory and experiment,” J. Opt. 17, 035610 (2015).

Yu, A.

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).
[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).
[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, 29068 (2016).
[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).
[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).
[PubMed]

Yu, M.

Yu, Y.

Yu, Y. Y.

Yuan, G.

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).
[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).
[PubMed]

Yuan, G. H.

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

Yuan, W.

Yuan, X.

Yuan, X. C.

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

Zappe, H.

Zhang, K.

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).
[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, 29068 (2016).
[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).
[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).
[PubMed]

Zhang, L. S.

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

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).
[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).
[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, 29068 (2016).
[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).
[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).
[PubMed]

Zhao, Z.

Zhao, Z. Y.

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

Zheludev, N. I.

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

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).
[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).
[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, 031108 (2013).

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).
[PubMed]

F. M. Huang, Y. F. 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).

Zhitenev, N.

Zhong, M. C.

Zhou, J. H.

Zhu, M.

Zhu, S.

Zhu, Y.

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).
[PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

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, 031108 (2013).

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

W. C. Cheong, B. P. S. Ahluwalia, X. C. Yuan, L. S. Zhang, H. Wang, H. B. Niu, and X. Peng, “Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation,” Appl. Phys. Lett. 87, 024104 (2005).

Contemp. Phys. (1)

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).

IEEE Photonics Technol. Lett. (1)

G. Chen, Y. Y. Li, X. Y. Wang, Z. Q. Wen, F. Lin, L. R. Dai, L. Chen, Y. H. 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).

IEEE Trans. Antenn. Propag. (1)

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).

J. Nanophotonics (1)

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

J. Opt. (1)

T. Liu, T. Shen, S. M. Yang, and Z. D. Jiang, “Subwavelength focusing by binary multi-annular plates: design theory and experiment,” J. Opt. 17, 035610 (2015).

J. Opt. A, Pure Appl. Opt. (1)

F. M. Huang, Y. F. 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).

J. Opt. Soc. Am. (2)

R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. 8(6), 932–942 (1991).

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

Laser Photonics Rev. (2)

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

D. L. Tang, C. T. Wang, Z. Y. Zhao, Y. Q. Wang, M. B. Pu, X. Li, P. Gao, and X. G. Luo, “Ultrabroadband Superoscillatory Lens Composed by Plasmonic Metasurfaces for Subdiffraction Light Focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).

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. F. Wang, L. P. 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).

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
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Opt. Commun. (1)

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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Opt. Express (12)

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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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).
[PubMed]

Y. Liu, H. Xu, F. Stief, N. Zhitenev, and M. Yu, “Far-field superfocusing with an optical fiber based surface plasmonic lens made of nanoscale concentric annular slits,” Opt. Express 19(21), 20233–20243 (2011).
[PubMed]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
[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).
[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).
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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).
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J. Diao, W. Yuan, Y. Yu, Y. Zhu, and Y. Wu, “Controllable design of super-oscillatory planar lenses for sub-diffraction-limit optical needles,” Opt. Express 24(3), 1924–1933 (2016).
[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).
[PubMed]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[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).
[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).
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Figures (10)

Fig. 1
Fig. 1

(a) Generation of quasi-non-diffracting beam with a conical lens, where the incident wave is refracted towards the optical axis with the same refraction angle. (b) Converged wave refracted at the air-water interface, which makes the wave converging with a smaller range of conical angle. (c) Creation of point focus: the local gratings diffract the incident waves towards the same point on the optical axis with a large range of diffraction angle. (d) Generation of quasi-non-diffracting beam using compression of normalized angular spectrum: the local gratings diffract the incident waves towards different points on the optical axis with a small range of diffraction angle, using a shorter effective wavelength.

Fig. 2
Fig. 2

Contribution of the local grating at different radii on the lens to the formation of the optical needle, given by the relation between the position of the local grating and its corresponding focal position.

Fig. 3
Fig. 3

Optical intensity distribution and energy propagating on the propagation plane: (a) The formation of the optical needle by the first-order diffracted light by the local grating. (b) Poynting vector distributions around the optical needle, where the Poynting vectors distribute on the conical surfaces with an angle of approximately 45°, as indicated by the arrows. (c) Poynting vector distributions within the optical needle, which shows the forward propagating energy in the central lobes and inter-energy exchanges between the neighboring lobes.

Fig. 4
Fig. 4

Major parameters of the optical needle: central lobe intensity, transverse size of the central dark area, and sidelobe ratio distributions along the propagation direction.

Fig. 5
Fig. 5

Contribution of the different ring belt area on the lens to the formation of the optical needle. The central lobe intensity distribution along the propagation direction are obtained using numerical simulation, as the areas of (a) 0<r<316λ, (b) 316λ<r<423λ, (c) 423λ<r<527λ, and (d) 527λ<r<638λ on the lens are blocked, where the dashed curve gives the intensity distribution without blocking.

Fig. 6
Fig. 6

SEM images of the binary phase lens.

Fig. 7
Fig. 7

Experimental setup for optical needle measurement, including He-Ne laser, binary phase lens (BPL) illuminated with azimuthally polarized beam (APB), high numerical aperture objective lens, nano-positioner, tube lens, and complementary metal-oxide–semiconductor (CMOS) camera.

Fig. 8
Fig. 8

Transverse optical intensity obtained at (a) z = 250λ, (b) z = 260λ, (c) z = 270λ, (d) z = 280λ, (e) z = 290λ, and (f) z = 300λ. Optical intensity curves along the x axis are plotted along with their theoretical results, including the theoretical intensity and phase distribution.

Fig. 9
Fig. 9

Optical intensity distribution on the propagation plane: (a) experimental and (b) numerical results; (c) central lobe intensity; (d) transverse size; and (e) sidelobe ratio distribution along the optical axis obtained in the experiment, with their theoretical counterparts plotted for comparison.

Fig. 10
Fig. 10

Optical needle immersed in water: (a) Optical intensity distribution on the propagation plane, where the air-water interface is located at 220λ; (b) central lobe intensity, transverse size, and sidelobe ratio distribution along the optical axis; (c) Poynting vector distributions in the propagation plane.

Equations (3)

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f ( r ) = r [ 1 sin 2 θ ( r ) ] 1 / 2 / sin θ ( r ) = r { 1 [ λ eff / d ( r ) ] 2 } 1 / 2 [ λ eff / d ( r ) ] ,
d ( r ) = λ e f f / sin θ ( r ) ,
θ ( r ) = a tan ( r / f 0 ) .

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