Abstract

In the super resolution imaging system, a lens and an axicon that can generate spherical wavefronts and non-diffracting Bessel beams respectively are both essential yet difficult to integrate using the traditional approach. We propose a new concept of a “Bessel-lens” to indicate unique optical elements that merge the functionalities of lenses and axicons simultaneously. The Bessel-lens is a mission that is extremely difficult if not impossible for state-of-the-art technology because of the exotic phase profile. Via the geometric phases in space-variant nanoslits, planar Bessel-lenses are designed and experimentally characterized for the first time to generate subdiffraction beams. Compared with a planar lens and axicon with the same dimensions and numerical aperture, the proposed Bessel-lens possesses a higher imaging resolution, which may find applications in microscopy, nanofabrication and dense data storage.

© 2017 Optical Society of America

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2017 (2)

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref] [PubMed]

2016 (3)

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

2015 (6)

X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. 58(9), 594201 (2015).
[Crossref]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
[Crossref] [PubMed]

Y. Chen, X. Li, Y. Sonnefraud, A. I. Fernández-Domínguez, X. Luo, M. Hong, and S. A. Maier, “Engineering the phase front of light with phase-change material based planar lenses,” Sci. Rep. 5(1), 8660 (2015).
[Crossref] [PubMed]

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

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
[Crossref] [PubMed]

2014 (4)

P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22(21), 26212–26221 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

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]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

2011 (2)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

M. Weber and J. Huisken, “Light sheet microscopy for real-time developmental biology,” Curr. Opin. Genet. Dev. 21(5), 566–572 (2011).
[Crossref] [PubMed]

2009 (1)

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc. 236(1), 35–43 (2009).
[Crossref] [PubMed]

2007 (1)

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

2002 (2)

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref] [PubMed]

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 S. O. 3(6), 353–357 (2001).
[Crossref]

1999 (1)

1994 (1)

1987 (1)

1960 (1)

1954 (1)

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Alessandri, K.

Arbabi, A.

Arbabi, E.

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 S. O. 3(6), 353–357 (2001).
[Crossref]

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

Biener, G.

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Bomzon, Z.

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Byren, R.

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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]

Chen, J.-W.

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Chen, T.-Y.

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Chen, W. T.

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, X. Li, Y. Sonnefraud, A. I. Fernández-Domínguez, X. Luo, M. Hong, and S. A. Maier, “Engineering the phase front of light with phase-change material based planar lenses,” Sci. Rep. 5(1), 8660 (2015).
[Crossref] [PubMed]

Chiang, I.-D.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

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 S. O. 3(6), 353–357 (2001).
[Crossref]

Chu, C. H.

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

Dennis, M. R.

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]

Dodds, R. K.

Durnin, J.

Dyba, M.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

Fahrbach, F. O.

Fan, D.

Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref] [PubMed]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Faraon, A.

Fernández-Domínguez, A. I.

Y. Chen, X. Li, Y. Sonnefraud, A. I. Fernández-Domínguez, X. Luo, M. Hong, and S. A. Maier, “Engineering the phase front of light with phase-change material based planar lenses,” Sci. Rep. 5(1), 8660 (2015).
[Crossref] [PubMed]

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

Gao, H.

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
[Crossref] [PubMed]

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
[Crossref] [PubMed]

Gao, P.

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
[Crossref] [PubMed]

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

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Tsai, W.-Y.

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Wang, C.

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
[Crossref] [PubMed]

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

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Wang, C.-M.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Wang, Y.

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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[Crossref] [PubMed]

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

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
[Crossref] [PubMed]

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M. Weber and J. Huisken, “Light sheet microscopy for real-time developmental biology,” Curr. Opin. Genet. Dev. 21(5), 566–572 (2011).
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Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref] [PubMed]

West, P. R.

Wichmann, J.

Wildanger, D.

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc. 236(1), 35–43 (2009).
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P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Wu, X.

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
[Crossref] [PubMed]

Xiao, S.

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Yan, L.

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
[Crossref] [PubMed]

Yang, J.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Yang, K.-Y.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Yin, X.

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
[Crossref]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Zakharenkov, Y. A.

Zhao, Z.

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
[Crossref] [PubMed]

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

Zheludev, N. I.

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]

Zhou, J.

Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref] [PubMed]

Zhou, L.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Curr. Opin. Genet. Dev. (1)

M. Weber and J. Huisken, “Light sheet microscopy for real-time developmental biology,” Curr. Opin. Genet. Dev. 21(5), 566–572 (2011).
[Crossref] [PubMed]

J. Microsc. (1)

D. Wildanger, R. Medda, L. Kastrup, and S. W. Hell, “A compact STED microscope providing 3D nanoscale resolution,” J. Microsc. 236(1), 35–43 (2009).
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J. Opt. B-Quantum S. O. (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 S. O. 3(6), 353–357 (2001).
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D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Nano Lett. (4)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[Crossref] [PubMed]

P. C. Wu, W.-Y. Tsai, W. T. Chen, Y.-W. Huang, T.-Y. Chen, J.-W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Nat. Mater. (2)

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]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Nat. Methods (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8(5), 417–423 (2011).
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Opt. Express (3)

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Phys. Rev. A (1)

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
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Sci. Adv. (1)

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Sci. China Phys. Mech. (1)

X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. 58(9), 594201 (2015).
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Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5(1), 8434 (2015).
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Y. Chen, X. Li, Y. Sonnefraud, A. I. Fernández-Domínguez, X. Luo, M. Hong, and S. A. Maier, “Engineering the phase front of light with phase-change material based planar lenses,” Sci. Rep. 5(1), 8660 (2015).
[Crossref] [PubMed]

Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref] [PubMed]

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5(1), 15781 (2015).
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Figures (6)

Fig. 1
Fig. 1 Schematic of the metasurface based on geometric phases. (a) Sketch of metasurface. (b) Rectangular nano-apertures are arranged in a hexagonal lattice to increase the symmetry. The angle between the main axis and the x-axis is α. The distance between two adjacent apertures is L = 5.3 µm. The size of each nano-aperture is P = 3.8 µm and Q = 1 µm (c) The substrate of metasurface is Si, and metal layer is Au which thickness is h = 200 nm. (d) The simulation result of relationship between phase shift and orientation of the aperture α in green line, as well as with amplitude transmittance efficiency in red line.
Fig. 2
Fig. 2 Schematic of designing planar lens and planar axicon. (a) To focus a plane wave into a focal spot, a hyperboloidal phase profile should be impacted onto the incident light. The blue conical surface and red spherical surface present different wave front, on which the projections of point PF were PA and PL separately. The phase shifts of point PS on metasurface are proportional to the distance P L P A ¯ and P L P S ¯ for planar axicon and planar lens separately. The distance between point PS and point O was r. In our design, the radiuses of planar lens and planar axicon are equal, R. The focus spot of planar lens is PF, so in this figure, we present the condition of r = R. The focal length of planar lens is f, and meanwhile the focus of planar axicon is along the optical axis from point O to PF. (b) The phase profile of planar lens after modulo operation by 2π. (c) The phase profile of planar axicon after modulo operation by 2π. (d) The scanning electron microscope (SEM) image of the metasurface.
Fig. 3
Fig. 3 The focus results of planar lens and planar axicon. (a) The simulated focus result of planar lens by vector diffraction method. (b) The simulated focus result of planar axicon by vector diffraction method. (c) The transversal line of y = 0 µm in (a) and (b). (d) The experimental focus result of planar lens. (e) The experimental focus result of planar axicon. (f) The transversal line of y = 0 µm in (d) and (e).
Fig. 4
Fig. 4 The experimental setup and method of planar lens and planar Bessel lens for imaging. (a) The phase profile of planar lens. (b) The schematic designed method of planar lens. (c) The illustration of experimental setup. The part included by green cuboid is detailed shown in (b) and (e). (d) The phase profile of planar Bessel lens. (e) The operation principle of planar Bessel lens.
Fig. 5
Fig. 5 The imaging results of planar lens and planar Bessel-lens. (a) Simulated imaging result of planar lens (b) Simulated imaging result of planar Bessel-lens. (c) Experimental imaging result of planar lens. (d) Experimental imaging result of planar Bessel-lens.
Fig. 6
Fig. 6 The simulated imaging results of planar lens and planar Bessel-lens illuminated by incoherent light. The typical parts are circled by blue ellipse. (a) The object is composed of random distributed apertures whose radius is 25 µm. (b) The simulated imaging result of planar lens. (c) The simulated imaging result of planar Bessel-lens. (d) The imaging result of two point sources spacing at 92μm for planar lens with NA = 0.05. (e) The imaging result of two point sources spacing at 92μm for planar Bessel lens with NA = 0.05. (f) The transversal lines of y = 0 µm in (d) and (e).

Equations (6)

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ϕ L E N S ( r ) = P S P L ¯ * k = ( r 2 + f 2 f ) * k
ϕ L E N S ( r ) = r 2 2 f * k
ϕ A X I C O N ( r ) = P S P A ¯ * k = r * k * sin β
ϕ A X I C O N ( r ) = R f * r * k
ϕ L ( r ) = ϕ l e n s 1 ( r ) + ϕ l e n s 2 ( r ) = ( r 2 2 f 1 + r 2 2 f 2 ) * k
ϕ B e s s e l l e n s ( r ) = ϕ l e n s 1 ( r ) + ϕ a x i c o n ( r ) = ( r 2 2 f 1 + R f 2 r ) * k

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