Abstract

Particle nanotracking (PNT) is highly desirable in lab-on-a-chip systems for flexible and convenient multiparameter measurement. An ultrathin flat lens is the preferred imaging device in such a system, with the advantage of high focusing performance and compactness. However, PNT using ultrathin flat lenses has not been demonstrated so far because PNT requires the clear knowledge of the relationship between the object and image in the imaging system. Such a relationship still remains elusive in ultrathin flat lens-based imaging systems because they operate based on diffraction rather than refraction. In this paper, we experimentally reveal the imaging relationship of a graphene metalens using nanohole arrays with micrometer spacing. The distance relationship between the object and image as well as the magnification ratio is acquired with nanometer accuracy. The measured imaging relationship agrees well with the theoretical prediction and is expected to be applicable to other ultrathin flat lenses based on the diffraction principle. By analyzing the high-resolution images from the graphene metalens using the imaging relationship, 3D trajectories of particles with high position accuracy in PNT have been achieved. The revealed imaging relationship for metalenses is essential in designing different types of integrated optical systems, including digital cameras, microfluidic devices, virtual reality devices, telescopes, and eyeglasses, and thus will find broad applications.

© 2020 Chinese Laser Press

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2020 (2)

T. Yang, H. Lin, and B. Jia, “Ultrafast direct laser writing of 2D materials for multifunctional photonics devices,” Chin. Opt. Lett. 18, 023601 (2020).
[Crossref]

X. Li, S. Wei, H. Lin, Y. Zhao, and B. Jia, “Imaging rule of diffractive ultrathin flat lens,” Proc. SPIE 11440, 1144007 (2020).
[Crossref]

2019 (3)

G. Cao, H. Lin, S. Fraser, X. Zheng, B. Del, Z. Gan, and B. Jia, “Resilient graphene ultrathin flat lens in aerospace, chemical, and biological harsh environment,” ACS Appl. Mater. Interfaces 11, 20298–20303 (2019).
[Crossref]

Y. Yang, H. Lin, B. Y. Zhang, Y. Zhang, X. Zheng, A. Yu, M. Hong, and B. Jia, “Graphene-based multilayered metamaterials with phototunable architecture for on-chip photonic devices,” ACS Photon. 6, 1033–1040 (2019).
[Crossref]

H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
[Crossref]

2018 (3)

G. Cao, X. Gan, H. Lin, and B. Jia, “An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory,” Opto Electron. Adv. 1, 180012 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by super-oscillatory metasurface,” Laser Photon. Rev. 12, 1800064 (2018).
[Crossref]

2017 (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, 1602721 (2017).
[Crossref]

2016 (2)

D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

2015 (4)

X. Zheng, B. Jia, H. Lin, L. Qiu, D. Li, and M. Gu, “Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing,” Nat. Commun. 6, 8433 (2015).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

X. T. Kong, A. Khan, P. Kidambi, S. Deng, Y. Ali, B. Dlubak, P. Hiralal, and H. Butt, “Graphene-based ultrathin flat lenses,” ACS Photon. 2, 200–207 (2015).
[Crossref]

2013 (1)

C. Gardiner, Y. J. Ferreira, R. A. Dragovic, C. W. Redman, and I. L. Sargent, “Extracellular vesicle sizing and enumeration by nanoparticle tracking analysis,” J. Extracellular Vesicles 2, 19671 (2013).
[Crossref]

2012 (2)

E. Meijering, O. Dzyubachyk, and I. Smal, “Methods for cell and particle tracking,” Methods Enzymology 504, 183–200 (2012).
[Crossref]

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, 4932–4936 (2012).
[Crossref]

2011 (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[Crossref]

2010 (1)

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

2007 (1)

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36, 171–190 (2007).
[Crossref]

2006 (1)

X. Michalet, S. Weiss, and M. Jäger, “Single-molecule fluorescence studies of protein folding and conformational dynamics,” Chem. Rev. 106, 1785–1813 (2006).
[Crossref]

2005 (1)

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref]

2004 (2)

D. M. Chudakov, V. V. Verkhusha, D. B. Staroverov, E. A. Souslova, S. Lukyanov, and K. A. Lukyanov, “Photoswitchable cyan fluorescent protein for protein tracking,” Nat. Biotechnol. 22, 1435–1439 (2004).
[Crossref]

H. P. Babcock, C. Chen, and X. Zhuang, “Using single-particle tracking to study nuclear trafficking of viral genes,” Biophys. J. 87, 2749–2758 (2004).
[Crossref]

2003 (1)

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

2002 (1)

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, and R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 4, 826–831 (2002).
[Crossref]

1994 (1)

J. C. Crocker and D. G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref]

1977 (1)

Aieta, F.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

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, 4932–4936 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Ali, Y.

X. T. Kong, A. Khan, P. Kidambi, S. Deng, Y. Ali, B. Dlubak, P. Hiralal, and H. Butt, “Graphene-based ultrathin flat lenses,” ACS Photon. 2, 200–207 (2015).
[Crossref]

An, D.

D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Babcock, H. P.

H. P. Babcock, C. Chen, and X. Zhuang, “Using single-particle tracking to study nuclear trafficking of viral genes,” Biophys. J. 87, 2749–2758 (2004).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Bindokas, V. P.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, and R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 4, 826–831 (2002).
[Crossref]

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, 4932–4936 (2012).
[Crossref]

Block, S. M.

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36, 171–190 (2007).
[Crossref]

Brooks, A. S.

R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[Crossref]

Butt, H.

X. T. Kong, A. Khan, P. Kidambi, S. Deng, Y. Ali, B. Dlubak, P. Hiralal, and H. Butt, “Graphene-based ultrathin flat lenses,” ACS Photon. 2, 200–207 (2015).
[Crossref]

Cao, G.

G. Cao, H. Lin, S. Fraser, X. Zheng, B. Del, Z. Gan, and B. Jia, “Resilient graphene ultrathin flat lens in aerospace, chemical, and biological harsh environment,” ACS Appl. Mater. Interfaces 11, 20298–20303 (2019).
[Crossref]

G. Cao, X. Gan, H. Lin, and B. Jia, “An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory,” Opto Electron. Adv. 1, 180012 (2018).
[Crossref]

Capasso, F.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

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, 4932–4936 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Carr, B.

R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[Crossref]

Chang, C. T.

D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
[Crossref]

Chen, C.

H. P. Babcock, C. Chen, and X. Zhuang, “Using single-particle tracking to study nuclear trafficking of viral genes,” Biophys. J. 87, 2749–2758 (2004).
[Crossref]

Chen, W. T.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

Chong, T. K.

H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
[Crossref]

Chudakov, D. M.

D. M. Chudakov, V. V. Verkhusha, D. B. Staroverov, E. A. Souslova, S. Lukyanov, and K. A. Lukyanov, “Photoswitchable cyan fluorescent protein for protein tracking,” Nat. Biotechnol. 22, 1435–1439 (2004).
[Crossref]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref]

Datta, A. K.

D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
[Crossref]

de Sterke, C. M.

H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
[Crossref]

Del, B.

G. Cao, H. Lin, S. Fraser, X. Zheng, B. Del, Z. Gan, and B. Jia, “Resilient graphene ultrathin flat lens in aerospace, chemical, and biological harsh environment,” ACS Appl. Mater. Interfaces 11, 20298–20303 (2019).
[Crossref]

Deng, S.

X. T. Kong, A. Khan, P. Kidambi, S. Deng, Y. Ali, B. Dlubak, P. Hiralal, and H. Butt, “Graphene-based ultrathin flat lenses,” ACS Photon. 2, 200–207 (2015).
[Crossref]

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

Dlubak, B.

X. T. Kong, A. Khan, P. Kidambi, S. Deng, Y. Ali, B. Dlubak, P. Hiralal, and H. Butt, “Graphene-based ultrathin flat lenses,” ACS Photon. 2, 200–207 (2015).
[Crossref]

Dobson, P. J.

R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[Crossref]

Dragovic, R. A.

C. Gardiner, Y. J. Ferreira, R. A. Dragovic, C. W. Redman, and I. L. Sargent, “Extracellular vesicle sizing and enumeration by nanoparticle tracking analysis,” J. Extracellular Vesicles 2, 19671 (2013).
[Crossref]

R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[Crossref]

Dzyubachyk, O.

E. Meijering, O. Dzyubachyk, and I. Smal, “Methods for cell and particle tracking,” Methods Enzymology 504, 183–200 (2012).
[Crossref]

Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Ferguson, D. J. P.

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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
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X. Zheng, B. Jia, H. Lin, L. Qiu, D. Li, and M. Gu, “Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing,” Nat. Commun. 6, 8433 (2015).
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X. Li, S. Wei, H. Lin, Y. Zhao, and B. Jia, “Imaging rule of diffractive ultrathin flat lens,” Proc. SPIE 11440, 1144007 (2020).
[Crossref]

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by super-oscillatory metasurface,” Laser Photon. Rev. 12, 1800064 (2018).
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X. Li, S. Wei, H. Lin, Y. Zhao, and B. Jia, “Imaging rule of diffractive ultrathin flat lens,” Proc. SPIE 11440, 1144007 (2020).
[Crossref]

T. Yang, H. Lin, and B. Jia, “Ultrafast direct laser writing of 2D materials for multifunctional photonics devices,” Chin. Opt. Lett. 18, 023601 (2020).
[Crossref]

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[Crossref]

G. Cao, H. Lin, S. Fraser, X. Zheng, B. Del, Z. Gan, and B. Jia, “Resilient graphene ultrathin flat lens in aerospace, chemical, and biological harsh environment,” ACS Appl. Mater. Interfaces 11, 20298–20303 (2019).
[Crossref]

H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
[Crossref]

G. Cao, X. Gan, H. Lin, and B. Jia, “An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory,” Opto Electron. Adv. 1, 180012 (2018).
[Crossref]

X. Zheng, B. Jia, H. Lin, L. Qiu, D. Li, and M. Gu, “Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing,” Nat. Commun. 6, 8433 (2015).
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D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
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X. Michalet, S. Weiss, and M. Jäger, “Single-molecule fluorescence studies of protein folding and conformational dynamics,” Chem. Rev. 106, 1785–1813 (2006).
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S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, and R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 4, 826–831 (2002).
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Nollen, E. A. A.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, and R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 4, 826–831 (2002).
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H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
[Crossref]

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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
[Crossref]

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Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by super-oscillatory metasurface,” Laser Photon. Rev. 12, 1800064 (2018).
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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, 1602721 (2017).
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X. Zheng, B. Jia, H. Lin, L. Qiu, D. Li, and M. Gu, “Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing,” Nat. Commun. 6, 8433 (2015).
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C. Gardiner, Y. J. Ferreira, R. A. Dragovic, C. W. Redman, and I. L. Sargent, “Extracellular vesicle sizing and enumeration by nanoparticle tracking analysis,” J. Extracellular Vesicles 2, 19671 (2013).
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R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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C. Gardiner, Y. J. Ferreira, R. A. Dragovic, C. W. Redman, and I. L. Sargent, “Extracellular vesicle sizing and enumeration by nanoparticle tracking analysis,” J. Extracellular Vesicles 2, 19671 (2013).
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I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

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E. Meijering, O. Dzyubachyk, and I. Smal, “Methods for cell and particle tracking,” Methods Enzymology 504, 183–200 (2012).
[Crossref]

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D. M. Chudakov, V. V. Verkhusha, D. B. Staroverov, E. A. Souslova, S. Lukyanov, and K. A. Lukyanov, “Photoswitchable cyan fluorescent protein for protein tracking,” Nat. Biotechnol. 22, 1435–1439 (2004).
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D. M. Chudakov, V. V. Verkhusha, D. B. Staroverov, E. A. Souslova, S. Lukyanov, and K. A. Lukyanov, “Photoswitchable cyan fluorescent protein for protein tracking,” Nat. Biotechnol. 22, 1435–1439 (2004).
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D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
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H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
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R. A. Dragovic, C. Gardiner, A. S. Brooks, D. S. Tannetta, D. J. P. Ferguson, P. Hole, B. Carr, C. W. G. Redman, A. L. Harris, and P. J. Dobson, “Sizing and phenotyping of cellular vesicles using nanoparticle tracking analysis,” Nanomedicine 7, 780–788 (2011).
[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, 1602721 (2017).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
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D. M. Chudakov, V. V. Verkhusha, D. B. Staroverov, E. A. Souslova, S. Lukyanov, and K. A. Lukyanov, “Photoswitchable cyan fluorescent protein for protein tracking,” Nat. Biotechnol. 22, 1435–1439 (2004).
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Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by super-oscillatory metasurface,” Laser Photon. Rev. 12, 1800064 (2018).
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Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by super-oscillatory metasurface,” Laser Photon. Rev. 12, 1800064 (2018).
[Crossref]

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref]

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D. An, A. Warning, K. G. Yancey, C. T. Chang, V. R. Kern, A. K. Datta, P. H. Steen, D. Luo, and M. Ma, “Mass production of shaped particles through vortex ring freezing,” Nat. Commun. 7, 12401 (2016).
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Supplementary Material (1)

NameDescription
» Visualization 1       A video of the tracking process of the image by using the graphene metalens

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Figures (8)

Fig. 1.
Fig. 1. Design of the particle tracking system with a graphene metalens. (a) Schematic of the lab-on-a-chip particle tracking system with an integrated graphene metalens; inset, structure of graphene metamaterial; (b) reflective optical microscopic image of a fabricated graphene metalens; (c) atomic force microscope (AFM) image of a region of the fabricated graphene metalens; (d) SEM image of the full view and a region of the fabricated graphene metalens; (e) measured cross-sectional thickness distributions along the white dashed line in (c). Scale bars in (b) and (c) are 40 μm. Scale bar in (c) is 2.5 μm. Scale bar in the inset of (d) is 4 μm.
Fig. 2.
Fig. 2. Imaging performance of the graphene metalens. (a) Schematic of imaging experiment of the spot array object imaged by the graphene metalens. (b) SEM image of the spot array object; (c) optical image of the object and image from the graphene metalens; cross-sectional intensity distribution along the (d) horizontal lines and (e) vertical lines of the spots array from the sample and image. Scale bars in (b) and (c) are 5 μm. Scale bar in the inset of (b) is 0.4 μm.
Fig. 3.
Fig. 3. Imaging an object moving along the axial direction of the graphene metalens. (a) Schematic for measuring the object and image distances from the lens on the z-axis; (b) measured intensity distribution in the xz plane with different object distances from 250 to 350 μm; the white dashed line marks the focal plane of the lens where z=300  μm. (c) Calculated and experimentally measured image distance distributions as a function of the object distance.
Fig. 4.
Fig. 4. Particle tracking analysis using the graphene metalens. (a) SEM image of the fabricated object for PNT demonstration; (b) optical microscopic image of the object; (c) image of the object from the graphene metalens (see Visualization 1); (d) trajectories of three different featured particles as a function of the number of video frames; (e), (f) lateral positions of the object and the image along the x and y directions in different video frames. The frame rate is 15 fps. The scale bars in (a)–(c) are 4 μm.
Fig. 5.
Fig. 5. (a) Intensity distribution of theoretical results of the graphene metalens with different object distances from 160 to 480 μm; (b) image distance as a function of object distance with RS simulation model and analytical formula.
Fig. 6.
Fig. 6. (a) Schematic of the focusing characterization of the graphene flat lens; (b) simulated focal intensity distribution along the optical axis; (c) intensity distribution of the 3D focal spot of the graphene flat lens; experimentally measured intensity distributions in the (d) lateral and (e) axial planes; cross-sectional intensity distributions along the white dashed lines in the (f) lateral and (g) axial planes.
Fig. 7.
Fig. 7. Schematic diagram of the experimental setup used for imaging with the graphene metalens. The laser beam is a supercontinuum laser filtered by a narrowband filter (600 nm with bandwidth of 40 nm). The target was placed at the focal plane of the graphene metalens with the laser illumination. The Mitutoyo objective (100× magnification; NA, 0.8) was used for providing more intensive illumination on the target. A tube lens with focal length of f=150  mm (Thorlabs, TTL150-A) was selectively used to form an image on the CCD camera. The object is mounted on a 3D scanning stage.
Fig. 8.
Fig. 8. PNT movie frames. The images of the object and image from the graphene lens of the CTAM logo are recorded by the CCD with the number of frames marked in the figure. The pictures of image from the graphene metalens are flipped by 180° for easy comparison (see Visualization 1). The red and yellow dashed lines are used to mark the trajectories of the object and image. The frame rate is 15 fps.

Tables (1)

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Table 1. Design of the Graphene Metalens

Equations (10)

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1i+1o=2f.
1i+Δzi+1o+Δzo=2f.
Δxo=ΔxiM,Δyo=ΔyiM.
Δϕ=2πnd/λ,
ΔA=exp(4πkd/λ),
E2(r2,θ2,z)=12π02π0E1(r1,θ1)(ik1ε)×exp(ikε)εr1zdr1dθ,
ε=z2+r12+r222r1r2cos(θ1θ2),
Sp=exp(ik)R2+r12/R2+r12.
E2(r2,θ2,z)=Sp·12π02π0E1(r1,θ1)(ik1ε)exp(ikε)εr1zdr1dθ,
I=|E2|2.