Abstract

We propose a new approach of using carbon nanoparticles for correlation optical diagnostics of а complex scalar optical field created by scattering and diffraction of radiation off a rough surface. This surface is simulated and we generate a diffraction pattern of the amplitude and phase distribution in the far field. Carbon nanoparticles of a certain size and concentration are obtained by the bottom-up methods of hydrothermal synthesis of citric acid and urea followed by centrifugation. The optical properties of carbon nanoparticles, such as luminescence and absorption in the visible spectrum that essentially differs for different wavelengths, as well as particle size of about dozen nanometers, are the determining criteria for using these particles as probes for the optical speckle field. Luminescence made it possible to register the coordinate position of carbon nanoparticles in real time. The algorithm for reconstruction of the scalar optical field intensity distribution through the analysis of the nanoparticle positions is here displayed. The skeleton of the optical speckle field is analyzed by Hilbert transform to restore the phase. Special attention is paid to the restoration of the speckle field’s phase singularities.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

P. P. Maksimyak, C. Y. Zenkova, and V. M. Tkachuk, “Carbon Nanoparticles. Production, properties, perspectives of use,” Phys. Chem. Solid State 21(1), 13–18 (2020).
[Crossref]

2019 (3)

T. Latychevskaia, “Iterative phase retrieval for digital holography: tutorial,” J. Opt. Soc. Am. A 36(12), D31–D40 (2019).
[Crossref]

A. P. Demchenko, “Excitons in Carbonic Nanostructures,” C 5(4), 71 (2019).
[Crossref]

E. Liu, D. Li, X. Zhou, G. Zhou, H. Xiao, D. Zhou, P. Tian, R. Guo, and S. Qu, “Highly emissive carbon dots in solid state and their applications in light-emitting devices and visible light communication,” ACS Sustainable Chem. Eng. 7(10), 9301–9308 (2019).
[Crossref]

2017 (4)

J. B. Essner and G. A. Baker, “The emerging roles of carbon dots in solar photovoltaics: a critical review,” Environ. Sci.: Nano 4(6), 1216–1263 (2017).
[Crossref]

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

X. Liu, H.-B. Li, L. Shi, X. Meng, Y. Wang, X. Chen, H. Xu, W. Zhang, X. Fang, and T. Ding, “Structure and photoluminescence evolution of nanodots during pyrolysis of citric acid: from molecular nanoclusters to carbogenic nanoparticles,” J. Phys. Chem. C 5(39), 10302–10312 (2017).
[Crossref]

J. Schneider, C. J. Reckmeier, Y. Xiong, M. von Seckendorff, A. S. Susha, P. Kasák, and A. L. Rogach, “Molecular Fluorescence in Citric Acid-Based Carbon Dots,” J. Phys. Chem. C 121(3), 2014–2022 (2017).
[Crossref]

2016 (5)

2015 (4)

Y. Sun, P. Wang, Z. Lu, F. Yang, M. Meziani, G. LeCroy, Y. Liu, and H. Qian, “Host-guest carbon dots for enhanced optical properties and beyond,” Sci. Rep. 5(1), 12354 (2015).
[Crossref]

C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Different approaches to phase restoration of distant complex optical fields,” Opt. Appl. 45(2), 139–150 (2015).
[Crossref]

C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Phase retrieval of speckle fields based on 2D Hilbert transform,” Opt. Mem. Neural Networks 24(4), 303–308 (2015).
[Crossref]

C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Methods of restoring spatial phase distribution of complex optical fields in the approximation of singular optics,” Romanian Rep. in Phys. 67(4), 1401–1411 (2015).

2014 (6)

O. V. Angelsky, M. P. Gorsky, S. G. Hanson, V. P. Lukin, I. I. Mokhun, P. V. Polyanskii, and P. A. Ryabiy, “Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem,” Opt. Express 22(5), 6186–6193 (2014).
[Crossref]

M. O. Dekaliuk, O. Viagin, Y. V. Malyukin, and A. P. Demchenko, “Fluorescent carbon nanomaterials:“quantum dots” or nanoclusters?” Phys. Chem. Chem. Phys. 16(30), 16075–16084 (2014).
[Crossref]

S. Ghosh, A. M. Chizhik, N. Karedla Mariia, O. Dekaliuk, I. Gregor, H. Schuhmann, M. Seibt, K. Bodensiek, I. A. T. Schaap, O. Schulz, A. P. Demchenko, J. Enderlein, and A. I. Chizhik, “Photoluminescence of carbon nanodots: Dipole emission centers and electron–phonon coupling,” Nano Lett. 14(10), 5656–5661 (2014).
[Crossref]

T. G. Brown, M. A. Alonso, A. Vella, M. J. Theisen, S. T. Head, S. R. Gillmer, and J. D. Ellis, “Focused beam scatterometry for deep subwavelength metrology,” Proc. SPIE 8949, 89490Y (2014).
[Crossref]

K. Hola, Y. Zhang, Y. Wang, E. P. Giannelis, R. Zboril, and A. L. Rogach, “Carbon dots—Emerging light emitters for bioimaging, cancer therapy and optoelectronics,” Nano Today 9(5), 590–603 (2014).
[Crossref]

C. Y. Zenkova, “Interconnection of polarization properties and coherence of optical fields,” Appl. Opt. 53(10), B43–B52 (2014).
[Crossref]

2013 (1)

C. Zenkova, I. Soltys, and P. Angelsky, “The use of motion peculiarities of particles of the Rayleigh light scattering mechanism for defining the coherence properties of optical fields,” Opt. Appl. 43(2), 297–312 (2013).
[Crossref]

2012 (1)

2011 (3)

2008 (1)

2002 (1)

2001 (1)

2000 (1)

O. V. Angelskii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Y. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser phys.-Lawrence 10(5), 1136–1142 (2000).

1998 (1)

E. M. Gullikson, “13. Optical Properties of Materials,” Exp. Methods Phys. Sci. 31, 257–270 (1998).
[Crossref]

1986 (1)

N. Nakajima and T. Asakura, “Two dimensional phase retrieval using the logarithmic Hilbert transform and the estimation technique of zero information,” J. Phys. D: Appl. Phys. 19(3), 319–331 (1986).
[Crossref]

1978 (1)

G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, and M. W. L. Wheeler, “The Phase Problem in Scattering Phenomenon: The Zeros of Entire Functions and their Significance,” Proc. R. Soc. Lond. A 360(1700), 25–45 (1978).
[Crossref]

1976 (1)

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, “The phase problem,” Proc. R. Soc. London. 350, 191–212 (1976).

Alonso, M. A.

T. G. Brown, M. A. Alonso, A. Vella, M. J. Theisen, S. T. Head, S. R. Gillmer, and J. D. Ellis, “Focused beam scatterometry for deep subwavelength metrology,” Proc. SPIE 8949, 89490Y (2014).
[Crossref]

Alpmann, C.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Andrews, D. L.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Angelskaya, A. O.

Angelskii, O. V.

O. V. Angelskii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Y. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser phys.-Lawrence 10(5), 1136–1142 (2000).

Angelsky, O. V.

Angelsky, P.

C. Zenkova, I. Soltys, and P. Angelsky, “The use of motion peculiarities of particles of the Rayleigh light scattering mechanism for defining the coherence properties of optical fields,” Opt. Appl. 43(2), 297–312 (2013).
[Crossref]

Angelsky, P. O.

Angelsky, V.

Arkhelyuk, O. D.

O. V. Angelskii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Y. A. Ushenko, “Polarization-correlation studies of multifractal structures in biotissues and diagnostics of their pathologic changes,” Laser phys.-Lawrence 10(5), 1136–1142 (2000).

Asakura, T.

N. Nakajima and T. Asakura, “Two dimensional phase retrieval using the logarithmic Hilbert transform and the estimation technique of zero information,” J. Phys. D: Appl. Phys. 19(3), 319–331 (1986).
[Crossref]

Baker, G. A.

J. B. Essner and G. A. Baker, “The emerging roles of carbon dots in solar photovoltaics: a critical review,” Environ. Sci.: Nano 4(6), 1216–1263 (2017).
[Crossref]

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Berry, M. V.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Bigelow, N. P.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Bodensiek, K.

S. Ghosh, A. M. Chizhik, N. Karedla Mariia, O. Dekaliuk, I. Gregor, H. Schuhmann, M. Seibt, K. Bodensiek, I. A. T. Schaap, O. Schulz, A. P. Demchenko, J. Enderlein, and A. I. Chizhik, “Photoluminescence of carbon nanodots: Dipole emission centers and electron–phonon coupling,” Nano Lett. 14(10), 5656–5661 (2014).
[Crossref]

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T. G. Brown, M. A. Alonso, A. Vella, M. J. Theisen, S. T. Head, S. R. Gillmer, and J. D. Ellis, “Focused beam scatterometry for deep subwavelength metrology,” Proc. SPIE 8949, 89490Y (2014).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Methods of restoring spatial phase distribution of complex optical fields in the approximation of singular optics,” Romanian Rep. in Phys. 67(4), 1401–1411 (2015).

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T. G. Brown, M. A. Alonso, A. Vella, M. J. Theisen, S. T. Head, S. R. Gillmer, and J. D. Ellis, “Focused beam scatterometry for deep subwavelength metrology,” Proc. SPIE 8949, 89490Y (2014).
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Y. Sun, P. Wang, Z. Lu, F. Yang, M. Meziani, G. LeCroy, Y. Liu, and H. Qian, “Host-guest carbon dots for enhanced optical properties and beyond,” Sci. Rep. 5(1), 12354 (2015).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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C. Zenkova, I. Soltys, and P. Angelsky, “The use of motion peculiarities of particles of the Rayleigh light scattering mechanism for defining the coherence properties of optical fields,” Opt. Appl. 43(2), 297–312 (2013).
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P. P. Maksimyak, C. Y. Zenkova, and V. M. Tkachuk, “Carbon Nanoparticles. Production, properties, perspectives of use,” Phys. Chem. Solid State 21(1), 13–18 (2020).
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C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Pseudo-phase mapping of speckle fields using 2D Hilbert transformation,” Opt. Appl. 46(1), 153–162 (2016).
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C. Y. Zenkova, M. P. Gorsky, P. A. Ryabiy, and A. O. Angelskaya, “Additional approaches to solving the phase problem in optics,” Appl. Opt. 55(12), B78–B84 (2016).
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C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Phase retrieval of speckle fields based on 2D Hilbert transform,” Opt. Mem. Neural Networks 24(4), 303–308 (2015).
[Crossref]

C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Methods of restoring spatial phase distribution of complex optical fields in the approximation of singular optics,” Romanian Rep. in Phys. 67(4), 1401–1411 (2015).

C. Y. Zenkova, M. P. Gorsky, and P. A. Ryabiy, “Different approaches to phase restoration of distant complex optical fields,” Opt. Appl. 45(2), 139–150 (2015).
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C. Y. Zenkova, “Interconnection of polarization properties and coherence of optical fields,” Appl. Opt. 53(10), B43–B52 (2014).
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X. Liu, H.-B. Li, L. Shi, X. Meng, Y. Wang, X. Chen, H. Xu, W. Zhang, X. Fang, and T. Ding, “Structure and photoluminescence evolution of nanodots during pyrolysis of citric acid: from molecular nanoclusters to carbogenic nanoparticles,” J. Phys. Chem. C 5(39), 10302–10312 (2017).
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K. Hola, Y. Zhang, Y. Wang, E. P. Giannelis, R. Zboril, and A. L. Rogach, “Carbon dots—Emerging light emitters for bioimaging, cancer therapy and optoelectronics,” Nano Today 9(5), 590–603 (2014).
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E. Liu, D. Li, X. Zhou, G. Zhou, H. Xiao, D. Zhou, P. Tian, R. Guo, and S. Qu, “Highly emissive carbon dots in solid state and their applications in light-emitting devices and visible light communication,” ACS Sustainable Chem. Eng. 7(10), 9301–9308 (2019).
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E. Liu, D. Li, X. Zhou, G. Zhou, H. Xiao, D. Zhou, P. Tian, R. Guo, and S. Qu, “Highly emissive carbon dots in solid state and their applications in light-emitting devices and visible light communication,” ACS Sustainable Chem. Eng. 7(10), 9301–9308 (2019).
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E. Liu, D. Li, X. Zhou, G. Zhou, H. Xiao, D. Zhou, P. Tian, R. Guo, and S. Qu, “Highly emissive carbon dots in solid state and their applications in light-emitting devices and visible light communication,” ACS Sustainable Chem. Eng. 7(10), 9301–9308 (2019).
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ACS Sustainable Chem. Eng. (1)

E. Liu, D. Li, X. Zhou, G. Zhou, H. Xiao, D. Zhou, P. Tian, R. Guo, and S. Qu, “Highly emissive carbon dots in solid state and their applications in light-emitting devices and visible light communication,” ACS Sustainable Chem. Eng. 7(10), 9301–9308 (2019).
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Appl. Opt. (6)

Biophys. Rev. (1)

J. Stetefeld, S. A. McKenna, and T. R. Patel, “Dynamic light scattering: a practical guide and applications in biomedical sciences,” Biophys. Rev. 8(4), 409–427 (2016).
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A. P. Demchenko, “Excitons in Carbonic Nanostructures,” C 5(4), 71 (2019).
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Exp. Methods Phys. Sci. (1)

E. M. Gullikson, “13. Optical Properties of Materials,” Exp. Methods Phys. Sci. 31, 257–270 (1998).
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J. Opt. (1)

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmáán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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J. Opt. Soc. Am. A (1)

J. Phys. Chem. C (2)

X. Liu, H.-B. Li, L. Shi, X. Meng, Y. Wang, X. Chen, H. Xu, W. Zhang, X. Fang, and T. Ding, “Structure and photoluminescence evolution of nanodots during pyrolysis of citric acid: from molecular nanoclusters to carbogenic nanoparticles,” J. Phys. Chem. C 5(39), 10302–10312 (2017).
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Supplementary Material (1)

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» Visualization 1       An added video has been uploaded. This was specifically asked for by one of the reviewers.

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Figures (8)

Fig. 1.
Fig. 1. Two-dimensional (a) and three-dimensional (b) distributions of the heights of the object surface.
Fig. 2.
Fig. 2. Simulated diffraction pattern (a) and calculated phase map (b). The white square shows the part of the pattern undergoing further analysis: 1 – area of 30 × 30 µm2, 2 - area of 60 × 60 µm2.
Fig. 3.
Fig. 3. Ratio of the optical force components as a function of the size of carbon nanoparticles.
Fig. 4.
Fig. 4. The particles’ position in time: the initial random position of carbon nanoparticles (a); the tracks of nanoparticles during their motion (b); the position of the particles in the speckle field after their redistribution into the areas of minimum intensity (observation time 5 second) (c).
Fig. 5.
Fig. 5. Speckle field (a, b, c) with gradient lines of intensity (white lines with arrows) determining the motion of carbon nanoparticles (green tracks) (c) into the areas with singularities (red point) (a,b). The size of analyzed optical field is 1.8 × 1.8 µm2 (red square pointed in Fig. 5(a), (b), (c)).
Fig. 6.
Fig. 6. Demonstration of particles’ motion in time (see Visualization 1)
Fig. 7.
Fig. 7. Original optical field (a) (30 × 30 µm2), (c) (60 × 60 µm2) and corresponding reconstructed optical field (b), (d) through analyzing coordinate distribution of the nanoparticle motion tracks.
Fig. 8.
Fig. 8. Phase information: a) the restored phase map by applying of Hilbert transform, b) phase map with phase singularities (red points), identification of which is a result of the redistribution of carbon nanoparticles in the optical field; c) phase singularities obtained at the intersection of real (green lines) and imaginary (blue lines). Red points in white squares indicate the position of an intensity minimum without a singularity.

Equations (6)

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U ( ξ , ζ ) = z i λ x = 1 X y = 1 Y F ( x , y ) R 2 ( x , y , z , ξ , ζ ) exp { i k [ R ( x , y , z , ξ , ζ ) + 2 h ( x , y ) ] } ,
Re [ α ] = α = r 3 ( ε r 1 ) ( ε r + 2 ) + ε i 2 ( ε r + 2 ) 2 + ε i 2 , Im [ α ] = α = r 3 3 ε i ( ε r + 2 ) 2 + ε i 2 .
F g r a d = α 2 n E 2 , F a b s = n S C a b s c , F s c a t t = n S C s c a t t c ,
Here  E 2 = | E | 2 2 , a S I = c 8 π | E | 2 .
m i d v i d t = F o p t i + F s t i ,
x i ( t ) = x i ( t 0 ) + v x i t + a x i t 2 2 , y i ( t ) = y i ( t 0 ) + v y i t + a y i t 2 2 .