Abstract

Nanoparticles made of high index dielectric materials have seen a surge of interest and have been proposed for various applications, such as metalenses, light harvesting and directional scattering. With the advent of fabrication techniques enabling colloidal suspensions, the prospects of optical manipulation of such nanoparticles becomes paramount. High index nanoparticles support electric and magnetic multipolar responses in the visible regime and interference between such modes can give rise to highly directional scattering, in particular a cancellation of back-scattered radiation at the first Kerker condition. Here we present a study of the optical forces on silicon nanoparticles in the visible and near infrared calculated using the transfer matrix method. The zero-backscattering Kerker condition is investigated as an avenue to reduce radiation pressure in an optical trap. We find that while asymmetric scattering does reduce the radiation pressure, the main determining factor of trap stability is the increased particle response near the geometric resonances. The trap stability for non-spherical silicon nanoparticles is also investigated and we find that ellipsoidal deformation of spheres enables trapping of slightly larger particles.

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

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (1)

2017 (6)

Z. Wang, N. An, F. Shen, H. Zhou, Y. Sun, Z. Jiang, Y. Han, Y. Li, and Z. Guo, “Enhanced Forward Scattering of Ellipsoidal Dielectric Nanoparticles,” Nanoscale research letters 12, 58 (2017).
[Crossref] [PubMed]

J. Du, C.-H. Yuen, X. Li, K. Ding, G. Du, Z. Lin, C. T. Chan, and J. Ng, “Tailoring Optical Gradient Force and Optical Scattering and Absorption Force,” Sci. Reports 7, 18042 (2017).
[Crossref]

D. A. Shilkin, E. V. Lyubin, M. R. Shcherbakov, M. Lapine, and A. A. Fedyanin, “Directional Optical Sorting of Silicon Nanoparticles,” ACS Photonics 4, 2312–2319 (2017).
[Crossref]

T.-a. Yano, Y. Tsuchimoto, R. P. Zaccaria, A. Toma, A. Portela, and M. Hara, “Enhanced optical magnetism for reversed optical binding forces between silicon nanoparticles in the visible region,” Opt. Express 25, 431–439 (2017).
[Crossref] [PubMed]

W. Liu, “Generalized Magnetic Mirrors,” Phys. Rev. Lett. 119, 123902 (2017).
[Crossref]

S. Sukhov and A. Dogariu, “Non-conservative optical forces,” Reports on Prog. Phys. 80, 112001 (2017).
[Crossref]

2016 (3)

A. Andres-Arroyo, B. Gupta, F. Wang, J. J. Gooding, and P. J. Reece, “Optical Manipulation and Spectroscopy Of Silicon Nanoparticles Exhibiting Dielectric Resonances,” Nano Lett. 16, 1903–1910 (2016).
[Crossref] [PubMed]

R. Paniagua-Domínguez, Y. F. Yu, A. E. Miroshnichenko, L. A. Krivitsky, Y. H. Fu, V. Valuckas, L. Gonzaga, Y. T. Toh, A. Y. S. Kay, B. Luk’yanchuk, and A. I. Kuznetsov, “Generalized Brewster effect in dielectric metasurfaces,” Nat. Commun. 7, 10362 (2016).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref] [PubMed]

2015 (4)

A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. Tong, and M. Käll, “Laser Trapping of Colloidal Metal Nanoparticles,” ACS Nano 9, 3453–3469 (2015).
[Crossref] [PubMed]

M. Li, T. Lohmüller, and J. Feldmann, “Optical Injection of Gold Nanoparticles into Living Cells,” Nano Lett. 15, 770–775 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-Efficiency Dielectric Huygens’ Surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum Forward Light Scattering by Spherical and Spheroidal Dielectric Nanoparticles with High Refractive Index,” ACS Photonics 2, 993–999 (2015).
[Crossref]

2014 (2)

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11, 456–462 (2014).
[Crossref] [PubMed]

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

2013 (4)

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast Spinning of Gold Nanoparticles in Water Using Circularly Polarized Light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref] [PubMed]

M. Fedoruk, M. Meixner, S. Carretero-Palacios, T. Lohmüller, and J. Feldmann, “Nanolithography by Plasmonic Heating and Optical Manipulation of Gold Nanoparticles,” ACS Nano 7, 7648–7653 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

2012 (5)

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85, 035802 (2012).
[Crossref]

P. C. Ashok and K. Dholakia, “Optical trapping for analytical biotechnology,” Curr. Opin. Biotechnol. 23, 16–21 (2012).
[Crossref]

Z. Yan, J. E. Jureller, J. Sweet, M. J. Guffey, M. Pelton, and N. F. Scherer, “Three-Dimensional Optical Trapping and Manipulation of Single Silver Nanowires,” Nano Lett. 12, 5155–5161 (2012).
[Crossref] [PubMed]

P. Spinelli, M. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

2011 (5)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011).
[Crossref] [PubMed]

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84, 053808 (2011).
[Crossref]

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics 5, 514–515 (2011).
[Crossref]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A 28, 54–60 (2011).
[Crossref]

2010 (5)

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’Yanchuk, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
[Crossref]

D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[Crossref] [PubMed]

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10, 439–445 (2010).
[Crossref] [PubMed]

V. D. Miljković, T. Pakizeh, B. Sepulveda, P. Johansson, and M. Käll, “Optical Forces in Plasmonic Nanoparticle Dimers,” The J. Phys. Chem. C 114, 7472–7479 (2010).
[Crossref]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 11428–11443 (2010).
[Crossref] [PubMed]

2009 (2)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[Crossref]

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8, 643–647 (2009).
[Crossref] [PubMed]

2008 (2)

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92, 1305–1310 (2008).
[Crossref]

2002 (1)

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[Crossref] [PubMed]

1996 (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[Crossref]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[Crossref]

1983 (1)

1971 (1)

P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825–839 (1971).
[Crossref]

1970 (1)

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Albella, P.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[Crossref]

An, N.

Z. Wang, N. An, F. Shen, H. Zhou, Y. Sun, Z. Jiang, Y. Han, Y. Li, and Z. Guo, “Enhanced Forward Scattering of Ellipsoidal Dielectric Nanoparticles,” Nanoscale research letters 12, 58 (2017).
[Crossref] [PubMed]

Andres-Arroyo, A.

A. Andres-Arroyo, B. Gupta, F. Wang, J. J. Gooding, and P. J. Reece, “Optical Manipulation and Spectroscopy Of Silicon Nanoparticles Exhibiting Dielectric Resonances,” Nano Lett. 16, 1903–1910 (2016).
[Crossref] [PubMed]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
[Crossref]

Ashkin, A.

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Ashok, P. C.

P. C. Ashok and K. Dholakia, “Optical trapping for analytical biotechnology,” Curr. Opin. Biotechnol. 23, 16–21 (2012).
[Crossref]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[Crossref]

Basu, A.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11, 456–462 (2014).
[Crossref] [PubMed]

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011).
[Crossref] [PubMed]

Boyer, D.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[Crossref] [PubMed]

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-Efficiency Dielectric Huygens’ Surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref] [PubMed]

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

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10, 439–445 (2010).
[Crossref] [PubMed]

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8, 643–647 (2009).
[Crossref] [PubMed]

Bryant, Z.

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ACS Nano (2)

A. Lehmuskero, P. Johansson, H. Rubinsztein-Dunlop, L. Tong, and M. Käll, “Laser Trapping of Colloidal Metal Nanoparticles,” ACS Nano 9, 3453–3469 (2015).
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D. A. Shilkin, E. V. Lyubin, M. R. Shcherbakov, M. Lapine, and A. A. Fedyanin, “Directional Optical Sorting of Silicon Nanoparticles,” ACS Photonics 4, 2312–2319 (2017).
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Adv. Opt. Mater. (1)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-Efficiency Dielectric Huygens’ Surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
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J. Appl. Phys. (1)

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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Mater. Today (1)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
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Nano Lett. (5)

A. Andres-Arroyo, B. Gupta, F. Wang, J. J. Gooding, and P. J. Reece, “Optical Manipulation and Spectroscopy Of Silicon Nanoparticles Exhibiting Dielectric Resonances,” Nano Lett. 16, 1903–1910 (2016).
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Z. Yan, J. E. Jureller, J. Sweet, M. J. Guffey, M. Pelton, and N. F. Scherer, “Three-Dimensional Optical Trapping and Manipulation of Single Silver Nanowires,” Nano Lett. 12, 5155–5161 (2012).
[Crossref] [PubMed]

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10, 439–445 (2010).
[Crossref] [PubMed]

Nanoscale research letters (1)

Z. Wang, N. An, F. Shen, H. Zhou, Y. Sun, Z. Jiang, Y. Han, Y. Li, and Z. Guo, “Enhanced Forward Scattering of Ellipsoidal Dielectric Nanoparticles,” Nanoscale research letters 12, 58 (2017).
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Nat. Commun. (4)

R. Paniagua-Domínguez, Y. F. Yu, A. E. Miroshnichenko, L. A. Krivitsky, Y. H. Fu, V. Valuckas, L. Gonzaga, Y. T. Toh, A. Y. S. Kay, B. Luk’yanchuk, and A. I. Kuznetsov, “Generalized Brewster effect in dielectric metasurfaces,” Nat. Commun. 7, 10362 (2016).
[Crossref] [PubMed]

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Silicon spheres subject to λ = 1064 nm plane wave excitation. (a) Schematic of the system. (b) Scattering efficiency and forward-to-backward scattering ratio versus size-parameter x, showing the well-known divergence at the first Kerker condition (xk = 0.776, rk = 131 nm). (c) Radiation pressure force on Si spheres in a plane wave (full black line) versus x, together with the pure electric (red) and magnetic dipole (blue) forces and the contribution from their interference (green), respectively. Note that the interference contribution decreases the radiation pressure, but the effect is strongest a higher radius than the first Kerker condition. The dashed curve in (c) shows that the sum of the two dipolar contributions completely dominates the radiation pressure force up until slightly above x = 1 where the magnetic quadrupole starts playing a role. (d) The total radiation pressure force normalized by the scattering cross section of the particle, demonstrating that the first Kerker condition is the optimal angular distribution of scattered radiation. The inset shows the scattering efficiency versus wavelength for a Si sphere in water with radius rk = 131 nm, fulfilling the first Kerker condition at λ = 1064 nm.
Fig. 2
Fig. 2 Optical forces on a silicon sphere in a focused laser beam. Optical force simulations of a Si sphere with radius r* = 124.8 nm (size parameter x* = 0.737) situated in water and illuminated by a circularly polarized laser beam with wavelength λ = 1064 nm focused by a lens with numerical aperture NA = 1.2. The chosen sphere radius corresponds to the most stable trap situation for this set of illumination parameters. (a) Schematic of the simulated system. (b) The optical force in the direction of the optical axis (z) normalized to incident power. The total force (black) is decomposed into its symmetric (green) and anti-symmetric (brown) parts, which we identify as the radiation pressure Fp, and the gradient force Fg, respectively. (c) The gradient force contributions from all multipoles (black), from only the electric dipole (red) and from only the magnetic dipole (blue). The gray dashed line, which shows the sum of the two dipolar contributions, perfectly overlaps with the black line. This demonstrates that the gradient force is strictly additive, i.e. there are no interference effects. (d) The radiation pressure from all multipoles (black), from only the electric dipole (red) and from only the magnetic dipole (blue). The green line shows the difference F p ( int ) = F p tot F p ( e ) F p ( m ) and demonstrates that interference between the induced electric and magnetic dipoles significantly reduces the radiation pressure. We note that the response for this particular size parameter is completely determined by the electric and magnetic dipole responses [c.f. Fig. 1(c)].
Fig. 3
Fig. 3 Trap stability and optical force contributions versus particle size for silicon spheres in water. (a) Axial potential depth normalized to incident laser power, W/P in, in units of kBT with T = 293.15 K. (b) Gradient force with all multipoles present (solid black line) and with only the electric dipole (red) or the magnetic dipole (blue) included in the calculation. The black dashed line shows the sum of the two dipolar contributions. Note that the gradient force components change sign upon crossing their respective resonance wavelengths. (c) Radiation pressure force from all multipoles (black) and from only the electric (red) or magnetic (blue) dipoles. The green line shows the dipole-dipole interference contribution F p ( int ) = F p tot F p ( e ) F p ( m ). The forces in (a) and (b) were calculated at z = 600 nm from the focus, where the gradient force is at its strongest [c.f. Fig. 2]. All calculations were performed for λ = 1064 nm, NA = 1.2 and circular polarization.
Fig. 4
Fig. 4 Trap stability for spheroidal silicon particles in water. The axial potential depth normalized to the incident power for spheroids with different aspect ratios a/b, where b is the half-axis along the spheroid symmetry axis. Thus, for aspect ratios > 1 (< 1) we have oblate (prolate) spheroids. The excitation is λ = 1064 nm in water. The particles considered here have the same volume as the spheres considered in Fig. 1(a) and the size is therefore shown as the radius of a sphere with that volume for ease of comparison. (a) The potential depth for incidence along the spheroid symmetry axis. (b) The potential depth for incidence 90 tilted from the spheroid symmetry axis. The regions with gray dashed lines correspond to parameter values where there is no axial potential well, making trapping impossible. We see that by changing the shape of the particles, there is no drastic gain in terms of being able to trap particles with higher volume.

Equations (3)

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F = S c n ^ T d S ,
F tot = F ( ed ) + F ( md ) + F ( int ) ,
W = z 0 z r F z d z ,

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