Abstract

We study the optical scattering force on the coated nanoparticles with gain core and nonlocal plasmonic shell in the long-wavelength limit, and demonstrate negative optical force acting on the nanoparticles near the symmetric and/or antisymmetric surface plasmon resonances. To understand the optical force behavior, we propose nonlocal effective medium theory to derive the equivalent permittivity for the coated nanoparticles with nonlocality. We show that the imaginary part of the equivalent permittivity is negative near the surface resonant wavelength, resulting in the negative optical force. The introduction of nonlocality may shift the resonant wavelength of the optical force, and strengthen the negative optical force. Two examples of Fano-like resonant scattering in such coated nanoparticles are considered, and Fano resonance-induced negative optical force is found too. Our findings could have some potential applications in plasmonics, nano-optical manipulation, and optical selection.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  33. T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
    [Crossref] [PubMed]
  34. T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  38. R. Chang and P. T. Leung, “Nonlocal effects on optical and molecular interactions with metallic nanoshells,” Phys. Rev. B 73(12), 125438 (2006).
    [Crossref]
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    [Crossref]
  41. Y. Huang and L. Gao, “Superscattering of light from core−shell nonlocal plasmonic nanoparticles,” J. Phys. Chem. C 118(51), 30170–30178 (2014).
    [Crossref]
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    [Crossref] [PubMed]
  43. Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
    [Crossref]
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    [Crossref]
  45. J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
    [Crossref] [PubMed]
  46. H. L. Fu, Y. Huang, and L. Gao, “Photophoresis of spherical particles with interfacial thermal resistance in micro-nano fluids,” Phys. Lett. A 377(39), 2815–2820 (2013).
    [Crossref]
  47. D. G. Baranov, E. S. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21(9), 10779–10791 (2013).
    [Crossref] [PubMed]

2017 (5)

2016 (3)

Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016).
[Crossref]

T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
[Crossref] [PubMed]

T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

2015 (2)

H. Chen, S. Liu, J. Zi, and Z. Lin, “Fano resonance-induced negative optical scattering force on plasmonic nanoparticles,” ACS Nano 9(2), 1926–1935 (2015).
[Crossref] [PubMed]

Y. Huang, J. J. Xiao, and L. Gao, “Antiboding and bonding lasing modes with low gain threshold in nonlocal metallic nanoshell,” Opt. Express 23(7), 8818–8828 (2015).
[Crossref] [PubMed]

2014 (4)

N. Wang, W. Lu, J. Ng, and Z. Lin, “Optimized optical “tractor beam” for core-shell nanoparticles,” Opt. Lett. 39(8), 2399–2402 (2014).
[Crossref] [PubMed]

Z. Li, S. Zhang, L. Tong, P. Wang, B. Dong, and H. Xu, “Ultrasensitive size-selection of plasmonic nanoparticles by Fano interference optical force,” ACS Nano 8(1), 701–708 (2014).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Superscattering of light from core−shell nonlocal plasmonic nanoparticles,” J. Phys. Chem. C 118(51), 30170–30178 (2014).
[Crossref]

Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
[Crossref]

2013 (7)

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

O. Brzobohatý, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, “Experimental demonstration of optical transport sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: a simple model,” Phys. Rev. Lett. 111(9), 093901 (2013).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Equivalent permittivity and permeability and multiple Fano resonances for nonlocal metallic nanowires,” J. Phys. Chem. C 117(37), 19203–19211 (2013).
[Crossref]

D. G. Baranov, E. S. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21(9), 10779–10791 (2013).
[Crossref] [PubMed]

H. L. Fu, Y. Huang, and L. Gao, “Photophoresis of spherical particles with interfacial thermal resistance in micro-nano fluids,” Phys. Lett. A 377(39), 2815–2820 (2013).
[Crossref]

2012 (7)

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, Y. Luo, A. Wiener, J. B. Pendry, and S. A. Maier, “Theory of three-dimensional nanocrescent light harvesters,” Nano Lett. 12(11), 5946–5953 (2012).
[Crossref] [PubMed]

M. I. Tribelsky, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” EPL 97(4), 44005 (2012).
[Crossref]

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B 85(11), 115429 (2012).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

2011 (4)

C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
[Crossref]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

K. J. Webb and Shivanand, “Negative electromagnetic plane-wave force in gain media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(5), 057602 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[Crossref] [PubMed]

2006 (3)

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006).
[Crossref] [PubMed]

S. Banna, V. Berezovsky, and L. Schächter, “Experimental observation of direct particle acceleration by stimulated emission of radiation,” Phys. Rev. Lett. 97(13), 134801 (2006).
[Crossref] [PubMed]

R. Chang and P. T. Leung, “Nonlocal effects on optical and molecular interactions with metallic nanoshells,” Phys. Rev. B 73(12), 125438 (2006).
[Crossref]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

2000 (1)

L. Gao, J. T. K. Wan, K. W. Yu, and Z. Y. Li, “Effects of highly conducting interface and particle size distribution on optical nonlinearity in granular composites,” J. Appl. Phys. 88(4), 1893–1899 (2000).
[Crossref]

1991 (1)

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
[Crossref] [PubMed]

1988 (1)

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal response of a small coated sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

1986 (1)

1981 (1)

B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effects,” Phys. Rev. B 24(2), 554–561 (1981).
[Crossref]

1977 (1)

A. D. Boardman and B. V. Paranjape, “The optical surface modes of metal spheres,” J. Phys. F 7(9), 1935–1945 (1977).
[Crossref]

1973 (1)

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
[Crossref]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Aizpurua, J.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Alù, A.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

Andrianov, E. S.

Aradian, A.

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B 85(11), 115429 (2012).
[Crossref]

Argyropoulos, C.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

Ashkin, A.

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006).
[Crossref] [PubMed]

Banna, S.

S. Banna, V. Berezovsky, and L. Schächter, “Experimental observation of direct particle acceleration by stimulated emission of radiation,” Phys. Rev. Lett. 97(13), 134801 (2006).
[Crossref] [PubMed]

Bao, J.

T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

Baranov, D. G.

Berezovsky, V.

S. Banna, V. Berezovsky, and L. Schächter, “Experimental observation of direct particle acceleration by stimulated emission of radiation,” Phys. Rev. Lett. 97(13), 134801 (2006).
[Crossref] [PubMed]

Bian, X.

Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
[Crossref]

Bjorkholm, J. E.

Boardman, A. D.

A. D. Boardman and B. V. Paranjape, “The optical surface modes of metal spheres,” J. Phys. F 7(9), 1935–1945 (1977).
[Crossref]

Borisov, A. G.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Brzobohatý, O.

O. Brzobohatý, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, “Experimental demonstration of optical transport sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
[Crossref]

Cao, T.

T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
[Crossref] [PubMed]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chang, R.

R. Chang and P. T. Leung, “Nonlocal effects on optical and molecular interactions with metallic nanoshells,” Phys. Rev. B 73(12), 125438 (2006).
[Crossref]

Chantada, L.

Chen, G.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
[Crossref] [PubMed]

Chen, H.

H. Chen, S. Liu, J. Zi, and Z. Lin, “Fano resonance-induced negative optical scattering force on plasmonic nanoparticles,” ACS Nano 9(2), 1926–1935 (2015).
[Crossref] [PubMed]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chen, P. Y.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

Chu, S.

Chvatal, L.

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C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
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C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
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T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
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Z. Li, S. Zhang, L. Tong, P. Wang, B. Dong, and H. Xu, “Ultrasensitive size-selection of plasmonic nanoparticles by Fano interference optical force,” ACS Nano 8(1), 701–708 (2014).
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Du, L.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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Esteban, R.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
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Fang, H.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: a simple model,” Phys. Rev. Lett. 111(9), 093901 (2013).
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B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effects,” Phys. Rev. B 24(2), 554–561 (1981).
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T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
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Y. Huang, Y. M. Wu, and L. Gao, “Nonlocality-broaden optical bistability in a nonlinear plasmonic core-shell cylinder,” J. Phys. Chem. C 121(16), 8952–8960 (2017).
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Y. Huang, Y. M. Wu, and L. Gao, “Bistable near field and bistable transmittance in 2D composite slab consisting of nonlocal core-Kerr shell inclusions,” Opt. Express 25(2), 1062–1072 (2017).
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Y. Huang and L. Gao, “Equivalent permittivity and permeability and multiple Fano resonances for nonlocal metallic nanowires,” J. Phys. Chem. C 117(37), 19203–19211 (2013).
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H. L. Fu, Y. Huang, and L. Gao, “Photophoresis of spherical particles with interfacial thermal resistance in micro-nano fluids,” Phys. Lett. A 377(39), 2815–2820 (2013).
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C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
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Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
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J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
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Y. Huang, Y. M. Wu, and L. Gao, “Bistable near field and bistable transmittance in 2D composite slab consisting of nonlocal core-Kerr shell inclusions,” Opt. Express 25(2), 1062–1072 (2017).
[Crossref] [PubMed]

Y. Huang, Y. M. Wu, and L. Gao, “Nonlocality-broaden optical bistability in a nonlinear plasmonic core-shell cylinder,” J. Phys. Chem. C 121(16), 8952–8960 (2017).
[Crossref]

Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016).
[Crossref]

Y. Huang, J. J. Xiao, and L. Gao, “Antiboding and bonding lasing modes with low gain threshold in nonlocal metallic nanoshell,” Opt. Express 23(7), 8818–8828 (2015).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Superscattering of light from core−shell nonlocal plasmonic nanoparticles,” J. Phys. Chem. C 118(51), 30170–30178 (2014).
[Crossref]

Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
[Crossref]

Y. Huang and L. Gao, “Equivalent permittivity and permeability and multiple Fano resonances for nonlocal metallic nanowires,” J. Phys. Chem. C 117(37), 19203–19211 (2013).
[Crossref]

H. L. Fu, Y. Huang, and L. Gao, “Photophoresis of spherical particles with interfacial thermal resistance in micro-nano fluids,” Phys. Lett. A 377(39), 2815–2820 (2013).
[Crossref]

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O. Brzobohatý, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, “Experimental demonstration of optical transport sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics 7(2), 123–127 (2013).
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J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
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M. I. Tribelsky, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” EPL 97(4), 44005 (2012).
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Lee, R. B.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
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C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
[Crossref] [PubMed]

Li, Z.

Z. Li, S. Zhang, L. Tong, P. Wang, B. Dong, and H. Xu, “Ultrasensitive size-selection of plasmonic nanoparticles by Fano interference optical force,” ACS Nano 8(1), 701–708 (2014).
[Crossref] [PubMed]

Li, Z. Y.

L. Gao, J. T. K. Wan, K. W. Yu, and Z. Y. Li, “Effects of highly conducting interface and particle size distribution on optical nonlinearity in granular composites,” J. Appl. Phys. 88(4), 1893–1899 (2000).
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H. Chen, S. Liu, J. Zi, and Z. Lin, “Fano resonance-induced negative optical scattering force on plasmonic nanoparticles,” ACS Nano 9(2), 1926–1935 (2015).
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J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
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Luo, S.

J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
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Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: a simple model,” Phys. Rev. Lett. 111(9), 093901 (2013).
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A. I. Fernández-Domínguez, Y. Luo, A. Wiener, J. B. Pendry, and S. A. Maier, “Theory of three-dimensional nanocrescent light harvesters,” Nano Lett. 12(11), 5946–5953 (2012).
[Crossref] [PubMed]

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Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: a simple model,” Phys. Rev. Lett. 111(9), 093901 (2013).
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A. I. Fernández-Domínguez, Y. Luo, A. Wiener, J. B. Pendry, and S. A. Maier, “Theory of three-dimensional nanocrescent light harvesters,” Nano Lett. 12(11), 5946–5953 (2012).
[Crossref] [PubMed]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
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Mao, L.

T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
[Crossref] [PubMed]

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[Crossref] [PubMed]

Min, C.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

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Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
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M. I. Tribelsky, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” EPL 97(4), 44005 (2012).
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Mizrahi, A.

Mock, J. J.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
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C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
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Ni, Y. X.

Y. Huang, X. Bian, Y. X. Ni, A. E. Miroshnichenko, and L. Gao, “Nonlocal surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 89(5), 053824 (2014).
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T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

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R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
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Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: a simple model,” Phys. Rev. Lett. 111(9), 093901 (2013).
[Crossref] [PubMed]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, Y. Luo, A. Wiener, J. B. Pendry, and S. A. Maier, “Theory of three-dimensional nanocrescent light harvesters,” Nano Lett. 12(11), 5946–5953 (2012).
[Crossref] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
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Petrov, D.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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Qiu, C. W.

T. Cao, L. Mao, D. Gao, W. Ding, and C. W. Qiu, “Fano resonant Ge2Sb2Te5 nanoparticles realize switchable lateral optical force,” Nanoscale 8(10), 5657–5666 (2016).
[Crossref] [PubMed]

Qiu, C.-W.

T. Cao, J. Bao, L. Mao, T. Zhang, A. Novitsky, M. Nieto-Vesperinas, and C.-W. Qiu, “Controlling lateral Fano interference optical force with Au-Ge2Sb2Te5 hybrid nanostructure,” Nat. Photonics 3(10), 1934–1942 (2016).

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107(20), 203601 (2011).
[Crossref] [PubMed]

Qiu, M.

J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[Crossref] [PubMed]

Shen, J.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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Shen, Z.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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[Crossref]

Smith, D. R.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

Tabosa, J. W. R.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, “Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap,” Phys. Rev. Lett. 66(25), 3245–3248 (1991).
[Crossref] [PubMed]

Teperik, T. V.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

Tong, L.

Z. Li, S. Zhang, L. Tong, P. Wang, B. Dong, and H. Xu, “Ultrasensitive size-selection of plasmonic nanoparticles by Fano interference optical force,” ACS Nano 8(1), 701–708 (2014).
[Crossref] [PubMed]

Tribelsky, M. I.

M. I. Tribelsky, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” EPL 97(4), 44005 (2012).
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[Crossref] [PubMed]

J. Lu, H. Yang, L. Zhou, Y. Yang, S. Luo, Q. Li, and M. Qiu, “Light-induced pulling and pushing by the synergic effect of optical force and photophoretic force,” Phys. Rev. Lett. 118(4), 043601 (2017).
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Figures (7)

Fig. 1
Fig. 1

Schematic of the coated nanosphere embedded in the host medium with relative permittivity ε h . The coated particle is composed of a gain core with inner radius a and the relative permittivity ε c , and a nonlocal plasmonic shell with outer radius b and ε s (k,ω).

Fig. 2
Fig. 2

Evolution of the equivalent permittivity as gain is increased with Eq. (13), from (a) to (f). Parameters: ε g1 =2.1025 and f=0.03. The real and imaginary parts are denoted by the red solid lines and blue dash-dotted lines. The black dash line represents the value of 2 ε h .

Fig. 3
Fig. 3

Normalized optical force and equivalent permittivity as a function of the incident wavelength with f=0.03 (a-c) and f=0.3 (e-f) in nonlocal (red solid lines) and local (blue dash-dotted lines) cases.

Fig. 4
Fig. 4

Two plasmonic resonant wavelengths (blue lines), and corresponding normalized resonant optical forces (red lines) with increasing volume fractionf, in nonlocal (solid lines) and local (dash-dotted lines) cases, respectively.

Fig. 5
Fig. 5

Normalized optical force F/ F 0 with respect to incident wavelength and volume fractionf in nonlocal theory. Gray region indicates the parameter space for the pushing force, colored region indicates the pulling force. The circled region is magnified in the inset. The black region shows extremely large negative optical force much stronger than −15.

Fig. 6
Fig. 6

(a) Dependence of scattering efficiency on incident wavelength and aspect ratio for core-shell spheres under nonlocal frameworks. The yellow and blue lines show resonant and cloaking modes, respectively. (b)-(d) show corresponding scattering efficiency, normalized optical force and the equivalent permittivity with a=1.2nm(η=0.12), respectively.

Fig. 7
Fig. 7

(a) Scattering efficiency, (b) normalized optical force and (c) The real (solid line) and imaginary (dash-dotted line) parts of equivalent permittivity with a weaker damping coefficient above/below the plasma frequency/wavelength as a function of incident wavelength for f=0.6 in nonlocal theory.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

D(r)= ε s (r r ' ,ω) E( r ' ) d 3 r ' .
2 φ D (r)= E 0 [Aδ(ra)+Bδ(rb)]cosθ,
k 2 φ D (k)= E 0 [Aδ(ra)+Bδ(rb) ] e ikr cosθ d 3 r.
ε s (k,ω)= ε b ω p 2 ω(ω+iγ) β 2 k 2 ,
φ(k)= E 0 i4π[A a 2 j 1 (ka)+B b 2 j 1 (kb)] e i θ k k 2 ε s (k,ω)
φ D (r)= 1 ( 2π ) 3 φ D (k) e ikr d 3 k= 1 3 E 0 [ A a 3 r 2 +Br ]cosθ
φ(r)= 1 ( 2π ) 3 φ(k) e ikr d 3 k= E 0 2 π cosθ [A a 2 j 1 (ka)+B b 2 j 1 (kb)] j 1 (kr) ε s (k,ω) dk
{ φ c (r)= E 0 Crcosθ,r<a φ s (r)= E 0 2 π cosθ [A a 2 j 1 (ka)+B b 2 j 1 (kb)] j 1 (kr) ε s (k,ω) dk,a<r<b φ h (r)= E 0 ( D/ r 2 r )cosθ,r>b
φ D (r)= 1 3 E 0 [ A a 3 r 2 +Br ]cosθ,a<r<b
A= 9( G a G ab ε c G a ) ε h G ab (1+2 ε h / G b )( ε c +2 G a )+2 G a ( ε h + ε c G ab ε h ε c / G ab )f B= 9(2 G a G ab + ε c G ab ) ε h G ab (1+2 ε h / G b )( ε c +2 G a )+2 G a ( ε h + ε c G ab ε h ε c / G ab )f C= 3( G ab +2 G a ) ε h G ab (1+2 ε h / G b )( ε c +2 G a )+2 G a ( ε h + ε c G ab ε h ε c / G ab )f D= b 3 G ab (1 ε h / G b )( ε c +2 G a )+ G a [2( ε c G ab )+ ε h ( ε c / G ab 1)]f G ab (1+2 ε h / G b )( ε c +2 G a )+2 G a ( ε h + ε c G ab ε h ε c / G ab )f
α= α 0 /(1i 2 3 k 3 α 0 4π ε 0 ε h )
F = 1 2 k E 0 2 Im(α) ,
ε eq = G b G ab [( G ab +2f G a ) ε c +2 G a G ab (1f)] ( G ab 2 f G a G b ) ε c + G a G ab (2 G ab +f G b ) ,
ε eq = ε s [(1+2f) ε c +2(1f) ε s ] (1f) ε c +(2+f) ε s .
F =2π ε 0 ε h k b 3 E 0 2 3Im( ε eq ) ε h +2 (kb) 3 [ Re( ε eq ) ε h ] 2 /3 [ Re( ε eq )+2 ε h ] 2 + [ Im( ε eq ) ] 2 +4 (kb) 3 Im( ε eq ) ε h

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