Abstract

The effects of resonant mode interference on optical forces acting on gold core-silicon shell nanoparticles are theoretically investigated with the multipolar expansion method based on the Mie scattering theory. It is found that the total optical radiation force and its two components, the incident force and the recoil force, can be tuned flexibly by engineering the interference interaction among electric, magnetic, and anapole modes. The recoil force acting on the core-shell nanoparticles can be enhanced up to 17 pN compared with the pure silicon nanoparticles with the same size as that of the core-shell nanoparticles when the magnetic dipole resonant mode totally interferes with the electric dipole resonant mode. In addition, the incident force can also be improved to 25 pN by suppressing the interference between the electric dipole and the magnetic dipole resonances. More importantly, the maximum optical radiation force is not dominated by the strongest resonant scattering mode of the hybrid nanostructure due to the modes’ interference induced giant negative recoil forces. We hope our results not only improve the optical trapping and manipulation of core-shell nanoparticles but also help to understand the underlying physical mechanism regarding the tunable optical radiation forces induced by the tunable interference among different resonant modes in core-shell nanoparticles.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Broadband zero backward scattering by all-dielectric core-shell nanoparticles

Runmin Li, Xin Zhou, Mingcheng Panmai, Jin Xiang, Haiying Liu, Min Ouyang, Haihua Fan, Qiaofeng Dai, and Zhongchao Wei
Opt. Express 26(22) 28891-28901 (2018)

Tailoring optical pulling force on gain coated nanoparticles with nonlocal effective medium theory

X. Bian, D. L. Gao, and L. Gao
Opt. Express 25(20) 24566-24578 (2017)

Optical pulling and pushing forces exerted on silicon nanospheres with strong coherent interaction between electric and magnetic resonances

Hongfeng Liu, Mingcheng Panmai, Yuanyuan Peng, and Sheng Lan
Opt. Express 25(11) 12357-12371 (2017)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [Crossref]
  2. J. Chen, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
    [Crossref]
  3. 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]
  4. S. Sukhov and A. Dogariu, “Negative nonconservative forces: optical “tractor beams” for arbitrary objects,” Phys. Rev. Lett. 107(20), 203602 (2011).
    [Crossref] [PubMed]
  5. A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
    [Crossref] [PubMed]
  6. D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
    [Crossref] [PubMed]
  7. V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
    [Crossref]
  8. V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
    [Crossref]
  9. 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]
  10. 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]
  11. D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
    [Crossref]
  12. H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
    [Crossref]
  13. X. Y. Duan and Z. G. Wang, “Fano resonance in the optical scattering force upon a high-index dielectric nanoparticles,” Phys. Rev. A (Coll. Park) 96(5), 053811 (2017).
    [Crossref]
  14. 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. Rep. 7(1), 18042 (2017).
    [Crossref] [PubMed]
  15. J. Wu and X. Gan, “Three dimensional nanoparticle trapping enhanced by surface plasmon resonance,” Opt. Express 18(26), 27619–27626 (2010).
    [Crossref] [PubMed]
  16. K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, “Plasmon resonance-based optical trapping of single and multiple Au nanoparticles,” Opt. Express 15(19), 12017–12029 (2007).
    [Crossref] [PubMed]
  17. W. H. Huang, S. F. Li, H. T. Xu, Z. X. Xiang, Y. B. Long, and H. D. Deng, “Tunable optical forces enhanced by plasmonic modes hybridization in optical trapping of gold nanorods with plasmonic nanocavity,” Opt. Express 26(5), 6202–6213 (2018).
    [Crossref] [PubMed]
  18. R. R. Agayan, F. Gittes, R. Kopelman, and C. F. Schmidt, “Optical trapping near resonance absorption,” Appl. Opt. 41(12), 2318–2327 (2002).
    [Crossref] [PubMed]
  19. H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002).
    [Crossref] [PubMed]
  20. 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]
  21. 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(1), 1527 (2013).
    [Crossref] [PubMed]
  22. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
    [Crossref] [PubMed]
  23. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
    [Crossref] [PubMed]
  24. U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
    [Crossref] [PubMed]
  25. I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
    [Crossref] [PubMed]
  26. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
    [Crossref] [PubMed]
  27. Y. G. Liu, W. C. H. Choy, W. E. I. Sha, and W. C. Chew, “Unidirectional and wavelength-selective photonic sphere-array nanoantennas,” Opt. Lett. 37(11), 2112–2114 (2012).
    [Crossref] [PubMed]
  28. A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
    [Crossref] [PubMed]
  29. H. Liu, M. Panmai, Y. Peng, and S. Lan, “Optical pulling and pushing forces exerted on silicon nanospheres with strong coherent interaction between electric and magnetic resonances,” Opt. Express 25(11), 12357–12371 (2017).
    [Crossref] [PubMed]
  30. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
    [Crossref] [PubMed]
  31. W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
    [Crossref]
  32. T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
    [Crossref] [PubMed]
  33. P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  34. Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
    [Crossref]
  35. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1983).
  36. M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. NanoTechnol. 5(3), 265–272 (2006).
    [Crossref]
  37. D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
    [Crossref] [PubMed]
  38. D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
    [Crossref]
  39. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 335(11), 57–136 (1909).
    [Crossref]
  40. G. Li and Z. Tang, “Noble metal nanoparticle@metal oxide core/yolk-shell nanostructures as catalysts: recent progress and perspective,” Nanoscale 6(8), 3995–4011 (2014).
    [Crossref] [PubMed]
  41. H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
    [Crossref] [PubMed]

2018 (2)

2017 (7)

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

H. Liu, M. Panmai, Y. Peng, and S. Lan, “Optical pulling and pushing forces exerted on silicon nanospheres with strong coherent interaction between electric and magnetic resonances,” Opt. Express 25(11), 12357–12371 (2017).
[Crossref] [PubMed]

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

X. Y. Duan and Z. G. Wang, “Fano resonance in the optical scattering force upon a high-index dielectric nanoparticles,” Phys. Rev. A (Coll. Park) 96(5), 053811 (2017).
[Crossref]

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. Rep. 7(1), 18042 (2017).
[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).
[Crossref] [PubMed]

2016 (1)

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

2015 (2)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

2014 (5)

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[Crossref] [PubMed]

G. Li and Z. Tang, “Noble metal nanoparticle@metal oxide core/yolk-shell nanostructures as catalysts: recent progress and perspective,” Nanoscale 6(8), 3995–4011 (2014).
[Crossref] [PubMed]

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]

2013 (5)

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(1), 1527 (2013).
[Crossref] [PubMed]

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
[Crossref] [PubMed]

2012 (6)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Y. G. Liu, W. C. H. Choy, W. E. I. Sha, and W. C. Chew, “Unidirectional and wavelength-selective photonic sphere-array nanoantennas,” Opt. Lett. 37(11), 2112–2114 (2012).
[Crossref] [PubMed]

A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
[Crossref] [PubMed]

A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

2011 (4)

J. Chen, 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]

S. Sukhov and A. Dogariu, “Negative nonconservative forces: optical “tractor beams” for arbitrary objects,” Phys. Rev. Lett. 107(20), 203602 (2011).
[Crossref] [PubMed]

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

2010 (1)

2007 (1)

2006 (1)

M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. NanoTechnol. 5(3), 265–272 (2006).
[Crossref]

2002 (2)

R. R. Agayan, F. Gittes, R. Kopelman, and C. F. Schmidt, “Optical trapping near resonance absorption,” Appl. Opt. 41(12), 2318–2327 (2002).
[Crossref] [PubMed]

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1970 (1)

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

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 335(11), 57–136 (1909).
[Crossref]

Agayan, R. R.

Akita, T.

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

Alam, M.

M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. NanoTechnol. 5(3), 265–272 (2006).
[Crossref]

Ashkin, A.

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

Auguié, B.

D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
[Crossref] [PubMed]

Bakker, R. M.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

Belov, P. A.

Bozhevolnyi, S. I.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Brener, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Chan, C. T.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

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

Chen, H.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

Chen, J.

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

Cheng, Y.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Chew, W. C.

Chichkov, B. N.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Chipouline, A.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

Choy, W. C. H.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Davoyan, A. R.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 335(11), 57–136 (1909).
[Crossref]

Decker, M.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Deng, H. D.

Ding, K.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

Ding, W.

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Dogariu, A.

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

S. Sukhov and A. Dogariu, “Negative nonconservative forces: optical “tractor beams” for arbitrary objects,” Phys. Rev. Lett. 107(20), 203602 (2011).
[Crossref] [PubMed]

Dominguez, J.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Dong, B.

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]

Du, G.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

Du, J.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

Duan, X. Y.

X. Y. Duan and Z. G. Wang, “Fano resonance in the optical scattering force upon a high-index dielectric nanoparticles,” Phys. Rev. A (Coll. Park) 96(5), 053811 (2017).
[Crossref]

Engheta, N.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Evlyukhin, A. B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Feng, T.

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Fofang, N. T.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Fu, Y. H.

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(1), 1527 (2013).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Gan, X.

Gao, D.

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

Gao, L.

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

Gittes, F.

Gonzales, E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Guffey, M. J.

Guyot-Sionnest, P.

Haruta, M.

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

Hnatovsky, C.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Huang, W. H.

Huang, Y.

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

Ishida, T.

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

Jain, M.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Jian, J.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

Jiang, H. L.

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kajorndejnukul, V.

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

Käll, M.

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002).
[Crossref] [PubMed]

Kivshar, Y.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Kivshar, Y. S.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
[Crossref] [PubMed]

Kopelman, R.

Krasnok, A. E.

Krolikowski, W.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Kuznetsov, A. I.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[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(1), 1527 (2013).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Lan, S.

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Lavrinenko, A.

A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
[Crossref] [PubMed]

Le Ru, E. C.

D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
[Crossref] [PubMed]

Li, G.

G. Li and Z. Tang, “Noble metal nanoparticle@metal oxide core/yolk-shell nanostructures as catalysts: recent progress and perspective,” Nanoscale 6(8), 3995–4011 (2014).
[Crossref] [PubMed]

Li, Q.

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, S. F.

Li, X.

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. Rep. 7(1), 18042 (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]

Lin, Z.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

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]

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

Liu, H.

Liu, M.

Liu, S.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Liu, W.

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

Liu, X. J.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Liu, Y. G.

Long, Y. B.

Lu, J.

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]

Lu, W.

Luk, T. S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[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(1), 1527 (2013).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Ma, Q. Y.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Massoud, Y.

M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. NanoTechnol. 5(3), 265–272 (2006).
[Crossref]

Miroshnichenko, A. E.

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[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(1), 1527 (2013).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Neshev, D. N.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Ng, J.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

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]

Novikov, S. M.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Novitsky, A.

A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
[Crossref] [PubMed]

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]

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Panmai, M.

Pelton, M.

Peng, Y.

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Pesic, J.

Qiu, C. W.

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Reinhardt, C.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Sáenz, J. J.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Schebarchov, D.

D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
[Crossref] [PubMed]

Scherer, N. F.

Schmidt, C. F.

Sha, W. E. I.

Shi, L.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

Shi, R.

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

Shvedov, V.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Staude, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Sukhov, S.

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

S. Sukhov and A. Dogariu, “Negative nonconservative forces: optical “tractor beams” for arbitrary objects,” Phys. Rev. Lett. 107(20), 203602 (2011).
[Crossref] [PubMed]

Tang, Z.

G. Li and Z. Tang, “Noble metal nanoparticle@metal oxide core/yolk-shell nanostructures as catalysts: recent progress and perspective,” Nanoscale 6(8), 3995–4011 (2014).
[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]

Toussaint, K. C.

Wang, H.

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]

Wang, N.

Wang, P.

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]

Wang, Z. G.

X. Y. Duan and Z. G. Wang, “Fano resonance in the optical scattering force upon a high-index dielectric nanoparticles,” Phys. Rev. A (Coll. Park) 96(5), 053811 (2017).
[Crossref]

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Wu, D. J.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Wu, J.

Xiang, Z. X.

Xu, H.

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]

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002).
[Crossref] [PubMed]

Xu, H. T.

Xu, Q.

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

Xu, Y.

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Yang, H.

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]

Yang, Y.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

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]

Yao, J.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Ye, Q.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

Yu, H. Q.

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Yu, Y. F.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[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(1), 1527 (2013).
[Crossref] [PubMed]

Yuen, C. H.

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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

Zenin, V. A.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

Zhang, J.

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[Crossref] [PubMed]

Zhang, S.

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]

Zhang, W.

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Zhang, Y.

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

Zhou, L.

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]

Zywietz, U.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

ACS Nano (2)

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]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

ACS Photonics (1)

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-assisted strong field enhancement in individual all-dielectric nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

Ann. Phys. (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 335(11), 57–136 (1909).
[Crossref]

Appl. Opt. (1)

IEEE Trans. NanoTechnol. (1)

M. Alam and Y. Massoud, “A closed-form analytical model for single nanoshells,” IEEE Trans. NanoTechnol. 5(3), 265–272 (2006).
[Crossref]

J. Am. Chem. Soc. (1)

H. L. Jiang, T. Akita, T. Ishida, M. Haruta, and Q. Xu, “Synergistic catalysis of Au@Ag core-shell nanoparticles stabilized on metal-organic framework,” J. Am. Chem. Soc. 133(5), 1304–1306 (2011).
[Crossref] [PubMed]

J. Phys. Chem. C (1)

D. J. Wu, H. Q. Yu, J. Yao, Q. Y. Ma, Y. Cheng, and X. J. Liu, “Efficient magnetic resonance amplification and near-field enhancement from gain-assisted silicon nanospheres and nanoshells,” J. Phys. Chem. C 120(24), 13227–13233 (2016).
[Crossref]

Laser Photonics Rev. (1)

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

Nano Lett. (2)

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref] [PubMed]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Nanoscale (1)

G. Li and Z. Tang, “Noble metal nanoparticle@metal oxide core/yolk-shell nanostructures as catalysts: recent progress and perspective,” Nanoscale 6(8), 3995–4011 (2014).
[Crossref] [PubMed]

Nat. Commun. (3)

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5(1), 3402 (2014).
[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(1), 1527 (2013).
[Crossref] [PubMed]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref] [PubMed]

Nat. Photonics (3)

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

V. Kajorndejnukul, W. Ding, S. Sukhov, C. W. Qiu, and A. Dogariu, “Linear momentum increase and negative optical forces at dielectric interface,” Nat. Photonics 7(10), 787–790 (2013).
[Crossref]

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Chem. Chem. Phys. (1)

D. Schebarchov, B. Auguié, and E. C. Le Ru, “Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells,” Phys. Chem. Chem. Phys. 15(12), 4233–4242 (2013).
[Crossref] [PubMed]

Phys. Rev. A (Coll. Park) (3)

D. Gao, R. Shi, Y. Huang, and L. Gao, “Fano-enhanced pulling and pushing optical force on active plasmonic nanoparticles,” Phys. Rev. A (Coll. Park) 96(4), 043826 (2017).
[Crossref]

H. Chen, Q. Ye, Y. Zhang, L. Shi, S. Liu, J. Jian, and Z. Lin, “Reconfigurable lateral optical force achieved by selectively exciting plasmonic dark modes near Fano resonance,” Phys. Rev. A (Coll. Park) 96(2), 023809 (2017).
[Crossref]

X. Y. Duan and Z. G. Wang, “Fano resonance in the optical scattering force upon a high-index dielectric nanoparticles,” Phys. Rev. A (Coll. Park) 96(5), 053811 (2017).
[Crossref]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (8)

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal magnetic dipole scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[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).
[Crossref] [PubMed]

H. Xu and M. Käll, “Surface-plasmon-enhanced optical forces in silver nanoaggregates,” Phys. Rev. Lett. 89(24), 246802 (2002).
[Crossref] [PubMed]

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]

S. Sukhov and A. Dogariu, “Negative nonconservative forces: optical “tractor beams” for arbitrary objects,” Phys. Rev. Lett. 107(20), 203602 (2011).
[Crossref] [PubMed]

A. Novitsky, C. W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109(2), 023902 (2012).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: a class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

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

Sci. Rep. (2)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2(1), 492 (2012).
[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. Rep. 7(1), 18042 (2017).
[Crossref] [PubMed]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1983).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Schematic showing the Au core-Si shell nanoparticles excited with a linearly polarized plane EM wave. The linearly polarized plane wave illuminates on the Au core-Si shell nanoparticles along with x direction and the polarization direction is along with z direction, as shown in the inset.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 Evolution of the total scattering efficiency spectra (the first column) and the contributions of ED mode (the second column), MD mode (the third column), EQ mode (the fourth column), and MQ mode (the fifth column) to the total scattering efficiency with the increase of the radii of the core for the Au core-Si shell nanoparticle (the upper panel), the Si nanoparticle (the middle panel) and the Au nanoparticle (the lower panel).

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Four typical interferences between MD resonant mode and ED mode with the increase of Rcore: (a) partly interference (Rcore = 0 nm), (b) totally interference (Rcore = 42 nm), (c) pure MD mode (Rcore = 67 nm), and (d) pure ED mode (Rcore = 115 nm).

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Total radiation forces Ftotal (the first column), incident forces Fel (the second column) and Fml (the third column), and the recoil forces Felml (the fourth column), Felel+1 (the fifth column), and Fmlml+1 (the sixth column) as a function of the wavelength and the radii of the core for the Au core-Si shell nanoparticle (the upper panel), the Si nanoparticle (the middle panel) and the Au nanoparticle (the lower panel).

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5 Ftotal and the components Fel, Fml, Felml, Felel+1, and Fmlml+1 as a function of the wavelength for Rcore = 0 nm (a), Rcore = 42 nm (b), Rcore = 67 nm (c), and Rcore = 115 nm (d).

Download Full Size | PPT Slide | PDF

Fig. 6
Fig. 6 Evolutions of Ftotal and the components Fel, Fml, Felml, Felel+1, and Fmlml+1 at MD resonant mode (a) and ED resonant mode (b) when Rcore increases from 0 nm to 115 nm.

Download Full Size | PPT Slide | PDF

Fig. 7
Fig. 7 Far-field scattering pattern for Type I (a), Type II (b), Type III (c), and Type IV (d) in E plane and H plane. All far-field scattering intensities are normalized with the maximum far-field scattering intensity of Type II. The incident direction of the beam is the same as the inset in Fig. 1.

Download Full Size | PPT Slide | PDF

Equations (15)

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

a l = ψ l ( y ) [ ψ ′ l ( m 2 y ) − A l χ ′ l ( m 2 y ) ] − m 2 ψ ′ l ( y ) [ ψ l ( m 2 y ) − A l χ l ( m 2 y ) ] ξ l ( y ) [ ψ ′ l ( m 2 y ) − A l χ ′ l ( m 2 y ) ] − m 2 ξ ′ l ( y ) [ ψ l ( m 2 y ) − A l χ l ( m 2 y ) ] ,
b l = m 2 ψ l ( y ) [ ψ ′ l ( m 2 y ) − B l χ ′ l ( m 2 y ) ] − ψ ′ l ( y ) [ ψ l ( m 2 y ) − B l χ l ( m 2 y ) ] m 2 ξ l ( y ) [ ψ ′ l ( m 2 y ) − B l χ ′ l ( m 2 y ) ] − ξ ′ l ( y ) [ ψ l ( m 2 y ) − B l χ l ( m 2 y ) ] ,
A l = m 2 ψ l ( m 2 x ) ψ ′ l ( m 1 x ) − m 1 ψ ′ l ( m 2 x ) ψ l ( m 1 x ) m 2 χ l ( m 2 x ) ψ ′ l ( m 1 x ) − m 1 χ ′ l ( m 2 x ) ψ l ( m 1 x ) ,
B l = m 2 ψ l ( m 1 x ) ψ ′ l ( m 2 x ) − m 1 ψ ′ l ( m 1 x ) ψ l ( m 2 x ) m 2 χ ′ l ( m 2 x ) ψ l ( m 1 x ) − m 1 χ l ( m 2 x ) ψ ′ l ( m 1 x ) ,
ψ l ( x ) = x j l ( x ) ,   χ l ( x ) = x y l ( x ) ,   ξ l ( x ) = x h l ( 1 ) ( x ) = ψ l ( x ) + i χ l ( x ) .
Q s c a = 2 y 2 ∑ l = 1 ∞ ( 2 l + 1 ) ( | a l | 2 + | b l | 2 ) ,
Q e x t = 2 y 2 ∑ l = 1 ∞ ( 2 l + 1 ) [ Re ( a l ) + Re ( a l ) ] ,
Q a b s = Q e x t − Q s c a .
F t o t a l = n P 0 ( Q e x t − Q s c a 〈 cos θ 〉 ) / c ,
Q s c a 〈 cos θ 〉 = 4 y 2 ∑ l = 1 ∞ [ l ( l + 2 ) l + 1 Re ( a l a l + 1 ∗ + b l b l + 1 ∗ ) + 2 l + 1 l ( l + 1 ) Re ( a l b l ∗ ) ] ,
F t o t a l = n P 0 { 2 y 2 ∑ l = 1 ∞ ( 2 l + 1 ) [ Re ( a l ) + Re ( b l ) ]         − 4 y 2 ∑ l = 1 ∞ [ l ( l + 2 ) l + 1 Re ( a l a l + 1 ∗ + b l b l + 1 ∗ ) + 2 l + 1 l ( l + 1 ) Re ( a l b l ∗ ) ] } / c .
F e l = 2 n P 0 c y 2 ∑ l = 1 ∞ ( 2 l + 1 ) Re ( a l ) ,   F m l = 2 n P 0 c y 2 ∑ l = 1 ∞ ( 2 l + 1 ) Re ( b l ) ,
F e l e l + 1 = − 4 n P 0 c y 2 ∑ l = 1 ∞ l ( l + 2 ) l + 1 Re ( a l a l + 1 ∗ ) ,
F m l m l + 1 = − 4 n P 0 c y 2 ∑ l = 1 ∞ l ( l + 2 ) l + 1 Re ( b l b l + 1 ∗ ) ,
F e l m l = − 4 n P 0 c y 2 ∑ l = 1 ∞ 2 l + 1 l ( l + 1 ) Re ( a l b l ∗ ) .

Metrics