Abstract

Artificial magnetism enables various transformative optical phenomena, including negative refraction, Fano resonances, and unconventional nanoantennas, beamshapers, polarization transformers and perfect absorbers, and enriches the collection of electromagnetic field control mechanisms at optical frequencies. We demonstrate that it is possible to excite a magnetic dipole super-resonance at optical frequencies by coating a silicon nanoparticle with a shell impregnated with active material. The resulting response is several orders of magnitude stronger than that generated by bare silicon nanoparticles and is comparable to electric dipole super-resonances excited in spaser-based nanolasers. Furthermore, this configuration enables an exceptional control over the optical forces exerted on the nanoparticle. It expedites huge pushing or pulling actions, as well as a total suppression of the force in both far-field and near-field scenarios. These effects empower advanced paradigms in electromagnetic manipulation and microscopy.

© 2014 Optical Society of America

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  1. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).
  2. R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl Acad. Sci. USA 106, 1693–1698 (2009).
    [CrossRef] [PubMed]
  3. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
    [CrossRef]
  4. N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
    [CrossRef]
  5. H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
    [CrossRef] [PubMed]
  6. A. Alù, N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
    [CrossRef] [PubMed]
  7. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  8. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  10. M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. A 73, 765–767 (1983).
    [CrossRef]
  11. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
    [CrossRef]
  12. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13, 1806–1809 (2013).
    [PubMed]
  13. S. D. Campbell, R. W. Ziolkowski, “Simultaneous excitation of electric and magnetic dipole modes in a resonant core-shell particle at infrared frequencies to achieve minimal backscattering,” J. Sel. Top. Quantum Electron. 19, 4700209 (2013).
    [CrossRef]
  14. F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
    [CrossRef]
  15. S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 3927–3934 (2011).
    [CrossRef] [PubMed]
  16. C. Pfeiffer, A. Grbic, “Metamaterial Huygens surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 7401–7405 (2013).
    [CrossRef]
  17. T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
    [CrossRef]
  18. Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
    [CrossRef]
  19. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
    [CrossRef] [PubMed]
  20. H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561 (1980).
    [CrossRef]
  21. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).
  22. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
    [CrossRef] [PubMed]
  23. J. A. Gordon, R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15, 2622–2653 (2007).
    [CrossRef] [PubMed]
  24. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).
  25. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
    [CrossRef]
  26. S. Arslanagić, R. W. Ziolkowski, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipoleresonance and transparency effects” J. Opt. 12, 024014 (2010).
    [CrossRef]
  27. P. C. Chaumet, A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17, 2224–2234 (2009).
    [CrossRef] [PubMed]
  28. M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
    [CrossRef]
  29. M. Nieto-Vesperinas, R. Gómez-Medina, J. J. Sáenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A 28, 54–60 (2011).
    [CrossRef]
  30. R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
    [CrossRef]
  31. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
    [CrossRef]
  32. N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
    [CrossRef] [PubMed]
  33. N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
    [CrossRef]
  34. M. Wegener, J. L. García-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
    [CrossRef] [PubMed]
  35. Sigma-Aldrich Corporation, url: http://www.sigmaaldrich.com/materials-science/nanomaterials/lumidots.html (2013).
  36. S. D. Campbell, R. W. Ziolkowski, “The performance of active coated nanoparticles based on quantum-dot gain media,” Adv. OptoElectronics 36, 8786–8791 (2012).
  37. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).
  38. P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
    [CrossRef]
  39. I. Moreels, D. Kruschke, P. Glas, J. W. Tomm, “The dielectric function of PbS quantum dots in a glass matrix,” Opt. Mater. Express 2, 496–500 (2012).
    [CrossRef]
  40. T. Kudo, H. Ishihara, “Proposed nonlinear resonance laser technique for manipulating nanoparticles,” Phys. Rev. Lett. 109, 7402–7406 (2012).
    [CrossRef]
  41. A. Mizrahi, Y. Fainman, “Negative radiation pressure on gain medium structures,” Opt. Lett. 35, 3405–3407 (2010).
    [CrossRef] [PubMed]
  42. I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
    [CrossRef]
  43. S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
    [CrossRef]
  44. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).
  45. I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
    [CrossRef]
  46. A. Alù, N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and or double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
    [CrossRef]

2013 (9)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

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

S. D. Campbell, R. W. Ziolkowski, “Simultaneous excitation of electric and magnetic dipole modes in a resonant core-shell particle at infrared frequencies to achieve minimal backscattering,” J. Sel. Top. Quantum Electron. 19, 4700209 (2013).
[CrossRef]

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

C. Pfeiffer, A. Grbic, “Metamaterial Huygens surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 7401–7405 (2013).
[CrossRef]

T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[CrossRef]

Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

2012 (5)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

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

S. D. Campbell, R. W. Ziolkowski, “The performance of active coated nanoparticles based on quantum-dot gain media,” Adv. OptoElectronics 36, 8786–8791 (2012).

I. Moreels, D. Kruschke, P. Glas, J. W. Tomm, “The dielectric function of PbS quantum dots in a glass matrix,” Opt. Mater. Express 2, 496–500 (2012).
[CrossRef]

T. Kudo, H. Ishihara, “Proposed nonlinear resonance laser technique for manipulating nanoparticles,” Phys. Rev. Lett. 109, 7402–7406 (2012).
[CrossRef]

2011 (5)

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

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

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
[CrossRef] [PubMed]

S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 3927–3934 (2011).
[CrossRef] [PubMed]

2010 (7)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

S. Arslanagić, R. W. Ziolkowski, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipoleresonance and transparency effects” J. Opt. 12, 024014 (2010).
[CrossRef]

A. Mizrahi, Y. Fainman, “Negative radiation pressure on gain medium structures,” Opt. Lett. 35, 3405–3407 (2010).
[CrossRef] [PubMed]

P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
[CrossRef]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
[CrossRef]

2009 (4)

P. C. Chaumet, A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17, 2224–2234 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl Acad. Sci. USA 106, 1693–1698 (2009).
[CrossRef] [PubMed]

A. Alù, N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

2008 (3)

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

M. Wegener, J. L. García-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (2)

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Alù, N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and or double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1983 (1)

M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. A 73, 765–767 (1983).
[CrossRef]

1980 (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561 (1980).
[CrossRef]

Aizpurua, J.

Alù, A.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

A. Alù, N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

A. Alù, N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and or double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

Arslanagic, S.

S. Arslanagić, R. W. Ziolkowski, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipoleresonance and transparency effects” J. Opt. 12, 024014 (2010).
[CrossRef]

Asadchy, V. S.

Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Bilotti, F.

S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Boltasseva, A.

Bozhevolnyi, S. I.

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

Bratkovsky, A.

P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
[CrossRef]

Busch, K.

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

Cai, W.

Campbell, S. D.

S. D. Campbell, R. W. Ziolkowski, “Simultaneous excitation of electric and magnetic dipole modes in a resonant core-shell particle at infrared frequencies to achieve minimal backscattering,” J. Sel. Top. Quantum Electron. 19, 4700209 (2013).
[CrossRef]

S. D. Campbell, R. W. Ziolkowski, “The performance of active coated nanoparticles based on quantum-dot gain media,” Adv. OptoElectronics 36, 8786–8791 (2012).

Chantada, L.

Chaumet, P. C.

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

Chichkov, B. N.

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

Dionne, J. A.

S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 3927–3934 (2011).
[CrossRef] [PubMed]

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

Ederra, I.

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

Engheta, N.

A. Alù, N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

A. Alù, N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and or double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

Eriksen, R. L.

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

Evlyukhin, A. B.

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

Fainman, Y.

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

Froufe-Pérez, L. S.

Fu, L.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Fu, Y. H.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

García-Cámara, B.

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

García-Etxarri, A.

García-Pomar, J. L.

Gibbs, H. M.

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

Giessen, H.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Giles, C. L.

M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. A 73, 765–767 (1983).
[CrossRef]

Glas, P.

Gómez-Medina, R.

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
[CrossRef] [PubMed]

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

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
[CrossRef]

González, F.

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

Gonzalo, R.

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

Gordon, J. A.

Grbic, A.

C. Pfeiffer, A. Grbic, “Metamaterial Huygens surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 7401–7405 (2013).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).

Hartsfield, T.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Hendrickson, J.

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Holmström, P.

P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Ishihara, H.

T. Kudo, H. Ishihara, “Proposed nonlinear resonance laser technique for manipulating nanoparticles,” Phys. Rev. Lett. 109, 7402–7406 (2012).
[CrossRef]

Jain, M.

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

Kaiser, S.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Karilainen, A. O.

T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[CrossRef]

Kerker, M.

M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. A 73, 765–767 (1983).
[CrossRef]

Khitrova, G.

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

Konig, M.

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

Kruschke, D.

Kudo, T.

T. Kudo, H. Ishihara, “Proposed nonlinear resonance laser technique for manipulating nanoparticles,” Phys. Rev. Lett. 109, 7402–7406 (2012).
[CrossRef]

Kuznetsov, A. I.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Lapin, Z.

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

Le, K. Q.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

Li, H. H.

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561 (1980).
[CrossRef]

Li, X.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Liberal, I.

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Linden, S.

Liu, N.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Liu, X.-X.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

López, C.

Lukyanchuk, B.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

Meinzer, N.

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl Acad. Sci. USA 106, 1693–1698 (2009).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

Mizrahi, A.

Monticone, F.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Moreels, I.

Moreno, F.

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

Niemi, T.

T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[CrossRef]

Nieto-Vesperinas, M.

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

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

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
[CrossRef]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Novikov, S. M.

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

Novotny, L.

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

Olitsky, J. D.

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Person, S.

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

Pfeiffer, C.

C. Pfeiffer, A. Grbic, “Metamaterial Huygens surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 7401–7405 (2013).
[CrossRef]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

Ra’di, Y.

Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[CrossRef]

Rahmani, A.

Reinhardt, C.

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

Ruther, M.

Sáenz, J. J.

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

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

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

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
[CrossRef]

Scheffold, F.

Schurig, D.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Schweizer, H.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Shafiei, F.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

Sheikholeslami, S. N.

S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 3927–3934 (2011).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Suárez-Lacalle, I.

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Thylén, L.

P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
[CrossRef]

Tomm, J. W.

Tretyakov, S. A.

T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[CrossRef]

Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[CrossRef]

Tricarico, S.

S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
[CrossRef]

Vegni, L.

S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
[CrossRef]

Wang, D. S.

M. Kerker, D. S. Wang, C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. A 73, 765–767 (1983).
[CrossRef]

Wegener, M.

Wicks, G.

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

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

Yu, Y. F.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

Zhang, J.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

Ziolkowski, R. W.

S. D. Campbell, R. W. Ziolkowski, “Simultaneous excitation of electric and magnetic dipole modes in a resonant core-shell particle at infrared frequencies to achieve minimal backscattering,” J. Sel. Top. Quantum Electron. 19, 4700209 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

S. D. Campbell, R. W. Ziolkowski, “The performance of active coated nanoparticles based on quantum-dot gain media,” Adv. OptoElectronics 36, 8786–8791 (2012).

S. Arslanagić, R. W. Ziolkowski, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipoleresonance and transparency effects” J. Opt. 12, 024014 (2010).
[CrossRef]

J. A. Gordon, R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15, 2622–2653 (2007).
[CrossRef] [PubMed]

Zywietz, U.

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

Adv. Mater. (1)

N. Liu, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, “Plasmonic building blocks for magnetic molecules in three-dimensional optical metamaterials,” Adv. Mater. 20, 3859–3865 (2008).
[CrossRef]

Adv. OptoElectronics (1)

S. D. Campbell, R. W. Ziolkowski, “The performance of active coated nanoparticles based on quantum-dot gain media,” Adv. OptoElectronics 36, 8786–8791 (2012).

Appl. Phys. Lett. (1)

N. Meinzer, M. Konig, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99, 111104 (2011).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

T. Niemi, A. O. Karilainen, S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[CrossRef]

Y. Ra’di, V. S. Asadchy, S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[CrossRef]

J. Appl. Phys. (2)

A. Alù, N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and or double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

P. Holmström, L. Thylén, A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107, 4307–4313 (2010).
[CrossRef]

J. Nanophoton. (1)

R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5, 3512 (2011).
[CrossRef]

J. Opt. (1)

S. Arslanagić, R. W. Ziolkowski, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipoleresonance and transparency effects” J. Opt. 12, 024014 (2010).
[CrossRef]

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

J. Phys. Chem. Ref. Data (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9, 561 (1980).
[CrossRef]

J. Sel. Top. Quantum Electron. (1)

S. D. Campbell, R. W. Ziolkowski, “Simultaneous excitation of electric and magnetic dipole modes in a resonant core-shell particle at infrared frequencies to achieve minimal backscattering,” J. Sel. Top. Quantum Electron. 19, 4700209 (2013).
[CrossRef]

Nano Lett. (3)

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

S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11, 3927–3934 (2011).
[CrossRef] [PubMed]

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

Nat. Photon. (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[CrossRef]

Nature (London) (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) 466, 735–738 (2010).
[CrossRef]

Nature Commun. (1)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[CrossRef]

Nature Nanotech. (1)

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nature Nanotech. 8, 95–99 (2013).
[CrossRef]

Nature Photon. (2)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser”. Nature Photon. 460, 1110–1113 (2009).

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nature Photon. 2, 351–354 (2008).
[CrossRef]

Nature Sci. Reports (1)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, B. Lukyanchuk, “Magnetic light,” Nature Sci. Reports 2, 492 (2012).

Opt. Express (8)

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 428–443 (2010).
[CrossRef]

H.-K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef] [PubMed]

J. A. Gordon, R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15, 2622–2653 (2007).
[CrossRef] [PubMed]

M. Wegener, J. L. García-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
[CrossRef] [PubMed]

P. C. Chaumet, A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17, 2224–2234 (2009).
[CrossRef] [PubMed]

A. Alù, N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express 17, 5723–5730 (2009).
[CrossRef] [PubMed]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
[CrossRef] [PubMed]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. A (2)

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Electromagnetic force density in electrically and magnetically polarizable media,” Phys. Rev. A 88, 053808 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 3807–3816 (2013).
[CrossRef]

Phys. Rev. B (1)

S. Tricarico, F. Bilotti, L. Vegni, “Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B 82, 5109–5117 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

T. Kudo, H. Ishihara, “Proposed nonlinear resonance laser technique for manipulating nanoparticles,” Phys. Rev. Lett. 109, 7402–7406 (2012).
[CrossRef]

C. Pfeiffer, A. Grbic, “Metamaterial Huygens surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 7401–7405 (2013).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Proc. Natl Acad. Sci. USA (1)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl Acad. Sci. USA 106, 1693–1698 (2009).
[CrossRef] [PubMed]

Science (2)

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Other (4)

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).

Sigma-Aldrich Corporation, url: http://www.sigmaaldrich.com/materials-science/nanomaterials/lumidots.html (2013).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

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Figures (3)

Fig. 1
Fig. 1

(a) Scattering efficiency spectrum Qscat, and the contributions to it from the electric and magnetic dipoles, Q scat e and Q scat m, respectively, for the passive case, κ = 0. Inset: Sketch of the coated Si particle illuminated by a plane-wave, and the resulting dipolar excitations. (b) Qscat at the magnetic dipole resonance as a function of the imaginary part of the index of refraction, κ, as well as the mechanical force exerted on the nanoparticle, normalized to the incident electromagnetic power projected onto its physical area, F norm = F / ( S R π a 2 2 ). Insets: Top-right: Zero-force region. Bottom-right: Geometry.

Fig. 2
Fig. 2

First column: Scattering efficiency spectrum Qscat, and the contributions to it from the electric and magnetic dipoles, Q scat e and Q scat m. Second column: Scattering directivity patterns, Dscat, in the XZ- and YZ-planes. Dscat = 4πr2 ( · Sscat/Pscat), where S scat = 1 2 Re [ E scat × ( H scat ) * ] represents the time-averaged Poynting vector field associated with the scattered field, and P scat = S S scat r ^ d S is the time-averaged total scattered power. Third column: Colormap and quiver (arrow) plots of the electric field at the maximum of Qscat. Each row corresponds to a different gain value (a) κ = 0.1, (d) κ = 0.2, (c) κ = 0.275, and (d) κ = 0.365.

Fig. 3
Fig. 3

(a) Sketch of the geometry: Coated Si particle illuminated by two aligned electric and magnetic dipoles with balanced magnitudes Iel = Iml/η0 = 10mA · nm. Scattering directivity patterns in the XZ and XY-planes when the nanoparticle is located on the Z-axis. (b) Mechanical force F and (c) scattered power Pscat spectra (normalized to the power radiated by the source in free-space P0) when the nanoparticle is positioned on the −Z-axis at the distances d = 2a2, d = 4a2 and d = 20a2 from the source location. Colormaps of the (d) force magnitude and (e) scattered power (in dB scale, normalized, respectively, to 1 pN and P0) as functions of the particle location on the XZ-plane at λ = 708nm. The grey areas indicate those locations which are not physically accessible to the nanoparticle.

Equations (59)

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F = 1 2 Re { α e e E ( ) E * + α m m H ( ) H * η 0 k 0 4 6 π μ 0 [ α e e E × ( α m m H ) * ] }
F = 2 η 0 2 k 0 5 | I e l 4 π ( k 0 r ) | 2 { r ^ 2 k 0 3 3 η 0 | α e e | 2 sin θ ϕ ^ α e e ε 0 ω [ 2 ( k 0 r ) 2 + 3 ( k 0 r ) 4 ] cos θ } sin θ
α e e = j 6 π ε 0 k 0 3 b 1 T M , α m m = j 6 π μ 0 k 0 3 b 1 T E
b 1 T M = η s J ^ 1 ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η 0 J 1 ^ ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η 0 H ^ 1 ( 2 ) ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η s H ^ 1 ( 2 ) ( k 0 a 2 ) [ J 1 ^ ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ]
d 1 T M = η c J 1 ^ ( k c a 1 ) J ^ 1 ( k s a 1 ) η s J ^ 1 ( k c a 1 ) J 1 ^ ( k s a 1 ) η s J ^ 1 ( k c a 1 ) H ^ 1 ( 2 ) ( k s a 1 ) η c J n ^ ( k c a 1 ) H ^ 1 ( 2 ) ( k s a 1 )
b 1 T E = η s J ^ 1 ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η 0 J ^ 1 ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η 0 H ^ 1 ( 2 ) ( k 0 a 2 ) [ J 1 ^ ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ] η s H ^ 1 ( 2 ) ( k 0 a 2 ) [ J ^ 1 ( k s a 2 ) + d 1 T M H ^ 1 ( 2 ) ( k s a 2 ) ]
d 1 T E = η c J ^ 1 ( k c a 1 ) J 1 ^ ( k s a 1 ) η s J ^ 1 ( k c a 1 ) J ^ 1 ( k s a 1 ) η s J ^ 1 ( k c a 1 ) H ^ 1 ( 2 ) ( k s a 1 ) η c J ^ n ( k c a 1 ) H ^ 1 ( 2 ) ( k s a 1 )
E r e = η 0 k 0 2 4 π I e l 2 cos θ [ 1 ( k 0 r ) 2 + j ( k 0 r ) 3 ] e j k 0 r
E θ e = η 0 k 0 2 4 π I e l sin θ [ j k 0 r + 1 ( k 0 r ) 2 + j ( k 0 r ) 3 ] e j k 0 r
H ϕ e = k 0 2 4 π I e l sin θ [ j k 0 r + 1 ( k 0 r ) 2 ] e j k 0 r
E m = η 0 H e
H m = E e η 0
E = E e + E m = E e + η 0 H e
H = H e + H m = H e E e η 0
| E | 2 = | E e | 2 + | E m | 2 = | E e | 2 + η 0 2 | H e | 2
| H | 2 = | H e | 2 + | H m | 2 = | H e | 2 + | E e | 2 η 0 2
| E | 2 = η 0 2 | H | 2
P reac = ω 2 V ( μ 0 | H | 2 ε 0 | E | 2 ) d V = 0
P reac = lim r 0 S S I n ^ d S
S = S e + S m + S cross
S R = S R e + S R m + S R cross
S I = S I e + S I m + S I cross
S R = 2 S R e
P 0 = 2 P 0 e = η 0 k 0 2 6 π | I e l | 2
S I = S I cross = 2 ω c L S E e
L S E = ε 0 4 j ω ( E ) * × E
L S H = μ 0 4 j ω ( H ) * × H
L S E = L S E e + L S E m + L S E cross
L S H = L S H e + L S H m + L S H cross
L S E e = L S M m
L S E cross = L S M cross = S I e ω c
F = F e + F m + F e m
F e = 1 2 Re { α e e E ( ) E * } = α e e 4 | E | 2 + α e e [ η 0 k 0 S R ω ε 0 × L S E ]
F m = 1 2 Re { α m m H ( ) H * } = α m m 4 | H | 2 + α m m [ k 0 η 0 S R ω μ 0 × L S H ]
F e m = η 0 k 0 4 12 π μ 0 Re { p × m * } = η 0 k 0 4 6 π μ 0 { Re [ α e e α m m * ] S R Im [ α e e α m m * ] S I }
F = F grad + F rp + F curl + F int
F grad = 1 4 ( α e e | E | 2 + α m m | H | 2 )
F rp = η 0 k 0 ( α e e + α m m η 0 2 k 0 3 6 π μ 0 Re [ α e e α m m * ] ) S R
F curl = ω [ α e e ε 0 × L S E + α m m μ 0 × L S H ]
F int = η 0 k 0 4 6 π μ 0 Im [ α e e α m m * ] S I
F grad = 1 4 ( α e e + α m m η 0 2 ) | E | 2
F rp = η 0 k 0 ( α e e + α m m η 0 2 k 0 3 6 π μ 0 Re [ α e e α m m * ] ) S R
F curl = ω ε 0 [ ( α e e + α m m η 0 2 ) × L S E e + ( α e e α m m η 0 2 ) × S I e ω c ]
F int = 2 ω c η 0 k 0 4 6 π μ 0 Im [ α e e α m m * ] L S E e
r ^ F grad = C aux ( α e e + α m m η 0 2 ) [ sin 2 θ ( k 0 r ) 3 + 4 cos 2 θ ( k 0 r ) 5 + 3 2 cos 2 θ + sin 2 θ ( k 0 r ) 7 ]
θ ^ F grad = C aux ( α e e + α m m η 0 2 ) [ 1 ( k 0 r ) 3 2 ( k 0 r ) 5 1 ( k 0 r ) 7 ] sin θ cos θ
ϕ ^ F grad = 0
r ^ F rp = C aux 2 ( α e e + α m m η 0 2 k 0 3 6 π μ 0 Re [ α e e α m m * ] ) sin 2 θ ( k 0 r ) 2
θ ^ F rp = 0
ϕ ^ F rp = 0
r ^ F curl = C aux ( α e e + α m m η 0 2 ) 2 cos 2 θ sin 2 θ ( k 0 r ) 4
θ ^ F curl = C aux 2 ( α e e + α m m η 0 2 ) sin θ cos θ ( k 0 r ) 4
ϕ ^ F curl = C aux ( α e e α m m η 0 2 ) { 2 ( k 0 r ) 4 + 3 ( k 0 r ) 6 } sin θ cos θ
r ^ F int = 0
ϕ ^ F int = C aux 2 k 0 3 6 π μ 0 Im [ α e e α m m * ] sin θ cos θ ( k 0 r ) 3
θ ^ F int = 0
C aux = k 0 | η 0 k 0 2 4 π I e l | 2
α e e = α m m η 0 2
F = 2 k 0 4 3 | α e e | 2 S R + 2 α e e × S I e ω c = 2 η 0 2 k 0 5 | I e l 4 π ( k 0 r ) | 2 { r ^ 2 k 0 3 3 η 0 | α e e | 2 sin θ ϕ ^ α e e ε 0 ω [ 2 ( k 0 r ) 2 + 3 ( k 0 r ) 4 ] cos θ } sin θ

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