Abstract

A theoretical approach, based on the discrete dipole approximation, for multipole analysis of light scattering by arbitrary-shaped nanoparticles located near or on a plane surface is presented. The obtained equations include the first multipoles up to the magnetic quadrupole and electric octupole moments. It is discussed how the suggested approach can be applied to the problem of multipole scattering of surface plasmon polaritons. As an example, the theoretical framework is used for investigation of light scattering by cylindrical Si nanoparticles located on different dielectric substrates, manifesting resonant interaction of these particles with light.

© 2013 Optical Society of America

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  1. E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004).
    [CrossRef]
  2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  4. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance based dielectric metamaterial,” Mater. Today 12(12), 60–69 (2009).
    [CrossRef]
  5. N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
    [CrossRef]
  6. V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
    [CrossRef]
  7. A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20, 20599–20604 (2012).
    [CrossRef]
  8. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
    [CrossRef]
  9. B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012).
    [CrossRef]
  10. 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, 3749–3755 (2012).
    [CrossRef]
  11. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2012).
    [CrossRef]
  12. J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
    [CrossRef]
  13. M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 11428–11443 (2010).
    [CrossRef]
  14. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  15. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
    [CrossRef]
  16. T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
    [CrossRef]
  17. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
    [CrossRef]
  18. E. H. Brandt, “Levitation in physics,” Science 243, 349–355 (1989).
    [CrossRef]
  19. L. Shi, E. Xifré-Pérez, F. J. Garca de Abajo, and F. Meseguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express 20, 11247–11255 (2012).
    [CrossRef]
  20. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
    [CrossRef]
  21. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
    [CrossRef]
  22. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
    [CrossRef]
  23. P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
    [CrossRef]
  24. M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
    [CrossRef]
  25. C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
    [CrossRef]
  26. C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
    [CrossRef]
  27. M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  28. C. Hafner and G. Klaus, “Application of the multiple multipole (MMP) method to electrodynamics,” Int. J. Comp. Math. Elect. Electron. Eng. 4, 137–144 (1985).
    [CrossRef]
  29. M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A 18, 854–861 (2001).
    [CrossRef]
  30. E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
    [CrossRef]
  31. V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
    [CrossRef]
  32. T. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
    [CrossRef]
  33. A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
    [CrossRef]
  34. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  35. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  36. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
    [CrossRef]
  37. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  38. T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
    [CrossRef]
  39. A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
    [CrossRef]
  40. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).
  41. R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Clarendon, 2005).
  42. P. Mazur and B. R. A. Nijboer, “On the statistical mechanics of matter in an lectromagnetic field. I,” Physica 19, 971–986 (1953).
    [CrossRef]
  43. A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
    [CrossRef]
  44. A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
    [CrossRef]
  45. L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
    [CrossRef]
  46. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
    [CrossRef]
  47. Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
    [CrossRef]
  48. E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).
  49. G. Gantzounis, “Plasmon modes of axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 11321560–21565 (2009).
    [CrossRef]
  50. M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
    [CrossRef]
  51. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
    [CrossRef]

2012 (9)

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, 3749–3755 (2012).
[CrossRef]

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

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

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

L. Shi, E. Xifré-Pérez, F. J. Garca de Abajo, and F. Meseguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express 20, 11247–11255 (2012).
[CrossRef]

B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012).
[CrossRef]

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

2011 (8)

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
[CrossRef]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[CrossRef]

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

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

2010 (6)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

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

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

2009 (3)

G. Gantzounis, “Plasmon modes of axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 11321560–21565 (2009).
[CrossRef]

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

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

2008 (1)

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

2007 (3)

T. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

2006 (1)

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
[CrossRef]

2004 (2)

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2001 (1)

2000 (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

1997 (2)

Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
[CrossRef]

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

1996 (1)

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

1994 (1)

1989 (1)

E. H. Brandt, “Levitation in physics,” Science 243, 349–355 (1989).
[CrossRef]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1985 (1)

C. Hafner and G. Klaus, “Application of the multiple multipole (MMP) method to electrodynamics,” Int. J. Comp. Math. Elect. Electron. Eng. 4, 137–144 (1985).
[CrossRef]

1970 (1)

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

1953 (1)

P. Mazur and B. R. A. Nijboer, “On the statistical mechanics of matter in an lectromagnetic field. I,” Physica 19, 971–986 (1953).
[CrossRef]

Abb, M.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

Aizpurua, J.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

Albella, P.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

Andrews, D. L.

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Ashkin, A.

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

Bao, K.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Belov, P. A.

Biagioni, P.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

Bohren, C. F.

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

Bonod, N.

Bozhevolnyi, S. I.

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, 3749–3755 (2012).
[CrossRef]

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

Brandt, E. H.

E. H. Brandt, “Levitation in physics,” Science 243, 349–355 (1989).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Brucoli, G.

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Chan, C. T.

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

Chang, W.-S.

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

Chantada, L.

Chen, J.

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

Chichkov, B. N.

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, 3749–3755 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
[CrossRef]

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

Chipouline, A.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Cižmár, T.

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Dávila Romero, L. C.

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

de Groot, C. H.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

de Lange, O. L.

R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Clarendon, 2005).

Dholakia, K.

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Draine, B. T.

B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Eremin, Y.

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
[CrossRef]

Eremina, E.

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
[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, 3749–3755 (2012).
[CrossRef]

Etrich, C.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Evlyukhin, A. B.

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, 3749–3755 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
[CrossRef]

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

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Fendler, J. H.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

Fernández-Domnguez, A. I.

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Flatau, P. J.

Fu, Y. H.

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

Funston, A. M.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Gantzounis, G.

G. Gantzounis, “Plasmon modes of axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 11321560–21565 (2009).
[CrossRef]

Garca de Abajo, F. J.

L. Shi, E. Xifré-Pérez, F. J. Garca de Abajo, and F. Meseguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express 20, 11247–11255 (2012).
[CrossRef]

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Garca-Vidal, F. J.

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Giannini, V.

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Gómez-Medina, R.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Gu, B.

Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
[CrossRef]

Hafner, C.

C. Hafner and G. Klaus, “Application of the multiple multipole (MMP) method to electrodynamics,” Int. J. Comp. Math. Elect. Electron. Eng. 4, 137–144 (1985).
[CrossRef]

Halas, N. J.

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

Hecht, B.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Heck, S. C.

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

Helgert, C.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Huang, J.-S.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

Huffman, D. R.

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

Hutter, E.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Kivshar, Y. S.

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

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Klaus, G.

C. Hafner and G. Klaus, “Application of the multiple multipole (MMP) method to electrodynamics,” Int. J. Comp. Math. Elect. Electron. Eng. 4, 137–144 (1985).
[CrossRef]

Knight, M. W.

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

Krasnok, A. E.

Kuznetsov, A. I.

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

Lal, S.

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

Lassiter, J. B.

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

Lederer, F.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

Li, Z.

Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
[CrossRef]

Lin, Z.

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

Link, S.

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

Lippens, D.

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

Liz-Marzán, L. M.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Luk’yanchuk, B.

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

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Luk’yanchuk, B. S.

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

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Maier, S. A.

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martin, O. J. F.

M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A 18, 854–861 (2001).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Martn-Moreno, L.

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Mazur, P.

P. Mazur and B. R. A. Nijboer, “On the statistical mechanics of matter in an lectromagnetic field. I,” Physica 19, 971–986 (1953).
[CrossRef]

Menzel, C.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

Meseguer, F.

Miroshnichenko, A. E.

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

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

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Mühlig, S.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

Mulvaney, P.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Muskens, O. L.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

Myroshnychenko, V.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Ng, J.

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

Nieto-Vesperinas, M.

Nijboer, B. R. A.

P. Mazur and B. R. A. Nijboer, “On the statistical mechanics of matter in an lectromagnetic field. I,” Physica 19, 971–986 (1953).
[CrossRef]

Nordlander, P.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

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, 3749–3755 (2012).
[CrossRef]

Novo, C.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Novotny, L.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Palik, E.

E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

Papas, C. H.

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

Pastoriza-Santos, I.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Paulus, M.

M. Paulus and O. J. F. Martin, “Light propagation and scattering in stratified media: a Green’s tensor approach,” J. Opt. Soc. Am. A 18, 854–861 (2001).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Pertsch, T.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Petschulat, J.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Pohl, D. W.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Polman, A.

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

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[CrossRef]

Raab, R. E.

R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Clarendon, 2005).

Reinhardt, C.

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[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, 3749–3755 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
[CrossRef]

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

Righini, M.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[CrossRef]

Rockstuhl, C.

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

Rodrguez-Fernández, J.

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Rolly, B.

Sáenz, J. J.

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Seidel, A.

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

Shi, L.

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

Søndergaard, T. T.

T. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

Spinelli, P.

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

Stout, B.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Verschuuren, M. A.

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

Wang, Y.

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Wriedt, T.

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
[CrossRef]

Wu, Y.

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

Xifré-Pérez, E.

Xu, H.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

Yang, G.

Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
[CrossRef]

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Zhang, F.

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

Zhang, J.

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

Zhang, S.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

Zhao, Q.

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

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Zhou, J.

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

Zywietz, U.

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, 3749–3755 (2012).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

Adv. Mater. (1)

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

ASC Nano (1)

M. Abb, Y. Wang, P. Albella, C. H. de Groot, J. Aizpurua, and O. L. Muskens, “Interference, coupling, and nonlinear control of high-order modes in single asymmetric nanoantennas,” ASC Nano 6, 6462–6470 (2012).
[CrossRef]

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Chem. Rev. (2)

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

V. Giannini, A. I. Fernández-Domnguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011).
[CrossRef]

Chem. Soc. Rev. (1)

V. Myroshnychenko, J. Rodrguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. Garca de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[CrossRef]

Int. J. Comp. Math. Elect. Electron. Eng. (1)

C. Hafner and G. Klaus, “Application of the multiple multipole (MMP) method to electrodynamics,” Int. J. Comp. Math. Elect. Electron. Eng. 4, 137–144 (1985).
[CrossRef]

J. Appl. Phys. (1)

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

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

J. Phys. B (1)

T. Čižmár, L. C. Dávila Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

J. Phys. Chem. C (1)

G. Gantzounis, “Plasmon modes of axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 11321560–21565 (2009).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Mater. Today (1)

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

Metamaterials (1)

C. Menzel, S. Mühlig, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[CrossRef]

Nano Lett. (3)

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, 3749–3755 (2012).
[CrossRef]

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188–2192 (2009).
[CrossRef]

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11, 1657–1663 (2011).
[CrossRef]

Nat. Commun. (1)

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

Nat. Mater. (2)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef]

Nat. Photonics (2)

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

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[CrossRef]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Opt. Commun. (1)

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524–529 (2006).
[CrossRef]

Opt. Express (4)

Phys. Rev. B (7)

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of metaatoms,” Phys. Rev. B 83, 245119 (2011).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

A. B. Evlyukhin, G. Brucoli, L. Martn-Moreno, S. I. Bozhevolnyi, and F. J. Garca-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Z. Li, B. Gu, and G. Yang, “Modified self-consistent approach applied in near-field optics for mesoscopic surface defects,” Phys. Rev. B 55, 10883–10894 (1997).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, “Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions,” Phys. Rev. B 85, 245411 (2012).
[CrossRef]

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

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
[CrossRef]

Phys. Rev. E (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

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

Phys. Status Solidi B (1)

T. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

Physica (1)

P. Mazur and B. R. A. Nijboer, “On the statistical mechanics of matter in an lectromagnetic field. I,” Physica 19, 971–986 (1953).
[CrossRef]

Rep. Prog. Phys. (1)

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Sci. Rep. (1)

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

Science (1)

E. H. Brandt, “Levitation in physics,” Science 243, 349–355 (1989).
[CrossRef]

Other (6)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Clarendon, 2005).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic representation of a scattering system and the chosen Cartesian coordinate system. r 0 is the point where multipole moments are located; A is the observation point.

Fig. 2.
Fig. 2.

ECS spectra of cylindrical silicon nanoparticles located (a) in free space, (b) in air on glass substrate, and (c) in air on Si substrate. The particle dimensions are height 75 nm and diameter 150 nm. Normally incident linear-polarized plane waves are considered. Different curves present the total ECS and separate contributions of multipole modes (ED, electric dipole; MD, magnetic dipole; EQ, electric quadrupole).

Fig. 3.
Fig. 3.

SCS spectra into the back semi-space (back scattering) for cylindrical Si nanoparticles located in free space, and on glass and Si substrates. The nanoparticle sizes and irradiation conditions are the same as in Fig. 2.

Equations (66)

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P ext = ω 2 Im V s E 0 * ( r ) · P ( r ) d r ,
E ( r ) = ω 2 μ 0 V s G ^ FF ( r , r ) P ( r ) d r ,
P ( r ) = P ( r ) δ ( r r ) d r ,
δ ( r r 0 Δ r ) δ ( r r 0 ) ( Δ r · ) δ ( r r 0 ) + 1 2 ( Δ r · ) 2 δ ( r r 0 )
P ( r ) p δ ( r r 0 ) 1 6 Q ^ δ ( r r 0 ) + i ω [ × m δ ( r r 0 ) ] + 1 6 O ^ ( δ ( r r 0 ) ) i 2 ω [ × M ^ δ ( r r 0 ) ] ,
p = P ( r ) d r
Q ^ Q ^ ( r 0 ) = 3 ( Δ r P ( r ) + P ( r ) Δ r ) d r ,
m m ( r 0 ) = i ω 2 [ Δ r × P ( r ) ] d r ,
O ^ O ^ ( r 0 ) = Δ r Δ r Δ r ( · P ( r ) ) d r ,
M ^ M ^ ( r 0 ) = 2 i ω 3 [ Δ r × P ( r ) ] Δ r d r
P ext P ext p + P ext m + P ext Q + P ext M + P ext O .
σ ext = P ext P in σ ext p + σ ext m + σ ext Q + σ ext M + σ ext O ,
σ ext p = P ext p P in = ω 2 P in Im [ E 0 * ( r 0 ) · p ] ,
σ ext m = P ext m P in = ω 2 P in Im [ μ 0 H 0 * ( r 0 ) · m ( r 0 ) ] ,
σ ext Q = P ext Q P in = ω 24 P in Im [ { E 0 * ( r 0 ) + ( E 0 * ( r 0 ) ) T } : Q ^ ( r 0 ) ] ,
σ ext M = P ext M P in = ω 4 P in Im ( μ 0 [ H 0 * ( r 0 ) ] T : M ^ ( r 0 ) ) ,
σ ext O = P ext O P in = ω 12 P in Im β γ τ O β γ τ ( r 0 ) 2 γ τ E 0 β * ( r 0 ) .
β γ τ β γ τ .
G ^ FF ( r , r ) = g ^ ( r ) e ( N · r ) ,
E ( r ) = k 0 2 ε 0 g ^ ( r ) e ( N · r ) { p δ ( r r 0 ) 1 6 Q ^ δ ( r r 0 ) + i ω [ × m δ ( r r 0 ) ] + 1 6 O ^ ( δ ( r r 0 ) ) i 2 ω [ × M ^ δ ( r r 0 ) ] } d r ,
E ( r ) = k 0 2 ε 0 g ^ ( r ) e ( N · r 0 ) { p + 1 6 Q ^ N i ω [ N × m ] + 1 6 O ^ ( N N ) i 2 ω [ N × M ^ N ] } .
G ^ FF ( r , r ) = e i k d r 4 π r ( U ^ n n ) e i k d ( n · r ) ,
E ( r ) k 0 2 e i k d ( r n · r 0 ) 4 π ε 0 r ( [ n × [ p × n ] ] + 1 v d [ m × n ] + i k d 6 [ n × [ n × Q ^ n ] ] + i k d 2 v d [ n × ( M ^ n ) ] + k d 2 6 [ n × [ n × O ^ ( n n ) ] ] ) .
( U ^ n n ) b = [ n × [ b × n ] ]
E a ( r ) = ω 2 μ 0 V s { G ^ 0 FF ( r , r ) + G ^ R FF ( r , r ) } P ( r ) d r ,
E t ( r ) = ω 2 μ 0 V s G ^ T FF ( r , r ) P ( r ) d r ,
G ^ 0 FF ( r , r ) = e i k d r 4 π r ( U ^ n n ) e i k d ( n · r ) ,
G ^ R FF ( r , r ) = e i k d r 4 π r R ^ ( r ) e i k d ( n ˜ · r ) ,
G ^ T FF ( r , r ) = e i k S r 4 π r T ^ ( r ) e i k d ( n ˜ ˜ · r ) ,
E a ( r ) = E d ( r ) + E r ( r ) ,
E r ( r ) k 0 2 e i k d ( r n ˜ · r 0 ) ) 4 π ε 0 r R ^ ( r ) { p i k d 6 Q ^ n ˜ k d ω [ n ˜ × m ] k d 2 6 O ^ ( n ˜ n ˜ ) + i k d 2 2 ω [ n ˜ × M ^ n ˜ ] } .
E t ( r ) k 0 2 e i k S r i k d n ˜ ˜ · r 0 4 π ε 0 r T ^ ( r ) { p i k d 6 Q ^ n ˜ ˜ k d ω [ n ˜ ˜ × m ] k d 2 6 O ^ ( n ˜ ˜ n ˜ ˜ ) + i k d 2 2 ω [ n ˜ ˜ × M ^ n ˜ ˜ ] } .
d P = 1 2 ε 0 ε d μ 0 | E a | 2 r 2 d Ω ,
P b = 1 2 ε 0 ε d μ 0 0 π / 2 0 2 π | E a | 2 r 2 d sin θ d θ d φ ,
E a ( r ) = E d ( r ) + E r ( r ) + E SPP ( r ) ,
E SPP ( r ) = ω 2 μ 0 V s G ^ SPP ( r , r ) P ( r ) d r .
G ^ SPP FF ( r , r ) = S ^ p ( r ) e i k p ( n p · r ) ,
E SPP ( r ) k 0 2 e i k p n p · r 0 ε 0 S ^ p ( r ) { p k p ω [ n p × m ] i k p 6 Q ^ n p k p 2 6 O ^ ( n p n p ) + i k p 2 2 ω [ n p × M ^ n p ] } .
p ( φ ) d φ = μ 0 ε 0 ( 1 a 2 ) ( 1 a 4 ) 4 a k 0 | E SPP z | 2 ρ d φ ,
p j = α p E 0 ( r j ) + k 0 2 ε 0 α p G ^ S ( r j , r j ) p j + k 0 2 ε 0 α p l j N G ^ ( r j , r l ) p l ,
P ( r ) = j = 1 N p j δ ( r r j ) .
p = j = 1 N p j ; Q ^ ( r 0 ) = j = 1 N Q ^ j ( r 0 ) ; m ( r 0 ) = j = 1 N m j ( r 0 ) ; M ^ ( r 0 ) = j = 1 N M ^ j ( r 0 ) ; O ^ ( r 0 ) = j = 1 N O ^ j ( r 0 ) ,
Q ^ j ( r 0 ) = 3 ( ( r j r 0 ) p j + p j ( r j r 0 ) ) ,
m j ( r 0 ) = i ω 2 [ ( r j r 0 ) × p j ] ,
M ^ j ( r 0 ) = i 2 ω 3 [ ( r j r 0 ) × p j ] ( r j r 0 ) ,
O β β β j = 3 p j β ( β j β 0 ) 2 , O β β γ j = O β γ β j = O γ β β j = 2 p j β ( β j β 0 ) ( γ j γ 0 ) , O β γ τ j = p j β ( γ j γ 0 ) ( τ j τ 0 ) + p j γ ( β j β 0 ) ( τ j τ 0 ) + p j τ ( γ j γ 0 ) ( β j β 0 ) ,
P ( r ) P ( r ) d r δ ( r r 0 ) P ( r ) ( Δ r · ) δ ( r r 0 ) d r + 1 2 P ( r ) ( Δ r · ) 2 δ ( r r 0 ) d r +
P ( Δ r · δ ) = 1 2 ( P Δ r + Δ r P ) δ 1 2 [ δ × [ Δ r × P ] ] ,
1 2 P ( r ) ( Δ r · ) 2 d r δ ( r r 0 ) = 1 2 P ( r ) [ ( Δ r Δ r ) : ( ) δ ( r r 0 ) ] d r = 1 2 [ P ( r ) Δ r Δ r d r ] δ ( r r 0 ) .
P i Δ r j Δ r k = 1 3 ( Δ r i Δ r j Δ r k ( · P ) + ε i j l [ Δ r × P ] l Δ r k + ε i k l [ Δ r × P ] l Δ r j ) ,
P i Δ r j Δ r k d r = 1 3 O i j k + 1 2 i ω ( ε i j l M l k + ε i k l M l j ) ,
O ^ = Δ r Δ r Δ r ( · P ( r ) ) d r ,
M ^ = 2 i ω 3 [ Δ r × P ( r ) ] Δ r d r .
1 2 P ( r ) ( Δ r · ) 2 d r δ ( r r 0 ) = 1 6 O ^ ( δ ( r r 0 ) ) i 2 ω [ × M ^ δ ( r r 0 ) ] ,
( ε i j l M l k + ε i k l M l j ) ( δ ( r r 0 ) ) j k = 2 [ × M ^ δ ( r r 0 ) ] i .
E φ p ( r , φ , θ ) = k 0 2 e i k d r 4 π ε 0 r e i k d ( n r 0 ) ( 1 + r ( s ) e i k d 2 z 0 cos θ ) × ( p y cos φ p x sin φ ) ;
E θ p ( r , φ , θ ) = k 0 2 e i k d r 4 π ε 0 r e i k d ( n r 0 ) ( [ 1 r ( p ) e i k d 2 z 0 cos θ ] × ( p x cos φ cos θ + p y sin φ cos θ ) p z sin θ [ 1 + r ( p ) e i k d 2 z 0 cos θ ] ) ;
E φ m ( r , φ , θ ) = μ 0 ε 0 k 0 k d e i k d r 4 π r e i k d ( n r 0 ) × ( [ r ( s ) e i k d 2 z 0 cos θ 1 ] × ( m x cos φ cos θ + m y sin φ cos θ ) + m z sin θ [ r ( s ) e i k d 2 z 0 cos θ + 1 ] ) ;
E θ m ( r , φ , θ ) = μ 0 ε 0 k 0 k d e i k d r 4 π r e i k d ( n r 0 ) × [ 1 + r ( p ) e i k d 2 z 0 cos θ ] × ( m y cos φ m x sin φ ) .
r ( p ) = ε s cos θ ε d ε s / ε d sin 2 θ ε s cos θ + ε d ε s / ε d sin 2 θ ,
r ( s ) = cos θ ε s / ε d sin 2 θ cos θ + ε s / ε d sin 2 θ .
E SPP z p > ( φ , ρ , z ) = C k 0 2 ε 0 e a k p z 2 π k p ρ e i ( k p ρ π / 4 ) × e i k p ( n r 0 ) [ p z + i a ( p x cos φ + p y sin φ ) ] ; E SPP ρ p > ( φ , ρ , z ) = i a E SPP z p > ( φ , ρ , z ) ; H SPP φ p > ( φ , ρ , z ) = ε 0 μ 0 k p k 0 ( 1 a 2 ) E SPP z p > ( φ , ρ , z ) ;
E SPP z p < ( φ , ρ , z ) = a 2 e ( a 2 + 1 ) k p z / a E SPP z p > ( φ , ρ , z ) E SPP ρ p < ( φ , ρ , z ) = i a E SPP z p < ( φ , ρ , z ) ; H SPP φ p < ( φ , ρ , z ) = 1 a 2 ε 0 μ 0 k p k 0 ( 1 a 2 ) E SPP z p < ( φ , ρ , z ) ,
C = i a k p 2 ( 1 a 2 ) ( 1 a 4 ) .
E SPP z m > ( φ , ρ , z ) = C μ 0 ε 0 k 0 k p e a k p z 2 π k p ρ e i ( k p ρ π / 4 ) × e i k p ( n r 0 ) ( 1 a 2 ) [ m x sin φ m y cos φ ] ; E SPP ρ m > ( φ , ρ , z ) = i a E SPP z m > ( φ , ρ , z ) ; H SPP φ m > ( φ , ρ , z ) = ε 0 μ 0 k p k 0 ( 1 a 2 ) E SPP z m > ( φ , ρ , z ) ;
E SPP z m < ( φ , ρ , z ) = a 2 e ( a 2 + 1 ) k p z / a E SPP z m > ( φ , ρ , z ) E SPP ρ m < ( φ , ρ , z ) = i a E SPP z m < ( φ , ρ , z ) ; H SPP φ m < ( φ , ρ , z ) = 1 a 2 ε 0 μ 0 k p k 0 ( 1 a 2 ) E SPP z m < ( φ , ρ , z ) .

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