Abstract

The light scattering by a spherical particle with radial anisotropic permittivity ε and permeability μ are discussed in detail by expanding Mie theory. With the modified vector potential formulation, the electric anisotropy effects on scattering efficiency are addressed by studying the extinction, scattering, absorption and radar cross sections following the change of the transverse permittivity εt, the longitudinal permittivity εr and the particle size q. The huge scattering cross sections are shown by considering the possible coupling between active medium and plasmon polaritons and this will be possible to result in spaser from the active plasmons of small particle.

© 2010 Optical Society of America

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2010 (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]

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmon-enhanced fluorescence from single fluorophores end-linked to gold nanorods,” J. Am. Chem. Soc. 132, 5540–5541 (2010).
[CrossRef] [PubMed]

2009 (1)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

2008 (5)

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[CrossRef]

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16, 1385–1392 (2008).
[CrossRef] [PubMed]

H. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
[CrossRef]

B. S. Luk’yanchuk, and C.-W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys., A Mater. Sci. Process. 92, 773 (2008).
[CrossRef]

2007 (6)

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
[CrossRef]

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

M. T. Hill,  et al., “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

C. Genet, and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[CrossRef]

C.-W. Qiu, L. W. Li, T.-S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 026609 (2007).
[CrossRef]

2006 (5)

2005 (4)

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
[CrossRef] [PubMed]

A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
[CrossRef] [PubMed]

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
[CrossRef] [PubMed]

J. Seidel, S. Grafstroum, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

2004 (6)

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 056609 (2004).
[CrossRef]

E. Prodan, and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004).
[CrossRef] [PubMed]

M. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004).
[CrossRef] [PubMed]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

P. Andrew, and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306, 1002–1005 (2004).
[CrossRef] [PubMed]

R. J. Tarento, K. H. Bennemann, P. Joyes, and J. Van de Walle, “Mie scattering of magnetic spheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026606 (2004).
[CrossRef]

2003 (2)

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

D. J. Bergman, and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2001 (1)

2000 (2)

P. Andrew, and W. L. Barnes, “F¨orster energy transfer in an optical microcavity,” Science 290, 785–788 (2000).
[CrossRef] [PubMed]

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

1999 (1)

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-Harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
[CrossRef]

1997 (1)

S. Nie, and S. R. Emony, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

1996 (1)

C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382, 607–609 (1996).
[CrossRef] [PubMed]

1993 (1)

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, 664–673 (1993).
[CrossRef]

1991 (1)

Z. S. Wu, and Y. P. Wang, “Electromagnetic scattering for multilayered sphere: Recursive algorithms,” Radio Sci. 26, 13931401 (1991).
[CrossRef]

1989 (2)

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antenn. Propag. 37, 800–802 (1989).
[CrossRef]

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for threedimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[CrossRef]

1983 (1)

B. Liedberg, C. Nylander, and I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sens. Actuators 4, 299–304 (1983).
[CrossRef]

1951 (1)

A. L. Aden, and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 12421246 (1951).
[CrossRef]

Adegoke, J.

Adegoke, J. A.

Aden, A. L.

A. L. Aden, and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 12421246 (1951).
[CrossRef]

Alaverdyan, Y.

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
[CrossRef] [PubMed]

Andrew, P.

P. Andrew, and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306, 1002–1005 (2004).
[CrossRef] [PubMed]

P. Andrew, and W. L. Barnes, “F¨orster energy transfer in an optical microcavity,” Science 290, 785–788 (2000).
[CrossRef] [PubMed]

Anger, P.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[CrossRef]

Bahoura, M.

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Barnes, W. L.

P. Andrew, and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306, 1002–1005 (2004).
[CrossRef] [PubMed]

P. Andrew, and W. L. Barnes, “F¨orster energy transfer in an optical microcavity,” Science 290, 785–788 (2000).
[CrossRef] [PubMed]

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, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Bennemann, K. H.

R. J. Tarento, K. H. Bennemann, P. Joyes, and J. Van de Walle, “Mie scattering of magnetic spheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026606 (2004).
[CrossRef]

Bergman, D. J.

D. J. Bergman, and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Bharadwaj, P.

P. Bharadwaj, P. Anger, and L. Novotny, “Nanoplasmonic enhancement of single-molecule fluorescence,” Nanotechnology 18, 044017 (2007).
[CrossRef]

Chang, L.

A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
[CrossRef] [PubMed]

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]

Chong, T. C.

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
[CrossRef]

Dadap, J. I.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-Harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
[CrossRef]

Dahlin, A.

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
[CrossRef] [PubMed]

Drachev, V. P.

Ebbesen, T. W.

C. Genet, and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Eisenthal, K. B.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-Harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
[CrossRef]

Eisler, H.-J.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
[CrossRef] [PubMed]

Emony, S. R.

S. Nie, and S. R. Emony, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Eng, L.

J. Seidel, S. Grafstroum, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Fainman, Y.

Fu, Y.

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmon-enhanced fluorescence from single fluorophores end-linked to gold nanorods,” J. Am. Chem. Soc. 132, 5540–5541 (2010).
[CrossRef] [PubMed]

Genet, C.

C. Genet, and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Geng, Y. L.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 056609 (2004).
[CrossRef]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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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).
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Gordon, J. A.

Grafstroum, S.

J. Seidel, S. Grafstroum, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
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R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for threedimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
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Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 056609 (2004).
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A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
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Halas, N. J.

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).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
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P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
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J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-Harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
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T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
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Joyes, P.

R. J. Tarento, K. H. Bennemann, P. Joyes, and J. Van de Walle, “Mie scattering of magnetic spheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026606 (2004).
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Kall, M.

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
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A. L. Aden, and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 12421246 (1951).
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A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
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Kottmann, J. P.

Lakhtakia, A.

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antenn. Propag. 37, 800–802 (1989).
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Lakowicz, J. R.

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmon-enhanced fluorescence from single fluorophores end-linked to gold nanorods,” J. Am. Chem. Soc. 132, 5540–5541 (2010).
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N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
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C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382, 607–609 (1996).
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C.-W. Qiu, L. W. Li, T.-S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 026609 (2007).
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B. Liedberg, C. Nylander, and I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sens. Actuators 4, 299–304 (1983).
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H. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
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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).
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B. S. Luk’yanchuk, and C.-W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys., A Mater. Sci. Process. 92, 773 (2008).
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B. Liedberg, C. Nylander, and I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sens. Actuators 4, 299–304 (1983).
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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).
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P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
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C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382, 607–609 (1996).
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P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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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).
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B. Liedberg, C. Nylander, and I. Lundstrom, “Surface plasmon resonance for gas detection and biosensing,” Sens. Actuators 4, 299–304 (1983).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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Pohl, D. W.

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1608 (2005).
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Prodan, E.

E. Prodan, and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
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B. S. Luk’yanchuk, and C.-W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys., A Mater. Sci. Process. 92, 773 (2008).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
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Ritzo, B. A.

Seidel, J.

J. Seidel, S. Grafstroum, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31, 3022–3024 (2006).
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J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-Harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
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Shi, L. P.

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
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Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382, 607–609 (1996).
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Stout, B.

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
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R. J. Tarento, K. H. Bennemann, P. Joyes, and J. Van de Walle, “Mie scattering of magnetic spheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026606 (2004).
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Tribelsky, M. I.

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
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M. I. Tribelsky, and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97, 263902 (2006).
[CrossRef]

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R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for threedimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
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R. J. Tarento, K. H. Bennemann, P. Joyes, and J. Van de Walle, “Mie scattering of magnetic spheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026606 (2004).
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Van Duyne, R. P.

A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
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V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antenn. Propag. 37, 800–802 (1989).
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Varadan, V. V.

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antenn. Propag. 37, 800–802 (1989).
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B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
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Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Wu, X. B.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 056609 (2004).
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Z. S. Wu, and Y. P. Wang, “Electromagnetic scattering for multilayered sphere: Recursive algorithms,” Radio Sci. 26, 13931401 (1991).
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C.-W. Qiu, L. W. Li, T.-S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 026609 (2007).
[CrossRef]

Zhang, J.

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmon-enhanced fluorescence from single fluorophores end-linked to gold nanorods,” J. Am. Chem. Soc. 132, 5540–5541 (2010).
[CrossRef] [PubMed]

Zhang, X.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
[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).
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Zhou, Y.

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
[CrossRef]

Zhu, G.

Zich, R. S.

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for threedimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
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Zouhdi, S.

C.-W. Qiu, L. W. Li, T.-S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 026609 (2007).
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Appl. Phys. Lett. (1)

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (2)

B. S. Luk’yanchuk, and C.-W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys., A Mater. Sci. Process. 92, 773 (2008).
[CrossRef]

B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys., A Mater. Sci. Process. 89, 259–264 (2007).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antenn. Propag. 37, 800–802 (1989).
[CrossRef]

J. Am. Chem. Soc. (2)

A. J. Haes, L. Chang, W. L. Klein, and R. P. Van Duyne, “Detection of a biomarker for alzheimer’s disease from synthetic and clinical samples using a nanoscale optical biosensor,” J. Am. Chem. Soc. 127, 2264–2271 (2005).
[CrossRef] [PubMed]

Y. Fu, J. Zhang, and J. R. Lakowicz, “Plasmon-enhanced fluorescence from single fluorophores end-linked to gold nanorods,” J. Am. Chem. Soc. 132, 5540–5541 (2010).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

A. L. Aden, and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 12421246 (1951).
[CrossRef]

J. Chem. Phys. (1)

E. Prodan, and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004).
[CrossRef] [PubMed]

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

Nano Lett. (1)

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, “Plasmonic sensing characteristics of single nanometric holes,” Nano Lett. 5, 2335–2339 (2005).
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Nat. Mater. (1)

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).
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Figures (8)

Fig. 1
Fig. 1

The maximal value of Qext for each resonance mode as a function of the dissipative damping Im[εD] for the size q = 1 (A) and q = 0.5 (B). The Qext as a function of both frequency ω and Im[εD] for dipole and quadrupole modes of the particle with size q = 1 shown in the inset of (A).

Fig. 2
Fig. 2

The maximal value of Qext as a function of Re[εD] with different Im[εD] (A), the maximal or minimal values of Qsca and Qabs as a function of Im[εD] with Re[εD] = −2.2 (B), maximal value of Qext as a function of Im[εr] with different Re[εr] and the ratio εt/εr (C and D).

Fig. 4
Fig. 4

Log[Qext] as a function of permittivity εD and size q under the nondissipative limit (Im[εD] = 0) (A), the maximal value of Log[Qext] as a function of Re[εD] and Im[εD] (B), the maximal value of Log[Qsca] as a function of Im[εr] and the ratio |εt|/|εr| for Re[εr] = −2.5 and εt = (−2.5 + i Im[εr])|εt|/|εr|(C), Log[Qsca] as a function of the ratio |εt|/|εr| and size q for εr = −2.5 −0.1i and εt = (−2.5 −0.1i)|εt|/|εr|(D).

Fig. 3
Fig. 3

Log[Qmax ext] as a function of both εr and εt/εr (A), Qext as a function of q and εt/εr with fixed longitudinal permittivity εr = −2.5 (B) and Qext as a function of q and εr with fixed ratio εt/εr = 0.75 (C), with the nondissipative limit (Im[εr] = 0 and Im[εt] = 0).

Fig. 5
Fig. 5

the resonance cross section Log[Qsca] as a function of transverse permittivity (Re[εt] and Re[εt]) with the fixed longitudinal permittivity εr = 2.5 – 0.05i (A), the maximal value of scattering amplitude | b 1 e| as a function of Re[εt] and Im[εt] with the fixed εr = 2.5 – 0.05i (B).

Fig. 6
Fig. 6

the maximal value of scattering amplitude | b 1 e| as a function of Re[εr] and Re[εt] with fixed Im[εr](= −0.05) and Im[εt](= 0.008) for εr as active medium (A), with fixed Im[εr](= 0.001) and Im[εt](= −0.02) for εt as active medium (B).

Fig. 7
Fig. 7

the scattering amplitude Log [ | b 1 e | ] as a function of Re[εr] and q with fixed Im[εr](= −0.05) and Im[εt](= 0.008) (Re[εt] is chosen by the formula Re[εt] = −2.62 + 0.608Re[εr] − 0.110Re[εr]2 + 0.008Re[εr]3)(A), the scattering amplitude Log [ | b 1 e | ] as a function of Re[εr] and q with fixed Im[εr](= 0.001) and Im[εt](= −0.02) (Re[εt] is chosen by the formula Re[εt] = 0.389 – 0.154Re[εr])(B), the maximal value of scattering amplitude Log [ | b 1 e | ] as a function of f(Im[εr]) and Im[εt] with εr = 3 – f(Im[εt])Im[εt] i and Re[εt] = −1.5604 (C) and the maximal value of scattering amplitude Log [ | b 1 e | ] as a function of f(Im[εr]) and Im[εr] with Re[εr] = −12 and εt = 2.237 – f(Im[εr])Im[εr]i (D).

Fig. 8
Fig. 8

High scattering efficiencies with huge radar backscattering cross section. Qrbs as the function of size q for εr with the property of energy-gain (A and B) and for εt with the property of energy-gain (C and D).

Equations (17)

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H = i k 0 ɛ E and E = ik 0 μ H ,
ɛ = ( ɛ r 0 0 0 ɛ t 0 0 0 ɛ t ) and μ = ( μ r 0 0 0 μ t 0 0 0 μ t )
ɛ r ɛ t 2 Π TM r 2 + 1 r 2 sin θ θ ( sin θ Π TM θ ) + 1 r 2 sin 2 θ 2 Π TM φ 2 + k 0 2 ɛ r μ t Π TM = 0 ,
μ r μ r 2 Π TE r 2 + 1 r 2 sin θ θ ( sin θ Π TE θ ) + 1 r 2 sin 2 θ 2 Π TE φ 2 + k 0 2 ɛ t μ r Π TE = 0 ,
B l e = i l + 1 2 l + 1 l ( l + 1 ) b l e and B l m = i l + 1 2 l + 1 l ( l + 1 ) b l m ,
b l e = ɛ t Φ l ( k 0 a ) Φ v 1 ( k t a ) μ t Φ l ( k 0 a ) Φ v 1 ( k t a ) ɛ t ξ l ( k 0 a ) Φ v 1 ( k t a ) μ t ξ l ( k 0 a ) Φ v 1 ( k t a ) ,
b l m = ɛ t Φ l ( k 0 a ) Φ v 2 ( k t a ) μ t Φ l ( k 0 a ) Φ v 2 ( k t a ) ɛ t ξ l ( k 0 a ) Φ v 2 ( k t a ) μ t ξ l ( k 0 a ) Φ v 2 ( k t a ) ,
Φ l ( x ) = π x 2 J l + 1 2 ( x ) ,
ξ l ( x ) = π x 2 ( J l + 1 2 ( x ) + i N l + 1 2 ( x ) )
v 1 = [ l ( l + 1 ) ɛ t ɛ r + 1 4 ] 1 / 2 1 2 ,
v 2 = [ l ( l + 1 ) μ t μ r + 1 4 ] 1 / 2 1 2 .
Q ext = 2 k 0 2 a 2 l = 1 ( 2 l + 1 ) Re ( b l e + b l m ) , Q sca = 2 k 0 2 a 2 l = 1 ( 2 l + 1 ) [ | b l e | 2 + | b l m | 2 ] , Q rbs = 1 k 0 a Re | l = 1 ( 1 ) l ( 2 l + 1 ) ( b l e b l m ) | 2 .
b l e = F b e ( l ) F b e ( l ) + i G b e ( l ) and b l m = F b m ( l ) F b m ( l ) + i G b m ( l ) ,
F b e = ɛ t Φ l ( k 0 a ) Φ v 1 ( k t a ) μ t Φ l ( k 0 a ) Φ v 1 ( k t a ) , G b e = ɛ t χ l ( k 0 a ) Φ v 1 ( k t a ) μ t χ l ( k 0 a ) Φ v 1 ( k t a ) , F b m = ɛ t Φ l ( k 0 a ) Φ v 2 ( k t a ) μ t Φ l ( k 0 a ) Φ v 2 ( k t a ) , G b m = ɛ t χ l ( k 0 a ) Φ v 2 ( k t a ) μ t χ l ( k 0 a ) Φ v 2 ( k t a ) ,
ɛ D = 1 ω p 2 ω 2 + i γ ω with ω p = ( ne 2 ɛ 0 m 0 ) 1 / 2 ,
ɛ D = 1 3 ω R 2 + γ R 2 + i γ R ω R 3 ω R 2 + γ R 2 .
γ l = q 2 l + 1 ( l + 1 ) [ l ( 2 l 1 ) ! ! ] 2 ( d ɛ D / d ω ) l

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