Abstract

Studies on single scattering of electromagnetic waves by magnetic particles were reported in the 1980s by Kerker et al. [J. Opt. Soc. Am. 73, 765 (1983)] . They obtained that very small spherical particles with electric permittivity and magnetic permeability values such that ε=(4μ)(2μ+1) do not produce forward scattering. We show here that this condition contains an interesting exception at (ε=2, μ=2) when electric and magnetic resonances are present and around which the scattered field distribution is computed and described showing a polarization-insensitive behavior at the point (ε=2, μ=2).

© 2008 Optical Society of America

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  1. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377-445 (1908).
    [CrossRef]
  2. C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
    [CrossRef]
  3. W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
    [CrossRef]
  4. G. Videen and W. S. Bickel, “Light scattering resonance in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
    [CrossRef] [PubMed]
  5. F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
    [CrossRef] [PubMed]
  6. O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
    [CrossRef]
  7. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  8. V. Shalaev, “Optical negative-index metamaterial,” Nat. Photonics 1, 41-48 (2007).
    [CrossRef]
  9. B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
    [CrossRef]
  10. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
    [CrossRef] [PubMed]
  11. M. Kerker, D.-S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73, 765-767 (1983).
    [CrossRef]
  12. R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
    [CrossRef]
  13. B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
    [CrossRef]
  14. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

2008 (3)

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
[CrossRef]

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

2007 (5)

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

V. Shalaev, “Optical negative-index metamaterial,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

2006 (2)

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
[CrossRef] [PubMed]

1992 (1)

G. Videen and W. S. Bickel, “Light scattering resonance in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

1983 (1)

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Bickel, W. S.

G. Videen and W. S. Bickel, “Light scattering resonance in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

Bohren, C.

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

Chen, X.

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

Desai, R.

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

Feng, X.

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

García-Cámara, B.

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

Giles, C. L.

González, F.

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
[CrossRef] [PubMed]

Hägglund, C.

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
[CrossRef]

Hou, W.

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

Huffman, D.

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

Kasemo, B.

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
[CrossRef]

Kerker, M.

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Merchiers, O.

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

Metha, R. V.

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Moreno, F.

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
[CrossRef] [PubMed]

Parekh, K.

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

Patel, R.

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

Saiz, J. M.

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
[CrossRef] [PubMed]

Shalaev, V.

V. Shalaev, “Optical negative-index metamaterial,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Upadhayay, R. V.

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

Videen, G.

B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances by small particles with electric and magnetic properties,” J. Opt. Soc. Am. A 25, 327-334 (2008).
[CrossRef]

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

G. Videen and W. S. Bickel, “Light scattering resonance in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

Wang, D.-S.

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Yan, W.

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

Zäch, M.

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
[CrossRef]

Zhu, J.-J.

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Appl. Phys. Lett. (1)

C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008).
[CrossRef]

Biosens. Bioelectron. (1)

W. Yan, X. Feng, X. Chen, W. Hou, and J.-J. Zhu, “A super highly sensitive glucose biosensor based on Au nanoparticles-AgCl@polyaniline hybrid material,” Biosens. Bioelectron. 23, 925-931 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

V. Shalaev, “Optical negative-index metamaterial,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Opt. Commun. (1)

O. Merchiers, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ,” Opt. Commun. 269, 1-7 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

G. Videen and W. S. Bickel, “Light scattering resonance in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

R. V. Metha, R. Patel, R. Desai, R. V. Upadhayay, and K. Parekh, “Experimental evidence of zero forward scattering by magnetic spheres,” Phys. Rev. Lett. 96, 127402 (2006).
[CrossRef]

B. García-Cámara, F. Moreno, F. González, and J. M. Saiz, “Comment on `Experimental evidence of zero forward scattering by magnetic spheres',” Phys. Rev. Lett. 98, 179701 (2007).
[CrossRef]

Science (2)

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelength,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

3D plot of log ( Q ext ) as a function of the optical properties (ε and μ) in the negative–negative range for a spherical particle of R = 10 6 λ .

Fig. 2
Fig. 2

Scattering diagram for a very small particle ( R = 10 6 λ ) with optical properties ( ε = μ = 2 ) and for both incident polarizations: TE and TM.

Fig. 3
Fig. 3

Scattering diagram for a very small particle ( R = 10 6 λ ) for both incident polarizations: (a) TM and (b) TE and for several pairs of values of the optical constants around ( ε = 2 , μ = 2 ) that verify Kerker’s condition for zero forward scattering. The inset scale is for all pairs ( ε , μ ) diffferent for ( 2 , 2 ) , the latter requiring the left general scale, which is huge in comparison with the rest.

Fig. 4
Fig. 4

Scattering diagrams for a particle with R = 10 6 λ for both incident polarizations: (a) TM and (b) TE and for optical constants under (squares) or out of (circles) Kerker’s condition.

Equations (7)

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

I 1 = λ 2 4 π 2 r 2 3 2 ( a 1 π 1 ( cos θ ) + b 1 τ 1 ( cos θ ) ) 2 sin 2 ϕ ,
I 2 = λ 2 4 π 2 r 2 3 2 ( a 1 τ 1 ( cos θ ) + b 1 π 1 ( cos θ ) ) 2 sin 2 ϕ ,
a 1 = 2 i 3 x 3 ( ε 1 ε + 2 ) ,
b 1 = 2 i 3 x 3 ( μ 1 μ + 2 ) .
I 1 = λ 2 4 π 2 r 2 x 6 ( ε 1 ε + 2 ) + ( μ 1 μ + 2 ) cos ( θ ) 2 sin 2 ϕ ,
I 2 = λ 2 4 π 2 r 2 x 6 ( ε 1 ε + 2 ) cos ( θ ) + ( μ 1 μ + 2 ) 2 sin 2 ϕ .
ε = 4 μ 2 μ + 1 .

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