Abstract

In this paper, we consider the interaction of an electromagnetic field with two eccentric spheres. We propose a quasi-static approach in order to calculate the scattered field and the polarizability and the effective permittivity of the eccentric spheres. We analyze the behavior of the scattering parameters as a function of the dimension and position of the spherical inclusions. Moreover, we consider the case of plasmonic spheres and study the behavior of the plasmon resonances for different reciprocal positions of the two spheres.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. S. Kim and J. K. Chang, “Light scattering by two concentric optically active spheres: I. General theory,” J. Korean Phys. Soc. 45, 352–365 (2004).
  4. I. Arnaoudov and G. Venkov, “The transmission acoustic scattering problem for bi-spheres in low frequency regime,” Rend. Istit. Mat. Univ. Trieste XXXVIII, 73–93 (2006).
  5. J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
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  6. R. Dempsey, T. J. Gallagher, and B. K. P. Scaife, “Computation of the potential distribution for a composite dielectric sphere with a noncentral spherical inclusion polarized by a static uniform external field,” in 10th International Conference on Conduction and Breakdown in Dielectric Liquids (1990), pp. 243–247.
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    [CrossRef]
  8. F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
    [CrossRef]
  9. J. A. Roumeliotis, N. B. Kakogiannos, and J. D. Kanellopoulos, “Scattering from a sphere of small radius embedded into a dielectric one,” IEEE Trans. Microwave Theor. Tech. 43, 155–168 (1995).
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  12. R. Nozawa, “Bipolar expansion of screened Coulomb potentials, Helmholtz’ solid harmonics, and their addition theorems,” J. Math. Phys. 7, 1841–1860 (1966).
    [CrossRef]
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  21. M. P. Ioannidou and D. P. Chrissoulidis, “Electromagnetic-wave scattering by a sphere with multiple spherical inclusions,” J. Opt. Soc. Am. A 19, 505–512 (2002).
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  22. G. Videen, D. Ngo, P. Chýlek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
    [CrossRef]
  23. J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).
  24. A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
    [CrossRef]
  25. J. W. Meijs and M. J. Peters, “The EEG and MEG, using a model of eccentric spheres to describe the head,” IEEE Trans. Biomed. Eng. BME-34, 913–920 (1987).
    [CrossRef]
  26. B. N. Cuffin, “Eccentric sphere models of the head,” IEEE Trans. Biomed. Eng. 38, 871–878 (1991).
    [CrossRef]
  27. Y. Rudy, “The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography,” IEEE Trans. Biomed. Eng. BME-26, 392–399 (1979).
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  28. B. Miu and W. Yawei, “Scattering analysis for eccentric-sphere model of single-nuclear cell,” in 2011 Symposium on Photonics and Optoelectronics (SOPO) (2011), pp. 1–4.
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    [CrossRef]
  30. Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
    [CrossRef]
  31. J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
    [CrossRef]
  32. W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
    [CrossRef]
  33. P. Chýlek and G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
    [CrossRef]
  34. B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
    [CrossRef]
  35. O. Pea-Rodríguez and U. Pal, “Enhanced plasmonic behavior of bimetallic (Ag-Au) multilayered spheres,” Nanoscale Res. Lett. 6, 279–283 (2011).
    [CrossRef]
  36. C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
    [CrossRef]
  37. H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
    [CrossRef]
  38. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  39. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Hamilton Printing Company, 1998).
  40. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, 1953).
  41. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1940).
  42. A. Sihvola, Electromagnetic Mixing Formulas and Applications (The Institution of Electrical Engineers, 1999).
  43. A. Sihvola, “Character of surface plasmons in layered spherical structures,” Progress Electromagn. Res. 62, 317–331 (2006).
  44. Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Express 35, 1431–1433 (2010).
  45. U. K. Chettiar and N. Engheta, “Internal homogenization: effective permittivity of a coated sphere,” Opt. Express 20, 22976–22986 (2012).
    [CrossRef]

2013 (1)

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

2012 (3)

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

F. Vervelidou and D. Chrissoulidis, “Scattering of a pulsed wave by a sphere with an eccentric spherical inclusion,” J. Opt. Soc. Am. A 29, 605–616 (2012).
[CrossRef]

U. K. Chettiar and N. Engheta, “Internal homogenization: effective permittivity of a coated sphere,” Opt. Express 20, 22976–22986 (2012).
[CrossRef]

2011 (4)

K. Sasihithlu and A. Narayanaswamy, “Convergence of vectorial spherical wave expansion method applied to near-field radiative transfer,” Opt. Express 19, A772–A785 (2011).
[CrossRef]

O. Pea-Rodríguez and U. Pal, “Enhanced plasmonic behavior of bimetallic (Ag-Au) multilayered spheres,” Nanoscale Res. Lett. 6, 279–283 (2011).
[CrossRef]

C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
[CrossRef]

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

2010 (3)

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Express 35, 1431–1433 (2010).

2009 (1)

B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. Pure Appl. Opt. 11, 015705 (2009).

2008 (1)

2007 (3)

A. P. Moneda and D. P. Chrissoulidis, “Dyadic Green’s function of a sphere with an eccentric spherical inclusion,” J. Opt. Soc. Am. A 24, 1695–1703 (2007).
[CrossRef]

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
[CrossRef]

2006 (2)

I. Arnaoudov and G. Venkov, “The transmission acoustic scattering problem for bi-spheres in low frequency regime,” Rend. Istit. Mat. Univ. Trieste XXXVIII, 73–93 (2006).

A. Sihvola, “Character of surface plasmons in layered spherical structures,” Progress Electromagn. Res. 62, 317–331 (2006).

2004 (1)

J. S. Kim and J. K. Chang, “Light scattering by two concentric optically active spheres: I. General theory,” J. Korean Phys. Soc. 45, 352–365 (2004).

2002 (1)

2000 (1)

G. Gouesbet and G. Grhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).
[CrossRef]

1998 (1)

P. Chýlek and G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

1995 (3)

1994 (2)

1992 (2)

F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
[CrossRef]

1991 (1)

B. N. Cuffin, “Eccentric sphere models of the head,” IEEE Trans. Biomed. Eng. 38, 871–878 (1991).
[CrossRef]

1987 (1)

J. W. Meijs and M. J. Peters, “The EEG and MEG, using a model of eccentric spheres to describe the head,” IEEE Trans. Biomed. Eng. BME-34, 913–920 (1987).
[CrossRef]

1980 (1)

J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).

1979 (2)

Y. Rudy, “The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography,” IEEE Trans. Biomed. Eng. BME-26, 392–399 (1979).
[CrossRef]

J. G. Fikioris and N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. 69, 1359–1366 (1979).
[CrossRef]

1978 (1)

M. J. Caola, “Solid harmonics and their addition theorems,” J. Phys. A 11, L23–L25 (1978).
[CrossRef]

1966 (1)

R. Nozawa, “Bipolar expansion of screened Coulomb potentials, Helmholtz’ solid harmonics, and their addition theorems,” J. Math. Phys. 7, 1841–1860 (1966).
[CrossRef]

1964 (1)

J. Rheinstein, “Scattering of electromagnetic waves from dielectric coated conducting spheres,” IEEE Trans. Antennas Propag. 12, 334–340 (1964).
[CrossRef]

1951 (1)

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Aden, A.

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Arnaoudov, I.

I. Arnaoudov and G. Venkov, “The transmission acoustic scattering problem for bi-spheres in low frequency regime,” Rend. Istit. Mat. Univ. Trieste XXXVIII, 73–93 (2006).

Bharathi, M. S.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1940).

Borghese, F.

Brandl, D. W.

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

Caola, M. J.

M. J. Caola, “Solid harmonics and their addition theorems,” J. Phys. A 11, L23–L25 (1978).
[CrossRef]

Chang, J. K.

J. S. Kim and J. K. Chang, “Light scattering by two concentric optically active spheres: I. General theory,” J. Korean Phys. Soc. 45, 352–365 (2004).

Chen, H.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Chen, T.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Chettiar, U. K.

Chiu, S. H.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Chrissoulidis, D.

Chrissoulidis, D. P.

Chýlek, P.

P. Chýlek and G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

G. Videen, D. Ngo, P. Chýlek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
[CrossRef]

Cuffin, B. N.

B. N. Cuffin, “Eccentric sphere models of the head,” IEEE Trans. Biomed. Eng. 38, 871–878 (1991).
[CrossRef]

Cui, Y.

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Dempsey, R.

R. Dempsey, T. J. Gallagher, and B. K. P. Scaife, “Computation of the potential distribution for a composite dielectric sphere with a noncentral spherical inclusion polarized by a static uniform external field,” in 10th International Conference on Conduction and Breakdown in Dielectric Liquids (1990), pp. 243–247.

Denti, P.

Ding, D.

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Elsherbeni, A. Z.

A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
[CrossRef]

Engheta, N.

Feng, Y.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, 1953).

Fikioris, J. G.

J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).

J. G. Fikioris and N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. 69, 1359–1366 (1979).
[CrossRef]

Fuller, K. A.

Gallagher, T. J.

R. Dempsey, T. J. Gallagher, and B. K. P. Scaife, “Computation of the potential distribution for a composite dielectric sphere with a noncentral spherical inclusion polarized by a static uniform external field,” in 10th International Conference on Conduction and Breakdown in Dielectric Liquids (1990), pp. 243–247.

Geng, J.

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Gouesbet, G.

G. Gouesbet and G. Grhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).
[CrossRef]

Gounaris, G. P.

J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).

Grhan, G.

G. Gouesbet and G. Grhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).
[CrossRef]

Halas, N. J.

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

Han, G.

Han, M. Y.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Han, X.

B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. Pure Appl. Opt. 11, 015705 (2009).

Han, Y.

He, J.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Hng, H. H.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Hu, G.

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Huang, C. C.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Huang, G. D.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Huang, Y. K.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1940).

Ioannidou, M. P.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Hamilton Printing Company, 1998).

Kakogiannos, N. B.

J. A. Roumeliotis, N. B. Kakogiannos, and J. D. Kanellopoulos, “Scattering from a sphere of small radius embedded into a dielectric one,” IEEE Trans. Microwave Theor. Tech. 43, 155–168 (1995).
[CrossRef]

Kanellopoulos, J. D.

J. A. Roumeliotis, N. B. Kakogiannos, and J. D. Kanellopoulos, “Scattering from a sphere of small radius embedded into a dielectric one,” IEEE Trans. Microwave Theor. Tech. 43, 155–168 (1995).
[CrossRef]

Kerker, M.

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Kim, J. S.

J. S. Kim and J. K. Chang, “Light scattering by two concentric optically active spheres: I. General theory,” J. Korean Phys. Soc. 45, 352–365 (2004).

Kishk, A. A.

A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
[CrossRef]

Lavarello, R.

J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
[CrossRef]

Li, B. Q.

C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
[CrossRef]

Li, K.

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Li, W. P.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Liu, B.

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Liu, C.

C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
[CrossRef]

Liu, J.

Liu, S.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Low, M.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

McNew, J.

J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
[CrossRef]

Meijs, J. W.

J. W. Meijs and M. J. Peters, “The EEG and MEG, using a model of eccentric spheres to describe the head,” IEEE Trans. Biomed. Eng. BME-34, 913–920 (1987).
[CrossRef]

Mi, C. C.

C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
[CrossRef]

Miu, B.

B. Miu and W. Yawei, “Scattering analysis for eccentric-sphere model of single-nuclear cell,” in 2011 Symposium on Photonics and Optoelectronics (SOPO) (2011), pp. 1–4.

Moneda, A. P.

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, 1953).

Narayanaswamy, A.

Ngo, D.

Nordlander, P.

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

Nozawa, R.

R. Nozawa, “Bipolar expansion of screened Coulomb potentials, Helmholtz’ solid harmonics, and their addition theorems,” J. Math. Phys. 7, 1841–1860 (1966).
[CrossRef]

O’Brien, W. D.

J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
[CrossRef]

Pal, U.

O. Pea-Rodríguez and U. Pal, “Enhanced plasmonic behavior of bimetallic (Ag-Au) multilayered spheres,” Nanoscale Res. Lett. 6, 279–283 (2011).
[CrossRef]

Pan, M.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Parrikar, R. P.

A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
[CrossRef]

Pea-Rodríguez, O.

O. Pea-Rodríguez and U. Pal, “Enhanced plasmonic behavior of bimetallic (Ag-Au) multilayered spheres,” Nanoscale Res. Lett. 6, 279–283 (2011).
[CrossRef]

Peters, M. J.

J. W. Meijs and M. J. Peters, “The EEG and MEG, using a model of eccentric spheres to describe the head,” IEEE Trans. Biomed. Eng. BME-34, 913–920 (1987).
[CrossRef]

Pinnick, R. G.

Pu, K. Y.

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Ramanarayan, H.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Ren, K. F.

B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. Pure Appl. Opt. 11, 015705 (2009).

Rheinstein, J.

J. Rheinstein, “Scattering of electromagnetic waves from dielectric coated conducting spheres,” IEEE Trans. Antennas Propag. 12, 334–340 (1964).
[CrossRef]

Roumeliotis, J. A.

J. A. Roumeliotis, N. B. Kakogiannos, and J. D. Kanellopoulos, “Scattering from a sphere of small radius embedded into a dielectric one,” IEEE Trans. Microwave Theor. Tech. 43, 155–168 (1995).
[CrossRef]

J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).

Rudy, Y.

Y. Rudy, “The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography,” IEEE Trans. Biomed. Eng. BME-26, 392–399 (1979).
[CrossRef]

Saija, R.

Sasihithlu, K.

Scaife, B. K. P.

R. Dempsey, T. J. Gallagher, and B. K. P. Scaife, “Computation of the potential distribution for a composite dielectric sphere with a noncentral spherical inclusion polarized by a static uniform external field,” in 10th International Conference on Conduction and Breakdown in Dielectric Liquids (1990), pp. 243–247.

Seh, Z. W.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Shah, K. W.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Shanmugam, V.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Sihvola, A.

A. Sihvola, “Character of surface plasmons in layered spherical structures,” Progress Electromagn. Res. 62, 317–331 (2006).

A. Sihvola, Electromagnetic Mixing Formulas and Applications (The Institution of Electrical Engineers, 1999).

Sindoni, O. I.

Skaropoulos, N. C.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Tay, Y. Y.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Uzunoglu, N. K.

Venkov, G.

I. Arnaoudov and G. Venkov, “The transmission acoustic scattering problem for bi-spheres in low frequency regime,” Rend. Istit. Mat. Univ. Trieste XXXVIII, 73–93 (2006).

Vervelidou, F.

Videen, G.

P. Chýlek and G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

G. Videen, D. Ngo, P. Chýlek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
[CrossRef]

Wang, H.

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

Wang, Z.

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Werner, D. H.

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Express 35, 1431–1433 (2010).

Wu, Q.

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Express 35, 1431–1433 (2010).

Xing, S.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Xu, J.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Yan, B.

B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. Pure Appl. Opt. 11, 015705 (2009).

Yan, Q.

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

Yawei, W.

B. Miu and W. Yawei, “Scattering analysis for eccentric-sphere model of single-nuclear cell,” in 2011 Symposium on Photonics and Optoelectronics (SOPO) (2011), pp. 1–4.

Yeh, C. S.

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

Yun, B.

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Zeng, Y.

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Express 35, 1431–1433 (2010).

Zhang, S. Y.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Zhang, Y.

Zhang, Y. W.

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Acc. Chem. Res. (1)

H. Wang, D. W. Brandl, P. Nordlander, and N. J. Halas, “Plasmonic nanostructures: artificial molecules,” Acc. Chem. Res. 40, 53–62 (2007).
[CrossRef]

Angew. Chem. Int. Ed. (1)

Z. W. Seh, S. Liu, S. Y. Zhang, M. S. Bharathi, H. Ramanarayan, M. Low, K. W. Shah, Y. W. Zhang, and M. Y. Han, “Anisotropic growth of titania onto various gold nanostructures: synthesis, theoretical understanding, and optimization for catalysis,” Angew. Chem. Int. Ed. 50, 10140–10143 (2011).
[CrossRef]

Appl. Opt. (2)

J. A. Roumeliotis, J. G. Fikioris, and G. P. Gounaris, “Electromagnetic scattering from an eccentrically coated infinite metallic cylinder,” Appl. Opt. 51, 4488–4493 (1980).

F. Borghese, P. Denti, and R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–493 (1994).
[CrossRef]

Chem. Commun. (1)

W. P. Li, V. Shanmugam, C. C. Huang, G. D. Huang, Y. K. Huang, S. H. Chiu, and C. S. Yeh, “Eccentric inorganic-polymeric nanoparticles formation by thermal induced cross-linked esterification and conversion of eccentricity to raspberry-like Janus,” Chem. Commun. 49, 1609–1611 (2013).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

A. A. Kishk, R. P. Parrikar, and A. Z. Elsherbeni, “Electromagnetic scattering from an eccentric multilayered circular cylinder,” IEEE Trans. Antennas Propag. 40, 295–303 (1992).
[CrossRef]

J. Rheinstein, “Scattering of electromagnetic waves from dielectric coated conducting spheres,” IEEE Trans. Antennas Propag. 12, 334–340 (1964).
[CrossRef]

IEEE Trans. Biomed. Eng. (3)

J. W. Meijs and M. J. Peters, “The EEG and MEG, using a model of eccentric spheres to describe the head,” IEEE Trans. Biomed. Eng. BME-34, 913–920 (1987).
[CrossRef]

B. N. Cuffin, “Eccentric sphere models of the head,” IEEE Trans. Biomed. Eng. 38, 871–878 (1991).
[CrossRef]

Y. Rudy, “The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography,” IEEE Trans. Biomed. Eng. BME-26, 392–399 (1979).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

J. A. Roumeliotis, N. B. Kakogiannos, and J. D. Kanellopoulos, “Scattering from a sphere of small radius embedded into a dielectric one,” IEEE Trans. Microwave Theor. Tech. 43, 155–168 (1995).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

C. Liu, C. C. Mi, and B. Q. Li, “The plasmon resonance of a multilayered gold nanoshell and its potential bioapplications,” IEEE Trans. Nanotechnol. 10, 797–805 (2011).
[CrossRef]

J. Acoust. Soc. Am. (1)

J. McNew, R. Lavarello, and W. D. O’Brien, “Sound scattering from two concentric fluid spheres,” J. Acoust. Soc. Am. 122, 2968–2975 (2007).
[CrossRef]

J. Am. Chem. Soc. (1)

S. Xing, Y. Feng, Y. Y. Tay, T. Chen, J. Xu, M. Pan, J. He, H. H. Hng, Q. Yan, and H. Chen, “Reducing the symmetry of bimetallic Au@Ag nanoparticles by exploiting eccentric polymer shells,” J. Am. Chem. Soc. 132, 9537–9539 (2010).
[CrossRef]

J. Appl. Phys. (1)

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

J. Korean Phys. Soc. (1)

J. S. Kim and J. K. Chang, “Light scattering by two concentric optically active spheres: I. General theory,” J. Korean Phys. Soc. 45, 352–365 (2004).

J. Math. Phys. (1)

R. Nozawa, “Bipolar expansion of screened Coulomb potentials, Helmholtz’ solid harmonics, and their addition theorems,” J. Math. Phys. 7, 1841–1860 (1966).
[CrossRef]

J. Mod. Opt. (1)

G. Gouesbet and G. Grhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).
[CrossRef]

J. Opt. Pure Appl. Opt. (1)

B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. Pure Appl. Opt. 11, 015705 (2009).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

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

J. Phys. A (1)

M. J. Caola, “Solid harmonics and their addition theorems,” J. Phys. A 11, L23–L25 (1978).
[CrossRef]

Nanoscale Res. Lett. (1)

O. Pea-Rodríguez and U. Pal, “Enhanced plasmonic behavior of bimetallic (Ag-Au) multilayered spheres,” Nanoscale Res. Lett. 6, 279–283 (2011).
[CrossRef]

Opt. Commun. (2)

P. Chýlek and G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

B. Yun, Z. Wang, G. Hu, and Y. Cui, “Theoretical studies on the near field properties of non-concentric core–shell nanoparticle dimers,” Opt. Commun. 283, 2947–2952 (2010).
[CrossRef]

Opt. Express (3)

Progress Electromagn. Res. (1)

A. Sihvola, “Character of surface plasmons in layered spherical structures,” Progress Electromagn. Res. 62, 317–331 (2006).

Rend. Istit. Mat. Univ. Trieste (1)

I. Arnaoudov and G. Venkov, “The transmission acoustic scattering problem for bi-spheres in low frequency regime,” Rend. Istit. Mat. Univ. Trieste XXXVIII, 73–93 (2006).

Small (1)

J. Geng, K. Li, K. Y. Pu, D. Ding, and B. Liu, “Conjugated polymer and gold nanoparticle co-loaded PLGA nanocomposites with eccentric internal nanostructure for dual-modal targeted cellular imaging,” Small 8, 2421–2429 (2012).
[CrossRef]

Other (7)

B. Miu and W. Yawei, “Scattering analysis for eccentric-sphere model of single-nuclear cell,” in 2011 Symposium on Photonics and Optoelectronics (SOPO) (2011), pp. 1–4.

R. Dempsey, T. J. Gallagher, and B. K. P. Scaife, “Computation of the potential distribution for a composite dielectric sphere with a noncentral spherical inclusion polarized by a static uniform external field,” in 10th International Conference on Conduction and Breakdown in Dielectric Liquids (1990), pp. 243–247.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Hamilton Printing Company, 1998).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, 1953).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1940).

A. Sihvola, Electromagnetic Mixing Formulas and Applications (The Institution of Electrical Engineers, 1999).

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Figures (10)

Fig. 1.
Fig. 1.

Geometry of the problem: a dielectric sphere in a vacuum with an eccentric spherical inclusion.

Fig. 2.
Fig. 2.

Coefficients of the expansion series in Eq. (3) as a function of the order N, for different eccentricities of the internal sphere in the case of an eccentric PEC sphere inside a dielectric sphere (εs=2.25).

Fig. 3.
Fig. 3.

Real parts of the electric field components computed along a line of coordinates (x,z)=([Rs;0],1.5Rs) in the case of an eccentric PEC sphere inside a dielectric sphere (εs=2.25).

Fig. 4.
Fig. 4.

Real parts of the electric field components computed along a line of coordinates (x,z)=([Rs;0],1.5Rs) in the case of an eccentric dielectric sphere inside a dielectric sphere. The relative permittivity of the external sphere is εs=2.25, and that of the inclusion is εc=5.

Fig. 5.
Fig. 5.

Polarizability of a sphere of radius Rs with a spherical inclusion of radius Rc as a function of the distance between the centers of the spheres. The permittivities of the two spheres are the same as in Fig. 4. Different values of the ratio Rc/Rs are considered.

Fig. 6.
Fig. 6.

Real part of the electric field component along z on a point of the positive z axis at a distance 1.5Rs from the center of the external sphere as a function of the distance between the centers of the two spheres. The parameters of the two spheres are the same as in Fig. 5.

Fig. 7.
Fig. 7.

Geometry of two internally tangential spheres with different values of the radius of the internal sphere.

Fig. 8.
Fig. 8.

Effective permittivity of two internally tangential spheres as a function of the radius of the internal sphere. The parameters of the two spheres are the same as in Fig. 5.

Fig. 9.
Fig. 9.

Normalized polarizability of two eccentric spheres, with a dielectric external sphere with relative permittivity εs=4, and an internal sphere with radius Rc=Rs/2, as a function of the relative permittivity εc of the internal sphere.

Fig. 10.
Fig. 10.

Normalized polarizability of two eccentric spheres, with an internal sphere with radius Rc=Rs/2 and a relative permittivity εc=4, as a function of the relative permittivity εs of the external sphere.

Equations (30)

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

E0=E0z0,
Φ(r,ϑ,φ)=n=0m=nn(amnrn+bmnrn+1)Pnm(cosϑ)eimφ,
Φ0(r)=n=0(anrn+bnrn+1)Pn(cosϑ),
Φs(r)=n=0(ansrn+bnsrn+1)Pn(cosϑ).
Φ0(r)=Φs(r)forr=Rs,
ε0Φ0(r)r=εsΦs(r)rforr=Rs,
Φs(r)=U0forr=Rc,
limrΦ0(r)=E0.
rnPnm(cosϑ)eimφ=dnν=mn(1)nν(n+m)!(nν)!(m+ν)!·(rd)νPν(cosϑ)eimφ,
1rn+1Pnm(cosϑ)eimφ=1dn+1ν=mn(νm)!(nm)!(νn)!·(dr)ν+1Pν(cosϑ)eimφ.
rnPn(cosϑ)=dnν=0n(1)nνn!(nν)!ν!(rd)νPν(cosϑ),
1rnPn(cosϑ)=1dn+1ν=nν!n!(νn)!·(dr)ν+1Pν(cosϑ).
Φs(r)=n=0Pn(cosϑ)[(rd)nν=naνs(d)νγνn+(dr)n+1ν=0nbνs(d)ν+1λνn]
γνn=(1)νnν!(νn)!n!,
λνn=n!ν!(nν)!.
ππPm(cosϑ)Pn(cosϑ)dϑ=22n+1δmn.
EaRsn+bnRsn+1=ansRsn+bnsRsn+1,
nEaRsn1(n+1)bnRsn+2=ϵsϵ0[nansRsn1(n+1)bnsRsn+2],
Rcn(d)nν=naνsγνn(d)ν+(d)n+1Rcn+1ν=0nbνsλνn(d)ν+1=U0.
Φc(r)=n=0ancrnPn(cosϑ).
Φ0(r)=Φs(r)forr=Rs,
ε0Φ0(r)r=εsΦs(r)rforr=Rs,
Φs(r)=Φc(r)forr=Rc,
εsΦs(r)r=εcΦc(r)rforr=Rc.
bnR2n+1ansbnsR2n+1=E0δ1n,
ε0εsNnbnR2n+1ans+NnbnsR2n+1=ε0εsE0δ1n,
ν=n[aνs(d)νnγνn]+ν=1n[bνs(d)nνRc2n+1λνn]anc=0,
εsεcν=n[aνs(d)νnγνn]εsεcNnν=1n[bνs(d)nνRc2n+1λνn]anc=0.
α=4πε0b1E0.
εeff=ε0+αV1α3ε0V,

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