Abstract

Spherical nanoclusters (NCs) with a central dielectric core surrounded by several satellite plasmonic nanospheres have been recently investigated as aggregates supporting electric and magnetic collective resonances. Notably, the collective magnetic resonance has been exploited to provide magnetic properties in optics, i.e., materials with macroscopic relative permeability different from unity. The NCs discussed in this paper can be realized using state-of-the-art nanochemistry self-assembly techniques. Accordingly, perfectly regular disposition of the nanoplasmonic satellites is not possible and this paper constitutes the first comprehensive analysis of the effect of such irregularities onto the electric and magnetic collective resonances. In particular we will show that the peak of the scattering cross section associated to the magnetic resonance is very sensitive to certain irregularities and significantly less to others. It is shown here that “artificial magnetic” properties of NCs are preserved for certain degrees of irregularities of the nanosatellites positions, however they are strongly affected by irregularities in the plasmonic nanosatellites sizes and by the presence of “defects” caused by the absence of satellites in the process of self-assembly around the dielectric core. The “artificial electric” resonance is instead less affected by irregularities mainly because of its wider frequency bandwidth.

© 2013 OSA

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2012

2011

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett.11(9), 3927–3934 (2011).
[CrossRef] [PubMed]

A. Vallecchi, M. Albani, and F. Capolino, “Collective electric and magnetic plasmonic resonances in spherical nanoclusters,” Opt. Express19(3), 2754–2772 (2011).
[CrossRef] [PubMed]

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

D. Morits and C. Simovski, “Isotropic negative effective permeability in the visible range produced by clusters of plasmonic triangular nanoprisms,” Metamaterials (Amst.)5(3), 71–78 (2011).

2010

D. K. Morits and C. R. Simovski, “Negative effective permeability at optical frequencies produced by rings of plasmonic dimers,” Phys. Rev. B81(20), 205112 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

2009

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, “Model of isotropic resonant magnetism in the visible range based on core-shell clusters,” Phys. Rev. B79(4), 045111 (2009).
[CrossRef]

A. Alù and N. Engheta, “The quest for magnetic plasmons at optical frequencies,” Opt. Express17(7), 5723–5730 (2009).
[CrossRef] [PubMed]

2008

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

2007

2006

1986

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. Lond. A Math. Phys. Sci.405(1829), 329–344 (1986).
[CrossRef]

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys.59(8), 2609 (1986).
[CrossRef]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961).
[CrossRef]

Albani, M.

Alù, A.

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

Bao, K.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

Brandl, D.

Bürgi, T.

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov, G. Shvets, J. A. Fan, F. Capasso, D. Brandl, and P. Nordlander, “Plasmonic nanoclusters: a path towards negative-index metafluids,” Opt. Express15(21), 14129–14145 (2007).
[CrossRef] [PubMed]

Capolino, F.

Clare, B. W.

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. Lond. A Math. Phys. Sci.405(1829), 329–344 (1986).
[CrossRef]

Cunningham, A.

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Dintinger, J.

Dionne, J. A.

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett.11(9), 3927–3934 (2011).
[CrossRef] [PubMed]

Engheta, N.

Etrich, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Fan, J. A.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov, G. Shvets, J. A. Fan, F. Capasso, D. Brandl, and P. Nordlander, “Plasmonic nanoclusters: a path towards negative-index metafluids,” Opt. Express15(21), 14129–14145 (2007).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961).
[CrossRef]

García-Etxarri, A.

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett.11(9), 3927–3934 (2011).
[CrossRef] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

Halas, N. J.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Helgert, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Kepert, D. L.

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. Lond. A Math. Phys. Sci.405(1829), 329–344 (1986).
[CrossRef]

Kley, E.-B.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Lederer, A. F.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Lederer, F.

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

Manoharan, V. N.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Menzel, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Morits, D.

D. Morits and C. Simovski, “Isotropic negative effective permeability in the visible range produced by clusters of plasmonic triangular nanoprisms,” Metamaterials (Amst.)5(3), 71–78 (2011).

Morits, D. K.

D. K. Morits and C. R. Simovski, “Negative effective permeability at optical frequencies produced by rings of plasmonic dimers,” Phys. Rev. B81(20), 205112 (2010).
[CrossRef]

Mühlig, S.

J. Dintinger, S. Mühlig, C. Rockstuhl, and T. Scharf, “A bottom-up approach to fabricate optical metamaterials by self-assembled metallic nanoparticles,” Opt. Mater. Express2(3), 269–278 (2012).
[CrossRef]

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Nordlander, P.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov, G. Shvets, J. A. Fan, F. Capasso, D. Brandl, and P. Nordlander, “Plasmonic nanoclusters: a path towards negative-index metafluids,” Opt. Express15(21), 14129–14145 (2007).
[CrossRef] [PubMed]

Pacholski, C.

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Pedersen, N. E.

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys.59(8), 2609 (1986).
[CrossRef]

Pertsch, T.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Rockstuhl, C.

J. Dintinger, S. Mühlig, C. Rockstuhl, and T. Scharf, “A bottom-up approach to fabricate optical metamaterials by self-assembled metallic nanoparticles,” Opt. Mater. Express2(3), 269–278 (2012).
[CrossRef]

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Salandrino, A.

Scharf, T.

Scheeler, S.

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

Sheikholeslami, S. N.

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett.11(9), 3927–3934 (2011).
[CrossRef] [PubMed]

Shvets, G.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov, G. Shvets, J. A. Fan, F. Capasso, D. Brandl, and P. Nordlander, “Plasmonic nanoclusters: a path towards negative-index metafluids,” Opt. Express15(21), 14129–14145 (2007).
[CrossRef] [PubMed]

Simovski, C.

D. Morits and C. Simovski, “Isotropic negative effective permeability in the visible range produced by clusters of plasmonic triangular nanoprisms,” Metamaterials (Amst.)5(3), 71–78 (2011).

Simovski, C. R.

D. K. Morits and C. R. Simovski, “Negative effective permeability at optical frequencies produced by rings of plasmonic dimers,” Phys. Rev. B81(20), 205112 (2010).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, “Model of isotropic resonant magnetism in the visible range based on core-shell clusters,” Phys. Rev. B79(4), 045111 (2009).
[CrossRef]

Tretyakov, S. A.

C. R. Simovski and S. A. Tretyakov, “Model of isotropic resonant magnetism in the visible range based on core-shell clusters,” Phys. Rev. B79(4), 045111 (2009).
[CrossRef]

Tünnermann, A.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, A. F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B79(23), 233107 (2009).
[CrossRef]

Urzhumov, Y. A.

Vallecchi, A.

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

Waterman, P. C.

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys.59(8), 2609 (1986).
[CrossRef]

Wu, C.

J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett.10(11), 4680–4685 (2010).
[CrossRef] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008).
[CrossRef] [PubMed]

ACS Nano

S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano5(8), 6586–6592 (2011).
[CrossRef] [PubMed]

J. Appl. Phys.

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys.59(8), 2609 (1986).
[CrossRef]

Metamaterials (Amst.)

D. Morits and C. Simovski, “Isotropic negative effective permeability in the visible range produced by clusters of plasmonic triangular nanoprisms,” Metamaterials (Amst.)5(3), 71–78 (2011).

Nano Lett.

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Figures (21)

Fig. 1
Fig. 1

Types of irregularities that can occur in 3D spherical NCs realized by self-assembly techniques: (a) theoretical perfectly regular arrangement, (b) variable sizes of nanosatellites, (c) displacement of nanosatellites with respect to nominal positions, and (d) presence of nanosatellites defects.

Fig. 2
Fig. 2

(a) Sample tetrahedral NC with randomly variable particle size ( r 0 =20 , Δ r p =4 nm). (b) Particle size distribution for the simulated population of 100 NCs.

Fig. 3
Fig. 3

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 100 tetrahedral NCs with r 0 =20 nm and for Δ r p =4 nm from Fig. 2. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 4
Fig. 4

(a) Sample icosahedral NC with randomly variable particle size ( r 0 =15 , Δ r p =3 nm). (b) Particle size distribution for the simulated population of 100 NCs.

Fig. 5
Fig. 5

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 100 icosahedral NCs with r 0 =15 nm and for Δ r p =3 nm from Fig. 4. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 6
Fig. 6

(a) Sample 32-element NC with randomly variable particle size ( r 0 =10 , Δ r p =2 nm). (b) Particle size distribution for the simulated population of 100 NCs.

Fig. 7
Fig. 7

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 32-nanosatellites NCs with r 0 =10 nm and for Δ r p =2 nm from Fig. 6. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 8
Fig. 8

(a) Sample 48-element NC with randomly variable particle size ( r 0 =8.5 , Δ r p =1.7 nm). (b) Particle size distribution for the simulated population of 100 NCs.

Fig. 9
Fig. 9

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 48-nanosatellites NCs with r 0 =8.5 nm and for Δ r p =1.7 nm from Fig. 8. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 10
Fig. 10

(a) Sample tetrahedral NC with randomly variable particle positions ( r 0 =20 , ΔR=4 nm). (b) Distribution of nanoparticle displacement distances from their nominal positions for the simulated population of 100 NCs.

Fig. 11
Fig. 11

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 100 tetrahedral NCs with r 0 =20 nm and variable nanosatellites positions ( ΔR=4 ) nm from Fig. 10. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 12
Fig. 12

(a) Sample icosahedral NC with randomly variable particle positions ( r 0 =15 , ΔR=3 nm). (b) Distribution of nanoparticle displacement distances from their nominal positions for the simulated population of 100 NCs.

Fig. 13
Fig. 13

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 100 icosahedral NCs with r 0 =15 nm and variable nanosatellites positions ( ΔR=3 nm) from Fig. 12. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 14
Fig. 14

(a) Sample 32-element NC with randomly variable particle positions ( r 0 =10 , ΔR=2 nm). (b) Distribution of nanoparticle displacement distances from their nominal positions for the simulated population of 100 NCs.

Fig. 15
Fig. 15

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 32-nanosatellites NCs with r 0 =10 nm and variable nanosatellites positions ( ΔR=2 ) nm from Fig. 14. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 16
Fig. 16

(a) Sample 48-element NC with randomly variable particle positions ( r 0 =8.5 , ΔR=1.7 nm). (b) Distribution of nanoparticle displacement distances from their nominal positions for the simulated population of 100 NCs.

Fig. 17
Fig. 17

Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 48-nanosatellites NCs with r 0 =8.5 nm and variable nanosatellites positions ( ΔR=1.7 nm) from Fig. 16. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 18
Fig. 18

(a) Sample defective tetrahedral NC ( r 0 =20 nm) with 1 missing nanosatellite. (b) Scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles of the four tetrahedral NCs with 1 defect.

Fig. 19
Fig. 19

(a) Sample defective icosahedral NC ( r 0 =15 ) with 3 missing nanosatellites. (b) Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of 100 defective icosahedral NCs with variable locations of the 3 missing nanosatellites. The 5, 50, and 95 percentile curves are superimposed to the relative pdfs (color shaded stripes).

Fig. 20
Fig. 20

(a) Sample defective 32-element NC ( r 0 =10 nm) with 8 missing nanosatellites. (b) Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of defective 32-element NCs with variable locations of the 8 missing nanosatellites. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Fig. 21
Fig. 21

(a) Sample defective 48-element NC ( r 0 =8.5 nm) with 12 missing nanosatellites. (b) Statistics of the scattering efficiency contributions associated with the induced electric and magnetic dipole moments and the remaining higher order multipoles for the population of defective 48-element NCs with variable locations of the 12 missing nanosatellites. The 5, 50, and 95 percentile curves are superimposed to the relative empirical pdfs (color shaded stripes).

Equations (4)

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ε m = ε ω p 2 ω[ ω+iΓ( r p ) ]
Γ( r p )= Γ +A v F r p .
[ r p ]=( r 0 Δ r p )+2Δ r p rand(N)
[ Δ θ p ]= [ Δ R p ] ( r 0 +a+ t c ) = ΔRrand(N) ( r 0 +a+ t c ) ;[ Δ ϕ p ]=2πrand(N)

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