Abstract

Dielectric spheres which are much smaller than a wavelength and made of a large permittivity can support magnetic dipole modes of great purity. We investigate the coupling of such magnetic dipoles by studying sub-wavelength dielectric spheres arranged in clusters as pairs, chains, and rings. The coupling among the spheres creates hybridized modes, which may be used to engineer metamaterials with more degrees of freedom than by using single particles. Two methods of analysis are used: an approximate coupled dipole model and an exact transition-matrix approach. An experimental setup employs a focused Gaussian beam excitation. The magnetic coupling presented here is similar to the coupling of plasmonic modes in metal nanoparticles. Therefore, these experimental results are also a verification of several analogous plasmonic systems.

© 2010 Optical Society of America

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2009 (1)

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

2008 (6)

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles,” Phys. Rev. B 78, 085112 (2008).
[CrossRef]

W. Park and Q. Wu, “Negative effective permeability in metal cluster photonic crystal,” Solid State Commun. 146, 221–227 (2008).
[CrossRef]

W.-Y. Chien and T. Szkopek, “Multiple-multipole simulation of optical nearfields in discrete metal nanosphere assemblies,” Opt. Express 16, 1820–1835 (2008).
[CrossRef] [PubMed]

K. H. Fung and C. T. Chan, “Analytical study of the plasmonic modes of a metal nanoparticle circular array,” Phys. Rev. B 77, 205423 (2008).
[CrossRef]

B. Stout, J.-C. Auger, and A. Devilez, “Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations,” J. Opt. Soc. Am. A 25, 2549–2557 (2008).
[CrossRef]

2007 (5)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[CrossRef]

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

2006 (3)

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14, 1557–1567 (2006).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

2005 (5)

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

S. Riikonen, I. Romero, and F. J. García de Abajo, “Plasmon tunability in metallodielectric metamaterials,” Phys. Rev. B 71, 235104 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2004 (1)

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

2002 (2)

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14, 4035–4044 (2002).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple-scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

1999 (1)

F. J. García de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
[CrossRef]

1996 (1)

1995 (1)

1993 (1)

1971 (3)

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part I—Multipole expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. 19, 378–390 (1971).
[CrossRef]

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part II—Numerical and experimental results,” IEEE Trans. Antennas Propag. 19, 391–400 (1971).
[CrossRef]

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles,” Phys. Rev. B 78, 085112 (2008).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14, 1557–1567 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Auger, J. -C.

B. Stout, J.-C. Auger, and A. Devilez, “Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations,” J. Opt. Soc. Am. A 25, 2549–2557 (2008).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple-scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Bohren, C. F.

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

Brongersma, M. L.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

Bruning, J.

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part II—Numerical and experimental results,” IEEE Trans. Antennas Propag. 19, 391–400 (1971).
[CrossRef]

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part I—Multipole expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. 19, 378–390 (1971).
[CrossRef]

Chan, C. T.

K. H. Fung and C. T. Chan, “Analytical study of the plasmonic modes of a metal nanoparticle circular array,” Phys. Rev. B 77, 205423 (2008).
[CrossRef]

Chang, C. -C.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[CrossRef]

Chen, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Chen, J. I. L.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

Chern, R. -L.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).

Chien, W. -Y.

Devilez, A.

Ding, K. -H.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, 2000).
[CrossRef]

Du, B.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Engheta, N.

A. Alù and N. Engheta, “Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles,” Phys. Rev. B 78, 085112 (2008).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14, 1557–1567 (2006).
[CrossRef] [PubMed]

Etrich, C.

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Ford, G. W.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Fung, K. H.

K. H. Fung and C. T. Chan, “Analytical study of the plasmonic modes of a metal nanoparticle circular array,” Phys. Rev. B 77, 205423 (2008).
[CrossRef]

García de Abajo, F. J.

S. Riikonen, I. Romero, and F. J. García de Abajo, “Plasmon tunability in metallodielectric metamaterials,” Phys. Rev. B 71, 235104 (2005).
[CrossRef]

F. J. García de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
[CrossRef]

Gashinova, M. S.

O. G. Vendik and M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” in Proceedings of the 34th European Microwave Conference (IEEE, 2004), Vol. 3, pp. 1209–1212.

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998).

Grzegorczyk, T. M.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Huang, X.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Huffman, D. R.

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

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kang, L.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Koenderink, A. F.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Kong, J. A.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, 2000).
[CrossRef]

Kreibig, U.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Lafait, J.

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple-scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Lederer, F.

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Li, B.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Li, L.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Liu, X. -X.

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[CrossRef]

Lo, Y.

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part I—Multipole expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. 19, 378–390 (1971).
[CrossRef]

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part II—Numerical and experimental results,” IEEE Trans. Antennas Propag. 19, 391–400 (1971).
[CrossRef]

Mackowski, D. W.

Maier, S. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Markel, V. A.

Mishchenko, M. I.

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Moroz, A.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

O’Brien, S.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14, 4035–4044 (2002).
[CrossRef]

Ozin, G. A.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

Park, W.

W. Park and Q. Wu, “Negative effective permeability in metal cluster photonic crystal,” Solid State Commun. 146, 221–227 (2008).
[CrossRef]

Pendry, J. B.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14, 4035–4044 (2002).
[CrossRef]

Peng, L.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Penninkhof, J. J.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Pertsch, T.

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Polman, A.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Quinten, M.

Ran, L.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Riikonen, S.

S. Riikonen, I. Romero, and F. J. García de Abajo, “Plasmon tunability in metallodielectric metamaterials,” Phys. Rev. B 71, 235104 (2005).
[CrossRef]

Rockstuhl, C.

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Romero, I.

S. Riikonen, I. Romero, and F. J. García de Abajo, “Plasmon tunability in metallodielectric metamaterials,” Phys. Rev. B 71, 235104 (2005).
[CrossRef]

Salandrino, A.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Scharf, T.

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Schuller, J. A.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

Stout, B.

B. Stout, J.-C. Auger, and A. Devilez, “Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations,” J. Opt. Soc. Am. A 25, 2549–2557 (2008).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple-scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

Sweatlock, L. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

Szkopek, T.

Taubner, T.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Tretyakov, S.

S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

Tsang, L.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, 2000).
[CrossRef]

Vendik, O. G.

O. G. Vendik and M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” in Proceedings of the 34th European Microwave Conference (IEEE, 2004), Vol. 3, pp. 1209–1212.

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P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Weber, W. H.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Wu, Q.

W. Park and Q. Wu, “Negative effective permeability in metal cluster photonic crystal,” Solid State Commun. 146, 221–227 (2008).
[CrossRef]

Xie, Q.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

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V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

Zhang, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

Zhao, H.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhao, Q.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhou, J.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zia, R.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

Appl. Opt. (1)

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[CrossRef]

J. Bruning and Y. Lo, “Multiple scattering of EM waves by spheres part II—Numerical and experimental results,” IEEE Trans. Antennas Propag. 19, 391–400 (1971).
[CrossRef]

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S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Mod. Opt. (1)

B. Stout, J.-C. Auger, and J. Lafait, “A transfer matrix approach to local field calculations in multiple-scattering problems,” J. Mod. Opt. 49, 2129–2152 (2002).
[CrossRef]

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

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

J. Phys. Condens. Matter (2)

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14, 4035–4044 (2002).
[CrossRef]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

Nat. Photonics (1)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (10)

A. Alù and N. Engheta, “Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles,” Phys. Rev. B 78, 085112 (2008).
[CrossRef]

S. Riikonen, I. Romero, and F. J. García de Abajo, “Plasmon tunability in metallodielectric metamaterials,” Phys. Rev. B 71, 235104 (2005).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79, 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated non-magnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[CrossRef]

F. J. García de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B 60, 6086–6102 (1999).
[CrossRef]

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

K. H. Fung and C. T. Chan, “Analytical study of the plasmonic modes of a metal nanoparticle circular array,” Phys. Rev. B 77, 205423 (2008).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Phys. Rev. E (1)

R.-L. Chern, X.-X. Liu, and C.-C. Chang, “Particle plasmons of metal nanospheres: application of multiple scattering approach,” Phys. Rev. E 76, 016609 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. 99, 017401 (2007).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98, 157403 (2007).
[CrossRef] [PubMed]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[CrossRef] [PubMed]

Solid State Commun. (1)

W. Park and Q. Wu, “Negative effective permeability in metal cluster photonic crystal,” Solid State Commun. 146, 221–227 (2008).
[CrossRef]

Other (9)

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

O. G. Vendik and M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” in Proceedings of the 34th European Microwave Conference (IEEE, 2004), Vol. 3, pp. 1209–1212.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley-Interscience, 2000).
[CrossRef]

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Magnitudes of the Mie scattering coefficients of a dielectric sphere, having radius r s = 1.07   mm , permittivity ε s = 112 + 0.1 i , and unit permeability. The curves are a 1 electric dipole, b 1 magnetic dipole, a 2 electric quadrupole, and b 2 magnetic quadrupole. The magnetic dipole is dominant throughout the range of frequencies used in the experimental results, 11–15 GHz.

Fig. 2
Fig. 2

A cluster of N s particles, bounded by a dashed sphere. Particle j, in isolation, is modeled by T ¯ 1 ( j ) , and after calculating the multiple scattering solution the cluster within the dashed boundary is modeled by T ¯ clust . The incident wave is represented by a, and f is the total scattered field.

Fig. 3
Fig. 3

Schematic of the microwave horn and dielectric lens used to focus a Gaussian beam over a sample sphere. The setup is completed by the mirror image to receive the signal. Some of the curved wavefronts are shown with dashed lines; notice that there is a beam waist within the horn, not at its aperture.

Fig. 4
Fig. 4

Transmittance through various spacings of paired spheres. On the left are longitudinal modes, where the symmetry axis is parallel to the incident magnetic field, and on the right are transverse modes, where the symmetry axis is perpendicular to the incident magnetic field and parallel to the direction of incident field propagation. The arrows denote the resonant frequencies calculated with the coupled dipole theory, and empty arrowheads indicate uncoupled modes.

Fig. 5
Fig. 5

The normal modes of a chain of eight touching spheres, calculated with the coupled magnetic dipole model. The mode frequencies are shown for the longitudinal (L) and transverse (T) polarizations.

Fig. 6
Fig. 6

Transmittance through a chain of eight touching dielectric spheres. The top panel is for the chain axis parallel to the incident magnetic field, and the bottom panel is for the chain axis perpendicular to the incident magnetic field (and parallel to the propagation direction). The arrows denote the resonant frequencies calculated with the coupled magnetic dipole theory, and empty arrowheads indicate uncoupled modes.

Fig. 7
Fig. 7

The normal modes of a ring of four touching spheres. The arrows denote the induced magnetic dipole vectors.

Fig. 8
Fig. 8

The top two panels show the transmittance through a ring of touching dielectric spheres, for two orientations. The arrows denote the resonant frequencies calculated with the coupled magnetic dipole theory, and empty arrowheads indicate uncoupled modes. The bottom two panels show the calculated effective permittivity and permeability, using the T-matrix results, of a periodic metamaterial having the ring as the basis unit.

Fig. 9
Fig. 9

Comparison of the magnitudes of the effective electric polarizabilities of the ring, as arranged in the top panel in Fig. 8, and a single sphere of volume equal to the four spheres comprising the ring.

Equations (33)

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

H inc ( r ) = H 0 inc   exp ( i k inc r ) ,
b 1 = n h ψ 1 ( x s ) ψ 1 ( x h ) n s ψ 1 ( x h ) ψ 1 ( x s ) n h ψ 1 ( x s ) ξ 1 ( x h ) n s ξ 1 ( x h ) ψ 1 ( x s ) ,
α m = 6 π i k 0 3 b 1 .
f m c / 2 n s r s .
H ( r ) = e i k 0 r 4 π [ k 0 2 r ( I ¯ r ̂ r ̂ ) + ( 3 r ̂ r ̂ I ¯ ) ( 1 r 3 i k 0 r 2 ) ] m = G ¯ ( r ) m ,
H loc ( x j ) = H inc ( x j ) + k j N s H k ( x j x k ) ,
1 α m m j k j N s G ¯ ( x j x k ) m k = H inc ( x j ) .
A j k = { 1 / α m , j = k y ̂ G ¯ ( x j x k ) y , ̂ j k } .
F ( r ̂ ) = r e i k 0 r H sca = k 0 2 4 π j = 1 N s [ m j ( m j r ̂ ) r ̂ ] exp ( i k 0 r ̂ x j ) ,
C ext = 4 π k 0 | H 0 inc | 2 Im { F ( k ̂ inc ) H 0 inc } .
E inc ( r ) = E 0   Rg   Ψ T ( k 0 r ) a ,
E sca ( r ) = E 0 Ψ T ( k 0 r ) f ,
a l m M = i l + 1 π ( 2 l + 1 ) ( δ m , + 1 + δ m , 1 ) ,
a l m N = i l + 1 π ( 2 l + 1 ) ( δ m , + 1 δ m , 1 ) ,
f = T ¯ 1 a .
f = T ¯ clust a ,
T ¯ clust = j , k = 1 N s J ¯ ( 0 , j ) T ¯ N s ( j , k ) J ¯ ( k , 0 ) .
C ext = 1 k 0 2 Re { a T ¯ clust a } = 1 k 0 2 j , k = 1 N s Re { exp [ i k 0 z ̂ ( x k x j ) ] a T ¯ N s ( j , k ) a } ,
ε r , x x eff 1 ε r , x x eff + 2 = N 3 [ 1 α e , x x + i ( k 0 3 6 π ) ] 1 ,
μ r , y y eff 1 μ r , y y eff + 2 = N 3 [ 1 α m , y y + i ( k 0 3 6 π ) ] 1 ,
E dipole sca = η 0 k 0 3 4 π ( r ̂ × m ) h 1 ( 1 ) ( k 0 r ) ,
m = E 0 3 π η 0 k 0 3 [ ( f 1 , 1 M f 1 , 1 M ) x ̂ i ( f 1 , 1 M + f 1 , 1 M ) y ̂ + 2 f 1 , 0 M z ̂ ] .
α m , y y = | m y H y | H x = H z = 0 = i 3 π k 0 3 ( f 1 , 1 M + f 1 , 1 M ) .
α e , x x = | p x ε 0 E x | E y = E z = 0 = 3 π i k 0 3 ( f 1 , 1 N f 1 , 1 N ) .
T calc = I t I 0 1 C ext A b ,
Δ l = 1 N f i = 1 N f | C ext l ( f i ) C ext l 1 ( f i ) C ext l 1 ( f i ) | ,
Ψ T ( k r ) f = [ M ( k r ) N ( k r ) ] [ f M f N ] = l = 1 m = l l f l m M M l m ( k r ) + f l m N N l m ( k r ) .
M l m ( k r ) = h l ( 1 ) ( k r ) X l m ( r ̂ ) ,
N l m ( k r ) = 1 k r { l ( l + 1 ) h l ( 1 ) ( k r ) Y l m ( r ̂ ) + [ k r h l ( 1 ) ( k r ) ] Z l m ( r ̂ ) } ,
Y l m ( r ̂ ) = γ l m l ( l + 1 ) P l m ( cos   θ ) e i m ϕ r ̂ ,
X l m ( r ̂ ) = γ l m e i m ϕ [ i m sin   θ P l m ( cos   θ ) θ ̂ + d d θ P l m ( cos   θ ) ϕ ̂ ] ,
Z l m ( r ̂ ) = γ l m e i m ϕ [ d d θ P l m ( cos   θ ) θ ̂ + i m sin   θ P l m ( cos   θ ) ϕ ̂ ] ,
γ l m = ( 2 l + 1 ) ( l m ) ! 4 π l ( l + 1 ) ( l + m ) ! ,

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