We investigate the optical properties of a true three-dimensional metamaterial that was fabricated using a self-assembly bottom-up technology. The metamaterial consists of closely packed spherical clusters being formed by a large number of non-touching gold nanoparticles. After presenting experimental results, we apply a generalized Mie theory to analyze its spectral response revealing that it is dominated by a magnetic dipole contribution. By using an effective medium theory we show that the fabricated metamaterial exhibits a dispersive effective permeability, i.e. artificial magnetism. Although this metamaterial is not yet left-handed it might serve as a starting point for achieving bulk metamaterials by using bottom-up approaches.

© 2011 OSA

1. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
2. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31–37 (2008). [CrossRef]
3. T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79, 115430 (2009). [CrossRef]
4. D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with a SRR-like geometry,” Adv. Funct. Mater. 20, 1116–1124 (2010). [CrossRef]
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6. C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B 81, 035320 (2010). [CrossRef]
7. 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]
8. C. R. Simovski and S. A. Tretyakov, “Model of isotropic resonant magnetism in the visible range based on core-shell clusters,” Phys. Rev. B 79, 045111 (2009). [CrossRef]
9. A. Vallecchi, M. Albani, and F. Capolino, “Collective electric and magnetic plasmonic resonances in spherical nanoclusters,” Opt. Express 19, 2754–2772 (2011). [CrossRef] [PubMed]
10. V. Yannopapas, “Subwavelength imaging of light by arrays of metal-coated semiconductor nanoparticles: a theoretical study,” J. Phys.: Condens. Matter 20, 255201 (2008). [CrossRef]
11. 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]
12. 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]
13. V. Yannopapas, “Artificial magnetism and negative refractive index in three-dimensional metamaterials of spherical particles at near-infrared and visible frequencies,” Appl. Phys. A 87, 259–264 (2007). [CrossRef]
14. V. A. Tamma, J.-H. Lee, Q. Wu, and W. Park, “Visible frequency magnetic activity in silver nanocluster metamaterial,” Appl. Opt. 49, A11–A17 (2010). [CrossRef] [PubMed]
15. J. Bang, U. Jeong, D. Y. Ryu, T. P. Russell, and C. J. Hawker, “Block copolymer nanolithography: translation of molecular level control to nanoscale patterns,” Adv. Mater. 21, 4769–4792 (2009). [CrossRef]
16. H. Fan, “Nanocrystal-micelle: synthesis, self-assembly and application,” Chem. Commun. , 1383–1394 (2008). [CrossRef]
17. S. Frein, J. Boudon, M. Vonlanthen, T. Scharf, J. Barberá, G. Süss-Fink, T. Bürgi, and R. Deschenaux, “Liquid-crystalline thiol- and disulfide-based dendrimers for the functionalization of gold nanoparticles,” Helv. Chim. Acta 91, 2321–2337 (2008). [CrossRef]
18. P. W. K. Rothemund, “Folding DNA to create nanoscale shapes and patterns,” Nature 440, 297–302 (2006). [CrossRef] [PubMed]
19. C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009). [CrossRef]
20. V. Yannopapas, “Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres,” Phys. Rev. B 75, 035112 (2007). [CrossRef]
21. N. Shalkevich, A. Shalkevich, L. Si-Ahmed, and T. Bürgi, “Reversible formation of gold nanoparticle–surfactant composite assemblies for the preparation of concentrated colloidal solutions,” Phys. Chem. Chem. Phys. 11, 10175–10179 (2009). [CrossRef] [PubMed]
22. G. Frens, “Controlled nucleation for the regulation of the particle size in monodisperse gold suspensions,” Nature (London), Phys. Sci. 241, 20–22 (1973).
23. Y.-l. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995). [CrossRef] [PubMed]
24. S. Mühlig, C. Rockstuhl, J. Pniewski, C. R. Simovski, S. A. Tretyakov, and F. Lederer, “Three–dimensional metamaterial nanotips,” Phys. Rev. B 81, 075317 (2010). [CrossRef]
25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
26. T. Okamoto, “Near-field spectral analysis of metallic beads,” in Near-Field Optics and Surface Plasmon Polaritons , S. Kawata, ed. (Springer, 2001), pp. 97–123. [CrossRef]
27. 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]
28. J. D. Jackson, “Radiating systems, multipole fields and radiation,” in Classical Electrodynamics , 3rd ed. (Wiley, 1999), pp. 407–455.
29. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
30. H. Yan, S. I. Lim, Y.-J. Zhang, Q. Chen, D. Mott, W.-T. Wu, D.-L. An, S. Zhou, and C.-J. Zhong, “Molecularly-mediated assembly of gold nanoparticles with interparticle rigid, conjugated and shaped aryl ethynyl structures,” Chem. Commun. 46, 2218–2220 (2010). [CrossRef]

Adv. Funct. Mater.

• D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with a SRR-like geometry,” Adv. Funct. Mater. 20, 1116–1124 (2010). [CrossRef]

Adv. Mater.

• J. Bang, U. Jeong, D. Y. Ryu, T. P. Russell, and C. J. Hawker, “Block copolymer nanolithography: translation of molecular level control to nanoscale patterns,” Adv. Mater. 21, 4769–4792 (2009). [CrossRef]

Appl. Opt.

• Y.-l. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995). [CrossRef] [PubMed]
• V. A. Tamma, J.-H. Lee, Q. Wu, and W. Park, “Visible frequency magnetic activity in silver nanocluster metamaterial,” Appl. Opt. 49, A11–A17 (2010). [CrossRef] [PubMed]

Appl. Phys. A

• V. Yannopapas, “Artificial magnetism and negative refractive index in three-dimensional metamaterials of spherical particles at near-infrared and visible frequencies,” Appl. Phys. A 87, 259–264 (2007). [CrossRef]

Chem. Commun.

• H. Fan, “Nanocrystal-micelle: synthesis, self-assembly and application,” Chem. Commun. , 1383–1394 (2008). [CrossRef]
• H. Yan, S. I. Lim, Y.-J. Zhang, Q. Chen, D. Mott, W.-T. Wu, D.-L. An, S. Zhou, and C.-J. Zhong, “Molecularly-mediated assembly of gold nanoparticles with interparticle rigid, conjugated and shaped aryl ethynyl structures,” Chem. Commun. 46, 2218–2220 (2010). [CrossRef]

Helv. Chim. Acta

• S. Frein, J. Boudon, M. Vonlanthen, T. Scharf, J. Barberá, G. Süss-Fink, T. Bürgi, and R. Deschenaux, “Liquid-crystalline thiol- and disulfide-based dendrimers for the functionalization of gold nanoparticles,” Helv. Chim. Acta 91, 2321–2337 (2008). [CrossRef]

J. Phys.: Condens. Matter

• V. Yannopapas, “Subwavelength imaging of light by arrays of metal-coated semiconductor nanoparticles: a theoretical study,” J. Phys.: Condens. Matter 20, 255201 (2008). [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]

Nature

• P. W. K. Rothemund, “Folding DNA to create nanoscale shapes and patterns,” Nature 440, 297–302 (2006). [CrossRef] [PubMed]

Nature (London), Phys. Sci.

• G. Frens, “Controlled nucleation for the regulation of the particle size in monodisperse gold suspensions,” Nature (London), Phys. Sci. 241, 20–22 (1973).

Nature Mater.

• N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31–37 (2008). [CrossRef]

Opt. Express

• A. Vallecchi, M. Albani, and F. Capolino, “Collective electric and magnetic plasmonic resonances in spherical nanoclusters,” Opt. Express 19, 2754–2772 (2011). [CrossRef] [PubMed]

Phys. Chem. Chem. Phys.

• N. Shalkevich, A. Shalkevich, L. Si-Ahmed, and T. Bürgi, “Reversible formation of gold nanoparticle–surfactant composite assemblies for the preparation of concentrated colloidal solutions,” Phys. Chem. Chem. Phys. 11, 10175–10179 (2009). [CrossRef] [PubMed]

Phys. Rev. B

• 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. Mühlig, C. Rockstuhl, J. Pniewski, C. R. Simovski, S. A. Tretyakov, and F. Lederer, “Three–dimensional metamaterial nanotips,” Phys. Rev. B 81, 075317 (2010). [CrossRef]
• P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
• C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
• 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]
• C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009). [CrossRef]
• V. Yannopapas, “Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres,” Phys. Rev. B 75, 035112 (2007). [CrossRef]
• T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79, 115430 (2009). [CrossRef]
• C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B 81, 035320 (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. B 79, 045111 (2009). [CrossRef]

Phys. Rev. Lett.

• S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
• 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]

Science

• 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,” Science 328, 1135–1138 (2010). [CrossRef] [PubMed]

Other

• T. Okamoto, “Near-field spectral analysis of metallic beads,” in Near-Field Optics and Surface Plasmon Polaritons , S. Kawata, ed. (Springer, 2001), pp. 97–123. [CrossRef]
• J. D. Jackson, “Radiating systems, multipole fields and radiation,” in Classical Electrodynamics , 3rd ed. (Wiley, 1999), pp. 407–455.

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