J. Dorfmüller¹, W. Khunsin¹, R. Vogelgesang¹, C. Rockstuhl², A. Dmitriev³, F. Lederer², and K. Kern¹

Talk at the 2nd International Conference on Metamaterials, Photonic crystals and Plasmonics, META'10 in Cairo, February 2010.

¹Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
²Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller Universität Jena,
07743 Jena, Germany
³Applied Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden

We investigate nearest-neighbor interactions in amorphous plasmonic metamaterial. The analysis of large area near-field images, containing thousands of randomly distributed gold nanodiscs, allows us to extract statistical properties of neighbor interactions such as the variations of the local dipole strength and orientation as a function of nearest-neighbor environment.

Coupling between the basic motifs is an essential component of metamaterials. While there is a wealth of published results on periodic metamaterials, quasi-isotropic, "amorphous" systems, have received considerably less attention. Inherently, such systems require a statistical description of their microscopic properties with a non-obvious translation into macroscopic material parameters. Nearest-neighbor interactions have been studies in amorphous systems in the far-field as well as on isolated particle pairs [1,2]. In this work, we explore an amorphous plasmonic metamaterial by means of apertureless scanning nearfield optical microscopy (aSNOM) [3] and finite-difference, time-domain (FDTD) simulations.

Dipole-resonant randomized gold nano disc samples of different densities have been fabricated using Hole-Mask Colloidal Lithography [4]. From aSNOM measurements, we obtain topography and the local electric field component normal to the surface (magnitude and phase). With FDTD simulations we perform further numerical experiments to test, e.g., the influence of excitation conditions and whether a simplified Born-series-like perturbation description is suitable. Characterizing the individual discs' dipolar responses with Stokes formalism for the px and py states, we quantify the distributions in dipole strength and orientation as functions of nearest-neighbor distance. Curiously, plane-wave excited FDTD simulations show wider distributions than the mildly focused aSNOM measurements, probably due to long-range collective coupling effects. From our statistical distribution analysis, coupling effects appear to become negligible only for distances beyond 2.5 times the particle diameter, in agreement with observations reported in Ref. 1 and 2.

REFERENCES
1. Rechberge, W., Hohenau, A.., Leitner, A., Krenn, J. R., Lamprecht, B. and Aussenegg, F. R. "Optical properties of two interacting gold nanoparticles," Opt. Comm., Vol. 220, 137-141, 2003.
2. Su, K.-H., Wei, Q.-H., Zhang, X., Mock, J. J., Smith, D. R. and Schultz, S. "Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles," Nano. Lett., Vol. 3, 1087-1090, 2003.
3. Bek, A., Vogelgesang, R. and Kern, K. "Apertureless scanning near field optical microscope with sub-10 nm resolution," Rev. Sci. Instrum., Vol. 77, 043703, 2006.
4. Fredriksson, H., Alaverdyan, Y., Dmitriev, A., Langhammer, C., Sutherland, D. S., Zäch, M and Kasemo, B. "Hole-Mask Colloidal Lithography," Adv. Mater., Vol. 19, 4297-4302, 2007.