Jens Dorfmüller¹, Ralf Vogelgesang¹, R. Thomas Weitz¹, Worawut Khunsin¹, Carsten Rockstuhl², Christoph Etrich³, Thomas Pertsch³, Falk Lederer², Klaus Kern^1,4

Talk at the SPP4 in Amsterdam, June 2009

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
³Institute of Applied Physics, Friedrich-Schiller Universität Jena, 07743 Jena, Germany
⁴École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

Purpose
Localized surface plasmons, being a resonant excitation in metallic nanoparticles, provide intriguing opportunities for novel, ultra-efficient devices. They are being used, e.g., as sensors, building blocks of optical meta-materials [1], or in cancer treatment, and drive new ideas for all-optical signal processing. Understanding the intriguing interplay between the geometry of the nanoparticles and the field distribution of their eigenmodes is essential to optimize their resonant character. Their reliable experimental characterization can be viewed as a starting point of all further considerations. In the present work, we focus on the example of nano-wire antennas, whose Fabry-Pérot like eigenmodes are measured with a Scanning Near-Field Optical Microscope.

Methods
We use apertureless Scanning Near-Field Optical Microscopy (aSNOM) [2] with cross-polarized exciting and scattered radiation. This approach allows to map nearly unperturbed eigenmodes of plasmonic nanostructures [3], accessing predominantly the normal (z-) component. We study optical nano-wire antennas fabricated by electron beam lithography. In stark contrast to far-field measurements, aSNOM allows to compare plasmon resonances of many individual single wires simultaneously on a relatively small substrate area. We show measured amplitude and phase maps of the z-component of electromagnetic near-fields around these nano-structures. We compare our results to simulations obtained by finite-difference time-domain calculations.

Results
For an incident polarization parallel to the nanowire, the measured amplitude patterns around the nanowires reveal an increasing number of lobes with growing wire length. Only odd modes are observed. The magnitude is resonantly enhanced for certain nanowire lengths, indicating a standing wave of the charge density oscillation [4]. Neighboring lobes show a difference of ? in the phase. Both features indicate that the nanoparticles have to be understood as a resonator for the plasmon mode propagating in a cavity that is formed by the nanowires. The dipolar resonance is observed at a wire length of ??vac/5.6. Higher order resonances occur at approximately odd numbered multiples of the dipole resonance length. We also demonstrate the possibility to break the symmetry by rotating the sample, allowing to excite the otherwise symmetry-forbidden even modes.

Conclusions
The nano-wires can be interpreted as one-dimensional Fabry-Pérot interferometers for plasmons. Besides the phase accumulation due to propagation, we show that phase jumps occur at the ends of the nanowires in good agreement with a prediction from a recently introduced theory [5].
The excitation of the otherwise "dark", dipole-forbidden even order plasmonic modes [7] is explained as the combined action of non-parallel polarization and retardation. Depending on the angles between E-field, propagation direction, and wire axis, the matching of excitation and wire eigenmode fields can be varied continuously, allowing the excitation of all modes with correspondingly varying efficiency.

References
[1] T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, Opt. Lett. 33, 848-850 (2008)
[2] A. Bek, R. Vogelgesang, and K. Kern, Rev. Sci. Instrum. 77, 043703 (2006)
[3] R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, Nano Lett. 8, 3155-3159 (2008)
[4] G. Laurent, N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, Phys. Rev. B, 71, 045430 (2005)
[5] L. Novotny, Phys. Rev. Lett., 98, 266802 (2007)
[6] J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, K. Kern, submitted.
[7] P. Nordlander, C. Oubre, E. Prodan, K. Li, M. I. Stockman, Nano Lett. 4, 899-903 (2004)