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R. Esteban(1,2), G. W. Bryant(2) and J. Aizpurua(1)
1 Centro de Física de Materiales, Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center (DIPC), Donostia-San Sebastian, 20018, Spain 2 Joint Quantum Institute and Department of Physics, National Institute of Standards and Technology and University of Maryland, Maryland 20899-8423, USA Different experimental techniques are being currently explored to control nanometer and subnanometer gaps in plasmonic systems. A key motivation behind this work is the possibility to obtain very strong and localized near fields at narrow gaps, with significant spectroscopic applications. We discuss limitations and possibilities associated with such narrow gaps, as revealed by the often drastic effect of gap dimensionality, structural disorder and quantum effects on the strength and spatial distribution of the near fields. We first consider a simple linear optical antenna to analyze the differences between rounded and flat terminations at the gaps. We detail in particular how flat terminations and very narrow gaps give rise to a very rich behavior with two well defined families of modes, the first extending over the full antenna and the second over the gap region, as can be understood by simple models. In this study, the simplicity of the well defined structure helps to understand the origin and behavior of the plasmonic resonances, but new effects are also possible for much more complex and loosely controlled geometries. We consider in particular clusters of small metallic particles separated by narrow gaps, and describe how it is possible to excite chain resonances even for considerable disorder. Depending of the used wavelength, the excited modes can extend along long chains or be confined to dimers, More notably, these short and long chain modes do not present the same spatial distribution in the cluster, with efficient dimer excitation often occurring at the exterior of the aggregate, and long chains modes also frequently found in the interior. To conclude, we go beyond the standard classical approach to discuss the influence of quantum effects on plasmonic resonances when subnanometer gaps are present. Full quantum calculations are, however, only computationally affordable at the present time for small particles, not for typical plasmonic structures of interest. We describe a Quantum Corrected Model (QCM) that incorporates quantum tunnelling into a classical solver, allowing to study many of the relevant quantum-induced effects on the plasmonic response. The validity of this approach is checked for particles small enough to make possible direct comparison with full quantum results. The QCM calculations are then extended to larger structures relevant for experiments, and we discuss the observed modal redistribution and quenching of the near field. The QCM is very general, and constitutes a straightforward manner to incorporate quantum effects into many different plasmonic systems. |
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