Spatial Nonlocality in the Optical Response of Metal Nanoparticles

ARTICLE pubs.acs.org/JPCC

Spatial Nonlocality in the Optical Response of Metal Nanoparticles Christin David and F. Javier García de Abajo*
Instituto de Optica, Consejo Superior de Investigaciones Cientificas (CSIC), Serrano 121, 28006 Madrid, Spain

bS Supporting Information ABSTRACT: Spatial nonlocality is known to play an important role in nano-optics when small nanometer-sized structures are involved, but few efforts have been made to assess nonlocal effects in a rigorous way. We present two different approaches to account for nonlocality in metal nanoparticles: (i) the nonretarded specular reflection model and (ii) the retarded hydrodynamical model. Excellent agreement with available experiments is obtained from our parameter-free simulations, which lead to dramatic differences with respect to local theory. Both models predict sizable plasmon blue shifts and broadenings in individual metal nanoparticles, nanoshells, particle dimers, and Yagi
Uda antennas. An analysis of plasmon resonances for varying particle size and spacing allows us to separate nonlocal and retardation effects within the hydrodynamical model. We find a wide range of geometrical parameters for which nonlocal effects coexist with significant retardation. This study is particularly relevant for broad, active areas involving applications of local field enhancement to biosensing and nonlinear optics in plasmonics.

T

he optical properties of metal nanoparticles have been the subject of considerable interest over the past few years,1
4 leading to a dramatic improvement in the sensitivity of biosensors,5,6 light collection in photovoltaics,7
9 and prospects for nonlinear photonics at the nanoscale.10 Experimental access to small distances below 10 nm in the interparticle spacing, the radius of curvature of sharp tips, and the thickness of curved metallic layers has been demonstrated in metallic dimers,10,11 nanoshells,12,13 and nanostars,14 for which spatial dispersion in the materials response is known to be important.15 However, most reported electromagnetic simulations involving nanostructures rely on the use of local, frequency-dependent dielectric functions,16 which neglect spatial dispersion and should actually be reserved only for insulators and core-polarization in metals.17 We show below that the blue shift and dramatic broadening that are observed in the plasmon bands of 20 nm. Particle Arrays. The effect of nonlocality is even stronger when more particles are involved, such as in the Yagi
Uda nanoantenna considered in Figure 6. Similar structures have been recently used to pattern the angular distribution of emission from single molecules.47 The difference between local and nonlocal descriptions is clearly observed in the spectra of Figure 6a, showing a significant plasmon shift, especially if one relates it to the distance between the emission peak wavelength and the gold plasmon threshold ∼20 nm. But the difference is even more striking when we examine the angular distribution of emission.

’ CONCLUSION We are providing a solid description of nonlocal effects from two parameter-free models of a very different nature that produce similar results in the case of small structures for which retardation can be neglected. In particular, we are predicting blue shifts and broadenings originating in nonlocality for individual gold spheres and nanoshells and also for closely spaced particle dimers and Yagi
Uda antennas. Some minor differences between both models are identified through analytics for small spheres, but the main qualitative conclusions are the same. Additionally, the 19474

dx.doi.org/10.1021/jp204261u |J. Phys. Chem. C 2011, 115, 19470–19475

The Journal of Physical Chemistry C hydrodynamical model allows us to simultaneously incorporate retardation and nonlocal effects, which turn out to produce important corrections in the plasmon wavelength of large particles separated by narrow gaps. Our results pave the way toward a comprehensive, computationally affordable description of nonlocality for arbitrary nanometallic morphologies.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional information on Mie scattering coefficients in the hydrodynamical model, scattering by a homogeneous sphere, scattering by a nanoshell, and comparison between specular-reflection and hydrodynamical models for a sphere. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work has been supported by the Spanish MICINN (MAT2010-14885 and Consolider NanoLight.es) and the European Commission (FP7-ICT-2009-4-248909-LIMA and FP7-ICT-2009-4-248855-N4E). ’ REFERENCES (1) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668–677. (2) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025–1102. (3) Liz-Marz
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