Resonant Field Enhancements from Metal Nanoparticle Arrays

Abstract

Theoretical and semiempirical studies of two-dimensional (2D) metal nanoparticle arrays under periodic boundary conditions yield quantitative estimates of their electromagnetic (EM) field factors, revealing a critical relationship between particle size and interparticle spacing. A new theory based on the RLC circuit analogy has been developed to produce analytical values for EM field enhancements within the arrays. Numerical and analytical calculations suggest that the average EM enhancements for Raman scattering (G h) can approach 2 × 10 11 for Ag nanodisks (5 × 10 10 for Au) and 2 × 10 9 for Ag nanosphere arrays (5 × 10 8 for Au). Radiative losses related to retardation or damping effects are less critical to the EM field enhancements from periodic arrays compared to that from other nanostructured metal substrates. These findings suggest a straightforward approach for engineering nanostructured arrays with direct application toward surface-enhanced Raman scattering (SERS).Nanostructured metal-dielectric interfaces often exhibit enhanced optical phenomena at visible and near-infrared (NIR) frequencies via excitation of surface plasmon modes. 1,2 The enticing possibilities of engineering such properties for applications in photonics and chemical sensing have led to a resurgence of activity in the design of plasmonic materials with subwavelength dimensions. 3 Enhanced electromagnetic (EM) field effects can be generated either in a broad spectral range, as is the case for disordered metal-dielectric composites, 2,4 or at select frequencies from periodically ordered metal nanostructures. Periodicity plays a key role in tuning the optical response of the latter, and has been documented in experimental and theoretical investigations of plasmonenhanced effects such as surface-enhanced Raman scattering (SERS), 5-7 extraordinary optical transmission, [8][9][10] and robust photonic band gaps at visible and NIR wavelengths. [11][12][13] SERS has attracted widespread attention because of its demonstrated potential for single-molecule spectroscopy and chemical sensing with high information content. [14][15][16] The rational design of optimized SERS substrates remains a challenging goal, despite extensive efforts to elucidate the physical basis of signal enhancement. Several theoretical studies have described highly localized EM fields at the junction of metal nanostructures, 7,17-19 with local EM enhancement factors G loc ) |E loc (λ)/E 0 (λ)| 4 as high as 10 11 -10 12 for a two-particle system. 20 However, less attention has been paid to the average EM enhancement factors (G h ) 〈G loc 〉), which has greater relevance for the design and optimization of SERS-based chemical sensors. In this regard, García-Vidal and Pendry have provided electrodynamics calculations on periodic nanostructured metal films with G h values on the order of 10 6 , a level of activity commonly observed in many experimental systems. 7 Here we provide numerical calculations and a simple analytical theory for calculating EM field enhancements in...

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