Size Dependence of the Plasmon Ruler Equation for Two-Dimensional Metal Nanosphere Arrays

The optical properties of fcc metal (gold and silver) nanostructures have recently been the focus of intense scientific study. The driving force for the interest is because, upon interaction with incident electromagnetic waves, such as light, these metal nanostructures exhibit localized surface plasmon resonance (LSPR). 4 The LSPR results in both an enhancement of the near-field electromagnetic fields, 7 with potential Raman enhancements of up to 10, and the far-field optical efficiencies, 10 with applications in optical sensing and imaging, miniaturized photonic devices, and photothermal cancer therapies, 20 among many others. Many of these optical applications involve not an individual nanoparticle, but collections, or arrays of the nanoparticles that are arranged in a manner such that the optical properties can be enhanced and exploited. 23 Two examples of this are the enhancement in electromagnetic fields that can occur at nanometer separations between individual nanoparticles that is useful for single molecule sensing and detection, and the utilization of multidimensional arrays and arrangements of nanostructures for enhanced plasmon coupling and biosensing applications. Because of this, there have been many studies, both experimental 39 and theoretical, 49 that have investigated the optical properties of either dimers or one and two-dimensional (2D) arrays of fcc metal nanoparticles, though it should be noted that the vast majority of such studies, both experimental and theoretical, has focused on the far simpler dimer geometry. One key issue that was recently resolved for the case of interacting nanoparticle dimers was the development of an analytic expression for the dependence of the far-field optical properties and, specifically, the LSPR wavelength shift as a function of nanoparticle size and the gap between the nanoparticles. Such information is necessary to systematically optimize the arrangements of nanoparticles with predictable and repeatable optical properties for optical sensing applications. Specifically, Sonnichsen et al. and Reinhard et al. established a “plasmon ruler” to measure distances in biological systems based on the change in optical properties that result from the