A Kirchhoff solution to plasmon hybridization
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A Kirchhoff solution to plasmon hybridization Britain Willingham • Stephan Link
Received: 10 December 2012 / Accepted: 1 May 2013 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract Using Ohm’s law, a solution to plasmon hybridization via Kirchoff’s equations results in a simple and intuitive picture of a metal nanoparticle dimer as a capacitively coupled circuit. Calculated absorption spectra and surface charge densities show that dimers of different metallic composition support different super- and subradiant plasmons compared to homodimers. Strong screening of Coulomb interactions between nanoparticles of different metallic background prohibits the excitation of anti-bonding plasmons, while changes to the free electron conductivity upon a collective response result in coupled plasmon lifetimes which shift as a function of interparticle distance. Smaller separations then result in the longest lived plasmons.
Metal nanoparticles (MNPs) stand as a promising component in future optical devices where sustained plasmon lifetimes [1, 2] and amplified electromagnetic fields [3, 4] play a crucial role in experimental design. Applications using strongly coupled plasmons at MNP surfaces [5, 6] benefit from models that can characterize the natural heterogeneity of realistic systems [7] and exploit the variables which can alter or harness the intended response of a plasmonic device [8].
B. Willingham S. Link (&) Department of Chemistry, Laboratory for Nanophotonics, Rice University, 6100 Main St., Houston, TX 77005, USA e-mail: [email protected] S. Link Department of Electrical and Computer Engineering, Laboratory for Nanophotonics, Rice University, 6100 Main St., Houston, TX 77005, USA
Numerical implementations of Maxwell’s equations well describe the optical response of MNPs observed experimentally [8, 9] but often hide the inner workings of MNPs. Instead, small particle solutions offer keen insight into factors which can dictate the dynamics of surface plasmons such as a MNP’s shape [10–12], symmetries [13], surface irregularities [14] or material composition [15]. A consistent method to determine parameters such as the relaxation time s of surface plasmons [16], composed of free electrons of lifetime s 6¼ s , would facilitate the separation of the radiative decay channel upon implementation into full scattering solutions [17]. In this letter, we show that Ohm’s law results in passive circuit components which form the solution to plasmon hybridization [18] and represent the optical response of intrinsic mechanisms within MNPs [19]. Kirchhoff’s equations are used to solve for the plasmon modes and optical absorption for a dimer consisting of MNPs having different sizes, free electron densities or polarizable ionic backgrounds. By considering deviations in the free electron conductivity due to the formation of a collective oscillation within the intraband, an analytical equation for the decay rate of quasifree electrons shows a quadratic dependence on the photon energy hx. The hybridized lifetimes are then shown to shi
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