Semianalytical theory of plasmon nanoruler

We develop a new method based on the continuous-fraction approach as applied to the electrostatic boundary problem for determining surface plasmon resonances of coupled nanospheres. The resonance frequency dependence on interparticle gap (plasmon nanoruler effect) is determined by avoiding time-consuming numerical calculations even for very small interparticle separations, where known procedures face serious difficulties. Corrections due to retardation effects are accounted for, allowing description of larger nanopairs. Good agreement is demonstrated both with results of numerical calculations and with experimental data.