On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation

Localized surface plasmon resonances (LSPR) in lithographically fabricated gold (Au) nanodisc pairs are investigated using microabsorption spectroscopy and electrodynamic simulations. In agreement with previous work, we find that the fractional plasmon wavelength shift for polarization along the interparticle axis decays nearly exponentially with the interparticle gap. In addition, we find that the decay length is roughly about 0.2 in units of the particle size for different nanoparticle size, shape, metal type, or medium dielectric constant. The near-exponential distance decay and the interesting “universal” scaling behavior of interparticle plasmon coupling can be qualitatively explained on the basis of a dipolar-coupling model as being due to the interplay of two factors: the direct dependence of the single-particle polarizability on the cubic power of the particle dimension and the decay of the plasmonic near-field as the cubic power of the inverse distance. Using this universal scaling behavior, we are able to derive a “plasmon ruler equation” that estimates the interparticle separation between Au nanospheres in a biological system from the observed fractional shift of the plasmon band. We find good agreement of the interparticle separations estimated using this equation with the experimental observations of Reinhard et al. ( Nano Lett. 2005, 5, 2246−2252).