Quantitative Insights into a Plasmonic Ruler Equation from the Perspective of Enhanced Near Field

The plasmonic shift of resonance wavelength induced by near-field coupling enables one to measure nanoscale distances optically. Empirically, the well-known ruler equation correlating plasmon shift with interparticle spacing was proposed. Though it has been widely used in analyzing simulation and experimental outcomes, little is known about the underlying physical mechanism of the characteristic exponential form of the plasmon ruler equation and the universal decay constant therein. In this work, we attempt to decrypt these from the perspective of plasmon near-field enhancement. Based on an analytical quasi-normal mode formula for plasmon shifts, we proved that the exponential decaying electric field is the critical reason that results in the exponential form of the plasmon ruler equation and quantitatively, we found that the universal decay constant in the plasmon ruler equation actually reflects the range of the enhanced near field. This work hopefully helps to deepen the understanding of the mechanism of light-matter interaction in corresponding plasmonic processes.