Simple analytical expression for the dispersion of plasmonic structures with coaxial geometry

The optical properties of nanoscale apertures in optically thick metallic films have been intensely researched in the past years due to their fundamental importance in near-field optics. Here, we show that the entire dispersion behavior of a plasmonic structure with coaxial cross-section i.e., formed by a dielectric ring between a metallic core and a metallic cladding, is well-approximated by a simple analytical formula that relates the propagation constant of each mode to its angular frequency. The analytical theory and the numerical FDFD results are in excellent agreement with each other.