Surface response around a sharply resonant surface polariton mode is simply a Lorentzian

At the planar interface between a material and vacuum, the complex surface response S(ω)=[ε(ω)-1]/[ε(ω)+1], with ε(ω) being the relative complex dielectric permittivity of the material, exhibits resonances typical of the surface polariton modes, when ε(ω)∼-1. We show that for a moderately sharp resonance, S(ω) is satisfactorily described with a mere (complex) Lorentzian, independent of the details affecting the various bulk resonances describing ε(ω). Remarkably, this implies a quantitative correlation between the resonant behaviors of ℜe[S(ω)] and ℑm[S(ω)], respectively, associated to the dispersive and dissipative effects in the surface near-field. We show that this "strong resonance" approximation easily applies and discuss its limits, based on published data for sapphire, CaF_2, and BaF₂. An extension to interfaces between two media or to a non-planar interface is briefly considered.