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(omega)/DT epsilon(omega)-1]/ [epsilon(omega)+], with epsilon(omega) being the relative complex dielectric permittivity of the material, exhibits resonances typical of the surface polariton modes, when epsilon(omega)similar to-1. We show that for a moderately sharp resonance, S(omega) is satisfactorily described with a mere (complex) Lorentzian, independent of the details affecting the various bulk resonances describing epsilon(omega). Remarkably, this implies a quantitative correlation between the resonant behaviors of Re[S(omega)] and Sm[S(omega)], 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, CaF2, and BaF2. An extension to interfaces between two media or to a non-planar interface is briefly considered. (C) 2021 Optical Society of America