The normal-mode-analysis method is used to model the radiative spreading of long-range surface plasmon polariton modes injected into regions where the bound surface mode is cutoff or radiative. Mode cutoff is induced by an asymmetry between the index of refraction of the top cladding layer and that of the bottom. The analysis was performed at ${\lambda }_0=1.55\mathrm{\mu }\mathrm{m}$ for infinite-width (slab) metal waveguides where the metal was Au and the bounding dielectrics were ${\mathrm{SiO}}_2$ . Results show that a change in insertion loss of $>20\mathrm{dB}$ is possible for an appropriate waveguide geometry and dielectric asymmetry.