kgaps for surface polaritons on gratings

We show that $k$ gaps can occur in the dispersion curves of surface polaritons on metallic gratings as determined by reflectivity measurements in $p$ polarization. A $k$ gap (rather than the usual ω gap) opens up at a zone boundary, due to finite lifetime effects, when there is no direct coupling between the two branches crossing at the boundary. We present exact calculations of the reflectivity of a symmetric sawtooth grating ruled on silver that display this behavior, and obtain perturbation-theoretic, analytic expressions that explain it.