Determination of surface-polariton minigaps on grating structures: A comparison between constant-frequency and constant-angle scans

When surface polaritons propagate on a diffraction grating, their interaction with the periodic structure induces gaps in frequency in the dispersion relation. The dispersion curves near the gaps have been explored by two experimental methods: One may probe the reflectivity as a function of angle of incidence $\theta$, with radiation of fixed frequency $\omega$, or one may measure the reflectivity as a function of frequency, with angle of incidence fixed. In either case, resonant coupling to the incident photon produces narrow dips in the reflectivity. Information on the dispersion curve is extracted by following the position of the dip as a function of $\omega$ when $\theta$ is scanned, or its variation with $\theta$ when $\omega$ is scanned. In the minigap region, a theoretical study shows the first method can yield unphysical results, while those from the second method provide dispersion curves in good accord with theory.