The effects of the truncation and curvature of periodic surfaces: a strip grating

Equations are outlined for surfaces which are finite and curved in two dimensions (only locally periodic), as well as infinitely periodic in one dimension but truncated and curved in the second dimension. By removing the periodicity, a truncated strip-grating results and the scattered fields as well as an associated reflection coefficient are calculated. These numerically rigorous calculations are compared against two approximate solutions. The comparison is intended as a check of the approximate solutions toward their application, in particular, in the analysis of surfaces which are finite and curved in two dimensions. In general, the edge currents always differed from the currents induced on an infinite grating, while the interior strip currents on a finite grating (depending on the excitation wavelength) may or may not differ from those of an infinite grating. It is concluded that if a more accurate calculation of the spectral response is to be found, the interior currents must be better approximated