Symmetry and the reflectivity of diffraction gratings at normal incidence

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Abstract
We present a series of numerical calculations which illustrate the role of symmetry of the profile of a diffraction grating on its reflectivity at normal incidence. Here one finds reflectivity dips (or peaks) produced by grating-induced coupling of the incident photon to surface polaritons. When the grating profile has either even or odd parity, we find one of the two reflectivity dips expected at normal incidence is absent, in agreement with recent data. In addition, we find that the peaks are caused by the vanishing of certain Fourier components of the profile function. This result agrees with analogous results obtained in the theory of atom-surface scattering.