Rigorous diffraction theory is applied to compute the electromagnetic fields in the neighborhood of polygonal obstacles of three- and two-dimensional shape, including two-dimensional gratings. For obstacles such as a rectangular depression, a polygonal groove, or an array of grooves present in a metallic substrate, we calculate and measure significant departures from what a scalar diffraction approach would predict as soon as the width of the obstacle becomes smaller than one wavelength. For such widths, it is shown that the apparent depth of a groove can be smaller or larger than the geometrical depth, depending on the polarization of the incident light and on the optical constants of the substrate.
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