For gratings having an arbitrary symmetric profile, we prove that when the period becomes much finer than the wavelength the grating becomes equivalent to a graded uniaxial layer . We show for one polarization that this quasi-static equivalence holds when the ratio of wavelength to grating period exceeds 40 . We also present a simple physical model which explains the anisotropic nature of the equivalent layer . We take the case of a finely-textured copper surface, and show that it can be a good selective absorber for polarized light, but that its performance in unpolarized' light is much less satisfactory .

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