Abstract
We introduce a rigorous formulation for the problem of the diffraction by a finitely-conducting, bi-periodic surface. The formationon is based on a coordinate transformation which maps the grating surface onto a plane. The transformed Maxwell equations are resolved using an iterative technique. The numerical implementation is tested against a number of criteria, including a comparison with two recently developed formalisms. As well, it is shown to give results in agreement with the Reciprocity Theorem, which is derived for efficiencies of crossed gratings in unpolarized light. The method has been shown to work throughout the whole range of values of surface conductivity. We investigate the effect of a surface-corrugation on the solar absorptance of a metallic mirror. We discuss a useful equivalence property linking the behaviour of crossed gratings with that of classical gratings. We exhibit for the first time a grating in a highly-reflecting metal capable of totally absorbing unpolarized incident light.
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On leave from the Department of Theoretical Physics, School of Physics, University of Sydney, Sydney, N.S.W., 2006, Australia