Inverse scattering method in electromagnetic optics: Application to diffraction gratings

We present a theoretical and numerical method for solving problems of inverse scattering in optics given data on the far field, find the scattering object. This method is applied to perfectly conducting diffraction gratings. From the efficiency curve in a Littrow mounting and in the TE case, we derive the shape of the grating surface. Two different cases must be distinguished. The first problem, which we call “reconstruction,” is to compute the profile when the efficiency is experimentally known. In the second one, called “synthesis,” we give a priori an efficiency curve and look for the corresponding grating(s), if it actually exists. We show several theoretical reconstructions for various gratings, and present our first results in the very difficult field of synthesis. The relevance of this method in the domain of electromagnetic optics is then outlined by its application to two other problems.

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