The Perfectly Conducting Grating from the Point of View of Inverse Diffraction

Abstract

We present here the first study of gratings from the point of view of inverse diffraction. The problem is, given data on the far scattered field, to find the profile of the grating. A very general method is proposed here: using the concept of the Fréchet differential, we show that it is possible to find a numerical algorithm in order to reconstitute the profile. One encounters the fundamental instability, linked with all the problems of inverse scattering. In order to overcome this difficulty, we have used the Tikhonov method of regularization. Finally, we show several examples of reconstitution for various gratings. In the near future, we hope to apply our method to the case of finite conductivity gratings.