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We consider the electromagnetic inverse scattering problem for the Drude-Born-Fedorov model for periodic chiral structures known as chiral gratings both in $\mathbb{R}^2$ and $\mathbb{R}^3$. The Factorization method is studied as an analytical as well as a numerical tool for solving this inverse problem. The method constructs a simple criterion for characterizing shape of the periodic scatterer which leads to a fast imaging algorithm. This criterion is necessary and sufficient which  gives a uniqueness result in shape reconstruction of the scatterer. The required data consists of certain components of Rayleigh sequences of (measured) scattered fields caused by plane incident electromagnetic waves. We propose in this electromagnetic plane wave setting a rigorous analysis for the Factorization method. Numerical examples in two and three dimensions are also presented for showing the efficiency of the method.

The factorization method for the Drude-Born-Fedorov model for periodic chiral structures