A uniqueness theorem for an inverse problem in periodic diffractive optics

Consider a time-harmonic electromagnetic plane wave incident on a periodic structure in R 2 . The periodic structure separates two regions. In one region, the dielectric coefficient is assumed to be a fixed constant with non-zero imaginary part corresponding to the energy absorption. The other region contains perfectly reflecting material. The inverse problem is to determine the periodic structure or the shape of the interface from the scattered field. A uniqueness theorem is proved by an application of Holmgren's uniqueness theorem.