Unique Determination of Periodic Polyhedral Structures by Scattered Electromagnetic Fields

This work is concerned with the unique determination of a periodic diffraction grating profile in three dimensions by some scattered electromagnetic fields measured above the grating. In general, it is well known that global uniqueness may not be true when the measurement is only taken for one incident field. Our goal is to completely characterize the global uniqueness properties when the periodic structure is of polyhedral type. Corresponding to each incident plane wave, we are able to classify all unidentifiable structures into three classes and show that any periodic polyhedral structure can be uniquely determined by one incident field if and only if it belongs to none of the three classes. Consequently, the minimum number of incident waves required for the unique determination of a periodic polyhedral structure can be easily read.