Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectricstructure mounted on a perfectly conducting plate in three dimensions. Given thatuniqueness of solution holds, existence of solution follows from a well-known Fredholmframework for the variational formulation of the problem in a suitable Sobolev space. Inthis paper, we derive a Rellich identity for a solution to this variational problem undersuitable smoothness conditions on the material parameter. Under additional non-trappingassumptions on the material parameter, this identity allows us to establish uniqueness ofsolution for all positive wave numbers.
