Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric
structure mounted on a perfectly conducting plate in three dimensions. Given that
uniqueness of solution holds, existence of solution follows from a well-known Fredholm
framework for the variational formulation of the problem in a suitable Sobolev space. In
this paper, we derive a Rellich identity for a solution to this variational problem under
suitable smoothness conditions on the material parameter. Under additional non-trapping
assumptions on the material parameter, this identity allows us to establish uniqueness of
solution for all positive wave numbers.