  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 wave numbers.
