Clarification and extension of the optical reciprocity theorem

Clarifications on the optical reciprocity theorem are provided by explicitly proving the equivalence between the Lorentz lemma and the symmetry of the Green dyadic for the electromagnetic wave equation. This is achieved by explicitly including the surface term in the former so that different boundary conditions can be considered as required in the formulation of the latter. In addition, we shall also extend the theorem to include anisotropic magnetic materials with a nonlocal response, leading to a result which will be useful for the study of materials possessing such properties such as certain types of metamaterials.