We provide a simple physical proof of the reciprocity theorem of classical
electrodynamics in the general case of material media that contain linearly
polarizable as well as linearly magnetizable substances. The excitation source
is taken to be a point-dipole, either electric or magnetic, and the monitored
field at the observation point can be electric or magnetic, regardless of the
nature of the source dipole. The electric and magnetic susceptibility tensors
of the material system may vary from point to point in space, but they cannot
be functions of time. In the case of spatially non-dispersive media, the only
other constraint on the local susceptibility tensors is that they be symmetric
at each and every point. The proof is readily extended to media that exhibit
spatial dispersion: For reciprocity to hold, the electric susceptibility tensor
Chi_E_mn that relates the complex-valued magnitude of the electric dipole at
location r_m to the strength of the electric field at r_n must be the transpose
of Chi_E_nm. Similarly, the necessary and sufficient condition for the magnetic
susceptibility tensor is Chi_M_mn = Chi^T_M_nm.Comment: 15 pages, 2 figures, 28 equations, 21 reference
