Two-dimensional Green's function theory for the electrodynamics of a rotating medium.

We derive an exact spectral representation for the Green's function of Maxwell equations in a two-dimensional homogeneous and rotating environment. The formulation is developed in the medium (noninertial) rest frame, and it represents the response to a point source, where both the source and observation points rotate together with the medium. The closed form expression for the Green's function is derived for (nonrelativistic) slowly rotating media at finite distances. An approximate expression for the efficient evaluation of the Green's function, that avoids laborious summation of rotating-medium spherical harmonics, is provided and tested against the exact expression. Furthermore, it is shown that our spectral theory can provide a broad view of the optical response of rotating systems, from which the classical Sagnac effect is obtained as a special case.