Image buildup for the rectangular waveguide tensor Green's function

Tensor Green's functions, of both electric and magnetic type, are produced for the rectangular waveguide through summation of a doubly infinite series of free-space contributions obtained from endless imaging across (perfectly conducting) guide walls. The requisite summation is facilitated by resorting to a Fourier integral representation for the basic free-space kernel, followed by appeal to the Poisson summation formula. That latter, in particular, engenders, through Dirac delta function appearance, an automatic decomposition into waveguide modes. Indication is further made as to how the imaging method may naturally be extended to assemble mode-decomposed Green's functions in an axially bounded, rectangular cavity.