Study of eigenmodes in periodic waveguides using the Lorentz reciprocity theorem

Photonic crystals, frequency-selective surfaces, gratings, and many so-called metamaterials are composed of periodic arrangements of objects. Such an arrangement of objects quickly forms a periodic waveguide. In this paper, we investigate a number of properties of the eigenmodes in general periodic waveguides; using the Lorentz reciprocity theorem. Such an analysis seems to be missing in the literature. We present an original proof for the intimate relation between bidirectionality of a periodic waveguide and reciprocity. We also derive compact expressions for the excitation coefficients of the eigenmodes when the waveguide is excited by a source density or an incident field. The analysis is generalized to include periodic waveguides composed of anisotropic and bianisotropic materials.status: publishe