Geometrical optical approach for electromagnetic wave propagation in rectangular mine tunnels

Electromagnetic wave propagation inside an empty rectangular mine tunnel with imperfect walls is considered. The modal expansion of the fields is complicated by the coupling of the basic modes by the imperfect walls. To avoid this difficulty, and in view of the large guide dimensions relative to the free space wavelength, a geometrical ray approach is proposed. To provide a theoretical foundation for the method, we first consider an idealized waveguide model with two perfectly reflecting side walls. The modal field expansion for this prototype model is fully analyzed to provide a satisfactory comparison between the modal and the geometrical ray sums. The proposed general ray method is then applied to the rectangular waveguide when all four walls are imperfectly conducting. Finally, the influence of wall roughness is considered by a relatively simple method.