Coupling at cross, T and L junctions in tunnels

While the modal representation for a straight tunnel is well known, coupling into the branches at L, T and cross junctions has not been studied. In order to explain the coupling at these junctions in tunnels, we make use of modal analysis. For the propagation into branches off the main tunnel, mode coupling at the discontinuities is obtained by ray-mode conversion. By accounting for the mode diffraction at each comer in 2-D tunnels, we compute the coupling loss into cross-junctions, the arms of T-junctions and L-bends. The coupling loss at junctions of 3-D tunnels can be found from the mode coupling at 2-D waveguides because the discontinuities at the side walls only couple modes having the same variation in the vertical direction. Since the cross tunnel has four edges, they generate more comer diffracted modal fields than other structures, thus have the strongest coupling.