"Natural" definition of the modal impedances in non-homogeneous dielectric loaded rectangular waveguide.

In this paper, the definition of the modal impedances of the electromagnetic field in a nonhomogeneously filled waveguide is discussed. The presence of TM modal impedances, which are functions of the transverse coordinate, does not permit us to obtain a unique Z matrix of these guides. Hence, the evaluation of the scattering matrix can be involved. The introduction of a “natural” EM expansion overcomes this problem leading to the definition of a unique modal impedance and a unique Z matrix. This approach is applied to the simulation of the effect of a block of dielectric in an empty waveguide by “cascading” the S matrices of the existing junctions. Finally, this “natural” EM expansion is applied to the junction between an empty waveguide and a completely filled waveguide, obtaining an equivalent circuit which better represents the physics of this problem, and to the optical fibers