On the discontinuity problem at the input to an anisotropic waveguide

The problem considered is that of the discontinuity at the transverse plane separating two regions of a dissipationless uniform waveguide, one isotropic, the other anisotropic. The integral equation for this discontinuity is formulated in terms of the "four-vector" guides modes which propagate in the two regions. Variational expressions based on this integral equation are then given for the scattering coefficients which describe the effect of the junction on the propagating modes of the two regions. These variational expressions are then employed to obtain numerical results for the scattering coefficients at the transverse plane separating two regions of a rectangular waveguide, one empty, the other filled with a transversely magnetized dissipationless ferrite. These numerical results are found to agree reasonably well with those obtained from an alternative solution to this problem given by Sharpe and Heim.