A regularized approach to the calculation of the propagation modes in a perturbed waveguide

When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. Two complementary approaches to the determination of change induced by the insert are described. The first provides an analytic estimate when the insert is a small flat strip. The second approach converts the underlying boundary value problem to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix and stable numerical processes may be employed to find the propagation constants. The second approach is not constrained by the size or shape of the inserts, and thus provides an independent estimate of the accuracy of the analytic estimate of perturbation to the propagation constants of the empty waveguide; it also determines the empty waveguide parameters themselves.