Convergence of numerical solutions of iris-type discontinuity problems

The convergence of numerical solutions of several iris-type discontinuity problems in waveguides and periodic structures is investigated. It is demonstrated that the numerical solution of a set of equations obtained from a mode matching procedure (which corresponds to an integral equation formulation of the problem) may converge to an incorrect value if an improper ratio is chosen between the number of modal terms in the aperture and the number of terms retained in the kernel of the integral equation. The convergence properties of the set of equations obtained by an alternative mode matching procedure are discussed and general guidelines for efficient numerical computations are indicated.