To enforce the continuity of transverse electric and magnetic fields at boundaries, rectangular matrices containing the field distribution ('right eigenvectors') have to be inverted. This can be done with left eigenvectors. Here, it is shown how the latter ones can be determined with simple matrix products from previously determined right eigenvectors. For this purpose the relation between the transverse electric and magnetic fields known from Maxwell's equations is utilized.

An arbitrarily directed complex-source beam (CSB) is diffracted by an acoustically soft or hard semi-infinite circular cone. The method can be used to probe any desired part of the cone inclduing its tip. The scattered field is isolated by subtracting the incident from the diffracted field and can be used to derive diffraction coefficients for improving asymptotic methods such as the GTD or the UTD.