Axial scattering by a parabolic cylinder separating two penetrable media when focusing occurs

A parabolic-cylinder interface separates two different media that are either isorefractive or anti-isorefractive to each other. The primary field is symmetrically incident in a direction perpendicular to the focal axis of the interface. When focusing of energy on the focal axis occurs, the boundary-value problem is solved exactly by matching the field imploding on the axis to the one emanating from the axis.