Scattering of a surface wave by a discontinuity in reactance

The following two-dimensional scattering problem is solved exactly by a Wiener-Hopf procedure. The incident field is a TM surface wave traveling in the positive
x
direction and guided by a reactive surface in the plane
z=0
. The surface has normal reactance
X_{0}
if
x<0
, and
X_{1}
if
x>0
.
X_{0}
and
X_{1}
are assumed positive and real. The discontinuity produces reflected and transmitted surface waves and a radiated field. Closed form expressions are found for the magnitudes of these fields. The reflected, radiated, and transmitted power flows, relative to that of the incident field, are plotted in universal curves. Conservation of energy is verified exactly.