Diffraction of a cylindrical surface wave by a discontinuity in surface reactance

This scattering problem is essentially two-dimensional due to the circular symmetry of the incident TM mode, and is solved exactly by the Wiener-Hopf technique. As stated, the incident wave is the symmetrical TM axial surface wave, traveling in the positive x direction and guided by a reactive surface at r = a. The normal surface reactance is X
1
for x < 0 and X
2
for x > 0, where X
1
and X
2
are positive and real. The discontinuity produces transmitted, reflected, and radiated fields whose amplitudes are given in terms of integrals which are evaluated in specific cases by quadrature formulas. It is shown that the derived field components reduce to those of Kay [1] or Barlow and Brown multiplied by a constant coefficient, for the case of a plane surface, if the radius a is allowed to become very large. Coefficients of transmitted, reflected and radiated power, relative to the incident power are calculated in certain cases, with conservation of energy being verified.