ELECTROMAGNETIC-WAVES AT PARABOLIC BOUNDARIES

We first discuss the scattering of an electromagnetic plane wave at a perfectly conducting parabolic cylinder when the incident wave travels toward the edge of the cylinder and parallel to its axis. We get in t erms of Weber functions an exact solution which is simple enough to ma ke possible a comparison with approximate solutions developed to tackl e diffraction at rounded wedges. Then, we consider electromagnetic wav es capable of propagating inside the parabolic cylinder (eigenmodes). We prove that these eigenmodes correspond to the zeros of Weber functi ons which are real on the real axis. For the fundamental modes these W eber functions reduce to the Bessel functions J(+/-1/4) and we discuss the zeros of these functions.