M. Idemen et E. Erdogan, HIGH-FREQUENCY SURFACE CURRENTS INDUCED ON A SPHERICAL REFLECTOR BY THE EDGE-DIFFRACTION OF OBLIQUELY INCIDENT WAVES, Wave motion, 24(4), 1996, pp. 395-419
An explicit expression of the high-frequency surface current excited o
n a perfectly conducting spherical cap by the edge-diffraction of an o
bliquely incident wave is derived. The result is given in the GTD term
inology and shows the influence of the incidence angles on the transfe
r functions. To this end the real (physical) space is embedded into a
twofold extended abstract space in which an equivalent canonical probl
em is established, This latter yields a system of dual integral equati
ons whose kernels were not previously treated. By inverting these new
kernels, the system of dual equations is reduced to two independent Wi
ener-Hopf problems. From the asymptotic solutions of these problems, o
ne derives the expression of the edge-excited current along with the k
nown geometrical optics term. The resutlt can be used directly in prac
tical applications. If the incident ray becomes normal to the edge, th
en the resulting expressions are reduced to the already known expressi
ons. The basic idea and general formulas used here can also be used to
solve other diffraction problems with similar geometry.