Abstract
Fock's principle is extended to apply to the fields near the shadow boundary on a parabolic cylinder, illuminated by a plane wave propagating at an arbitrary angle but normal to the cylinder axis. By solving the wave equation in parabolic coordinates, with an impedance boundary condition at the surface and a radiation condition at infinity, we find that the fields thus obtained agree very well with those predicted by Fock's principle, as long as the observation point is near where the wave propagation vector is tangent to the cylinder. When the propagation vector is tangent to the cylinder's apex, Fock's principle gives the exact currents everywhere on the cylinder. These results are more general than those of Jones, which are limited to perfectly conducting cylinders.
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