On the Radiation Problem at High Frequencies

The angular distribution of radiation from a vibrating cylinder of arbitrary cross section is considered in the limit of high frequencies. An inhomogeneous integral equation of the first kind is derived for the distribution and is solved by the method of steepest descents. The first approximation yields the “geometric optics” result in which every element of the radiator radiates normally to itself. Higher order terms are obtained for the case in which the boundary conditions on the radiator surface vary smoothly. The case of an abrupt change in boundary condition is also solved and exhibits typical diffraction effects. The techniques used in this paper have a wide range of applicability to problems of radiation and scattering of waves as they occur in field physics.