The scattering cross section of a composite cylinder, geometric optics

The optical analogue of the scattering cross section of a composite cylinder is developed from a representation of the forward scattered amplitude as a continuous spectrum of radial eigenfunctions. The Debye approximation for the Hankel functions, which is valid when their arguments are large compared to the order, leads to a series of integrals which can be evaluated asymptotically by the method of stationary phase. The final result, for a certain range of parameters, is a diffraction correction plus a double sum of terms, each of which can be interpreted as an optical ray. It is shown that if the angular displacement between the incoming and scattered ray directions is
(2m + 1)\pi
, the ray must have been reflected at the conducting core of the cylinder at least
2m + 1
times. After the parameter ranges to which these results apply were determined, the nonlinear equations for the ray angles were solved on a large-scale digital computer and the scattering cross section of a number of composite cylinders was calculated as a function of frequency. The results are presented graphically.