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 least2m + 1times. 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.