Scattering of an electromagnetic plane wave by a Luneburg lens III Finely stratified sphere model

The parallel iteration procedure for computing scattering by a multilayer sphere is described. The procedure uses a successive doubling strategy applied to four sets of multiple-scattering amplitudes, which is reminiscent of the fast Fourier transform (FFT) algorithm. The procedure is then used to calculate scattering of a plane wave by a modified Luneburg lens. The evolution of the transmission rainbow for the Luneburg lens parameter f>1 into an orbiting ray for f=1 and into a series of morphology-dependent resonances for f<1 is studied, and various features of the scattered intensity as a function of scattering angle are commented on. It is found that some resonances are formed without the presence of an exterior centrifugal barrier to confine them.