Modified GTD for generating complex resonances for flat strips and disks

The complex resonance frequencies of a scatterer are important elements in target classification and identification. In the singularity expansion method (SEM), the resonances are defined by a homogeneous integral equation whose numerical solution is feasible in the low, but not in the high, frequency range. At high frequencies, the geometrical theory of diffraction (GTD) provides an attractive numerical alternative and, furthermore, incorporates an interpretation of the resonance generation process in terms of multiple wavefront (ray) traversals. Except for extremely simple scatterer configurations, the (damped) complex resonances are known to occupy an entire half of the complex frequency plane. Dominant and higher order creeping wave GTD applied to cylinders and spheres does indeed yield resonances arranged along a sequence of "layers" in that entire half-plane, but multiple edge diffracted GTD applied to flat strips and disks furnishes only a single (dominant) layer. By drawing analogies with higher order creeping waves on a smooth object, the conventional edge diffracted GTD field is here augmented by higher order ray fields undergoing higher order "slope diffraction." Each of these higher order ray fields can be made to satisfy its own resonance equation, which is now found to provide the missing layers, with remarkably accurate values for the resonances when compared, where available, with those calculated numerically by the moment and T-matrix methods. The success of higher order ray diffraction in predicting the complex resonance structure suggests that this mechanism may play a corrective role also in other edge dominated scattering phenomena.