Dimensionality reduction in the numerical evaluation of electro-magnetic scattering: from the Kirchhoff's integral method to a zero-dimensional approach

Abstract

A new, simple estimate of the diffraction coefficients, to be used in a ray tracing calculation, is derived applying the stationary phase technique to the boundary wave integral. This approach is shown to be the last step (0-dimensions) of a dimensionality reduction procedure which begins with the Kirchhoff's integral method (2-dimensions) and proceeds with the boundary wave approach (1-dimension). While the reduction – from three to two – of the dimensionality, requires the physical optics approximation and the reduction from two to one holds only for perfectly conducting solids with flat faces and spherical or plane incident waves, no additional price is paid to pass from one to zero dimensions. The Zero-Dimensional (ZD) approach is validated through numerical comparison with higher dimensionality methods and analytical (exact) results in a number of test cases.