Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium

A previously developed fast inhomogeneous plane wave algorithm is adapted to the analysis of the scattering from the objects above a multilayered medium. Based on the similarity of the inhomogeneous plane wave expansion of the Green´s function encountered in the layered medium study to its free space counterpart, the proper steepest descent path can be defined. By using the interpolation and extrapolation techniques, the translation matrix is diagonalized. The contributions of the pole and branch point, resulting from the deformation of the integration path, can be handled easily. Comparing with the previously developed methods in this area, this algorithm is simpler, more efficient, and more general. The multilevel fast inhomogeneous plane wave algorithm has been implemented and the numerical results show that O(N log N) computational complexity of the algorithm is achieved. The algorithm is validated by comparing the results from a conventional method of moments program