A Modified Fast Hankel Transform algorithm for calculating planar multilayered Green's function

When the Fast Hankel Transform filter technique is used to calculate the dyadic multilayered Green's functions, it can be difficult to obtain accurate numerical results because of the branch-cut singularity and the surface wave poles singularity. The Modified Fast Hankel Transform filter algorithm is proposed to overcome this problem by expressing the Bessel function with a complex argument as a sum of terms of product of Bessel function with the real part of the argument and Bessel function with the imaginary part of the argument. Then the Fast Han-kel Transform filter technique is applied to each expansion term. Numerical results confirm that the proposed approach has high accuracy and efficiency and successfully extends the applicability of the conventional Fast Hankel Transform method to general multilayered geometries.