In this paper, we improve the Ge-Esselle's (GE's) method and apply it to calculate the multilayered Green's functions in the shielded structures. In the improved GE's method, 1) the poles are first extracted using a recursively contour integration method ; 2) then the general pencil-of-function (GPOF)  is performed to approximate the part of the spectral-domain Green's functions (with the poles contributions being extracted) just along the real axis of kρ plane instead of the rooftop shaped path defined in ; 3) Subsequently, the GE's analytical method is employed to obtain the spatial-domain Green's functions. In step 2), a smoothing procedure is also performed here to eliminate the abrupt peak of the sampled spectral-domain Green's function caused by the finite machine accuracy of the poles locations. The numerical results in this paper show that the improved GE's method can accurately and efficiently calculate the Green's functions in the shielded multilayered structure.
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