Fast Solution of Dyadic Green's Functions for Planar Multilayered Media

Abstract

Integral equation methods have been a versatile tool for the electromagnetic analysis of microwave integrated circuits implemented in planar multilayered substrates. The electric and magnetic fields in the multilayered structures can be easily derived from the dyadic Green's function. Consequently, a large amount of research work has been dedicated to the study of fast methods for calculating the dyadic Green's functions in the multilayered media.

The fast Hankel transform filter technique has been proved to be an efficient method for calculating the dyadic Green's functions. However, the fast Hankel transform method is only applicable for shielded multilayered geometries, due to the branch-point singularity. To overcome this limitation, the proposed modified fast Hankel transform method deforms the integration path of Sommerfeld integral from the real axis to the quadrant and the Bessel function with a complex argument is expanded as a sum of terms. Numerical results confirm that the modified fast Hankel transform method has a good performance in accuracy and wide applications.

The discrete complex image method, the window function method and the modified fast Hankel transform method are three popular fast techniques for calculating the dyadic Green's functions in a multilayered medium. In order to provide detailed knowledge of the accuracy, efficiency and application range of the three fast methods, the robustness and efficiency of the three methods are carefully examined. The results indicate that discrete complex image method is effective for general multilayered cases and modified fast Hankel transform method is also a powerful tool, while the accuracy and efficiency of window function method is strongly dependent on the multilayered geometry.

Next, another aim of the research work is to systematically derive the spectral-domain Green's function used in the electric field integral equation for the multilayered uniaxial anisotropic medium and gyrotropic medium. Then, the spatial-domain Green's functions in the two kinds of media are calculated based on the fast methods. More importantly, the influence of material's anisotropy upon these dyadic Green's functions is investigated. The kDB coordinate system is exploited and integrated with the wave iterative technique to derive the spectral-domain Green's function. From the view of numerical results, it can be deduced that the dyadic Green's functions in both the spectral domain and spatial domain for the multilayered uniaxial anisotropic medium and gyrotropic medium are very accurate.

In conclusion, this study is the first to provide valuable insight into the merits and limitations of three popular fast methods for calculating the dyadic Green's functions in a multilayered medium. Moreover, the spatial-domain Green's functions in the multilayered uniaxial anisotropic medium and gyrotropic medium are successfully obtained for the first time. Finally, in view of the increasing application of anisotropic media to the integrated circuits and microstrip antenna, it is worthwhile to employ the dyadic Green's functions associated with the method of moments to analyze their properties for the future research study.