Rigorous Derivation and Fast Solution of Spatial-Domain Green´s Functions for Uniaxial Anisotropic Multilayers Using Modified Fast Hankel Transform Method

A fast solution for rigorously deriving and calculating spatial-domain dyadic Green´s functions for the planar multilayers of uniaxial media has been established based on the modified fast Hankel transform (MFHT) method. The kDB coordinate system is exploited and integrated with the wave iterative technique to obtain the spectral-domain Green´s function. This algorithm relies on the accurate expressions of unbounded dyadic Green´s function and scattered Green´s function in uniaxial media, which can be classified into the ordinary and extraordinary waves. The newly developed MFHT method is then employed for the calculation of the dyadic Green´s function in the planar multilayered uniaxial anisotropic media. The validity of the algorithm thus developed and the efficiency of the MFHT method are verified through numerical examples. The spatial-domain Green´s function can, for the first time, deal with the multilayered uniaxial anisotropic media, and more importantly, the influence of material´s anisotropy upon the Green´s function is demonstrated. It provides a promising tool to analyze the integrated microwave circuits and optical devices when complex materials are involved.