An efficient closed-form expression of spatial Green´s function for finite dielectric substrate using characteristic Green´s function-perfectly matched layer method

An efficient closed-form spatial Green´s function solution is derived for open finite dielectric substrate. By placing perfectly matched layer (PML) that is backed by perfect electric conductor (PEC) in semi-infinite layer at the top and/or bottom and by using characteristic Green´s function (CGF) technique, a closed-form series representation of spatial Green´s function is obtained. Utilizing the eigenmodes of the closed structure by PML called the Berenger and quasi-leaky wave poles, continuous spectrum contribution of the original structure is simply evaluated. Derived Green´s function is exact for separable structure while it is approximate for nonseparable one. By importing Generalized scattering matrix (GSM) in CGF formulation, more exact results for nonseparable structures are obtained. Analytic knowledge of the source and observation points dependence allows very efficient computation and storage of the Green´s function. Excellent agreements with the rigorous method of moments (MOM) are demonstrated.