Homogenized Green´s Functions for an Aperiodic Line Source Over Planar Densely Periodic Artificial Impedance Surfaces

The accurate electromagnetic analysis of artificial periodic surfaces formed as planar layers with complicated periodic metallization patterns, having a grid period much smaller than the effective wavelength (densely periodic), is important for the design and analysis of a variety of electromagnetic structures. However, full-wave modeling can be extremely time-consuming and computationally expensive, especially for aperiodic sources in close proximity to periodic surfaces. In this paper, we describe approximate homogenized models for a Green´s function that treats planar patterned screens (grids) as quasi-dynamic homogenized impedance surfaces and dielectric layers in a fully dynamic manner. The resulting Green´s functions are only slightly more complicated than those for dielectric layers without metallization and can be numerically computed using standard methods for layered media. We restrict attention to line sources and compare numerical results from this method with those from a full-wave array scanning method, which is more complex analytically and much more demanding to evaluate numerically. Very good agreement is found between the two methods except for source and/or field points extremely close to the metallization layer, confirming the accuracy of the homogenized representations of periodic surfaces for near-field sources.