On the relevance of two-dimensional models for radiation of statistical sources in stratified media

We present analytical closed-form expressions for the radiation patterns of 2-D line sources and 3-D point dipoles embedded in a general multilayered configuration. While the former are simplified model sources, used as a preliminary analytical step to reduce derivation complexity, the latter have been shown experimentally to reproduce the electromagnetic behavior of many elementary statistical sources. By decomposing the sources to current elements generating pure transverse electric (TE) or transverse magnetic (TM) polarized radiation, we arrive at a unified format for the radiation pattern expression for all sources considered. Analyzing the common 1-D (characteristic) Green's function, we show that the normalized TE-polarized emission of model 2-D electric line sources reproduces exactly the measured TE-polarized radiation of statistical (3-D) dipoles with random in-plane orientation; the connection between the TM-polarized emission of the two species is discussed, and physical interpretation is provided via the unified expression. These results specify the precise relations between the 2-D and 3-D models, providing intuition as well as guidelines for proper usage of simplified 2-D results for analysis of realistic 3-D statistical configurations.