On the relevance of two-dimensional sources for modelling optical emission from layered media

We present analytical closed-form expressions for the radiation patterns of 2D line sources and 3D point dipoles embedded in a general multi-layered 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 behaviour of elementary (molecular) optical 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. Analyzing the common 1D Green's function, we show that the normalized TE-polarized emission of the model 2D electric line sources reproduces exactly the TE-polarized radiation of molecular (3D) dipoles, and discuss the relations between the TM-polarized emission of the two species. These results specify the precise relations between the 2D and 3D models, thus providing intuition as well as guidelines for proper usage of simplified 2D results for analysis of realistic 3D optical systems.