On the validity of two-dimensional models for radiation of optical sources in stratified media

We present a unified analytical closed-form expression 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 usually as a preliminary analytical step, the latter have been shown experimentally to reproduce the electromagnetic behaviour of elementary (molecular) optical sources. Analyzing the unified expression, derived using a decomposition of the point dipoles into current elements producing pure transverse electric (TE) or transverse magnetic (TM) fields, we show that measured TE-polarized radiation patterns of realistic 3D electric point dipoles exactly matches the TE-polarized radiation patterns of the model 2D electric line sources, if normalized appropriately. Moreover, we discuss the differences between the TM-polarized emission of the 2D and 3D sources, and provide a clear physical interpretation via the unified expression. 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.