The Limits of Transmittance of an Interface and Their Effects on Light Extraction

We have investigated the upper limit for transmittance of electromagnetic radiation through an interface between two materials of differing refractive indexes. This limit was previously established using thermodynamic arguments [A. Lenef, J. F. Kelso, and A. Piquette, Opt. Lett., 39, 3058 (2014)]. We show that this limit is absolute and can also be derived independently from classical electromagnetic theory. The maximum enhancement of transmittance through an interface is shown to be similar to 4% compared to that of a perfectly flat surface for a Lambertian distribution of light. Using a semi-infinite slab enclosed by two surfaces, one of which is a mirror, we show how relatively unimportant the enhancement of the single-interface transmittance could be compared to other cavity-related effects for extracting a photon. Neither a planar reflecting surface nor a roughened surface could alone significantly improve the extraction efficiency. However, higher extraction efficiency could be achieved through a combination of reflection and roughened faces which allows a photon to escape ultimately because of multiple reflections and scattering. It is shown through numerical simulation using geometrical optics that the reflectance of the mirror and the absorption of the bulk material could be significantly more important than the surface transmittance in this case. (C) The Author(s) 2017. Published by ECS.