Efficiency scaling of non-coherent upconversion in a one-dimensional model system

A very promising approach to obtain efficient upconversion of light is the use of triplet-triplet annihilation of excitations in molecular systems. In real materials, besides upconversion, many other physical processes take place--fluorescence, phosphorescence, non-radiative decay, annihilation, diffusion--and compete with upconversion. The main objective of this work is to design a proof of principle model that can be used to shed light on the interplay between these processes. Ultimately, we want to establish general principles that may guide experimentalists toward the design of solid state materials with maximum efficiency. Here we show, in a one-dimensional model system, that upconversion can be optimized by varying the ratio between the two molecular species used in triplet-triplet-annihilation based upconversion systems, even in the presence of undesired losses through phosphorescence, non-radiative decay, or annihilation. We derive scaling laws for this ratio and for the maximum efficiency of upconversion, as a function of the diffusion rate J, as well as of the creation and of the decay rate of the excitations.