Markov chains for modeling complex luminescence, absorption, and scattering in nanophotonic systems.

We developed a method to model fluorescence, absorption, and scattering in nanophotonic systems using ergodic Markov chains. Past works have used absorbing Markov chains to find the long-run angle-dependent distribution of emitted photons. In contrast, we use ergodic Markov chains to focus on the steady state distribution of photons within various media, giving additional insight into the macroscopic optical response during illumination. We show that the method reproduces Beer-Lambert's Law and Kirchhoff's Law, and can quantify deviations from these laws when their assumptions are violated. We also use the method to model luminescent solar concentrators (LSCs) based on semiconductor nanocrystals.