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

Area of Science:

• Nanophotonics and Optical Physics
• Statistical Mechanics and Computational Modeling

Background:

• Traditional methods using absorbing Markov chains focus on photon emission trajectories.
• Understanding the steady-state distribution of photons is crucial for macroscopic optical properties.

Purpose of the Study:

• To develop a novel method for modeling light propagation (fluorescence, absorption, scattering) in nanophotonic systems.
• To analyze the steady-state photon distribution and its relation to macroscopic optical responses.
• To investigate the validity and limitations of established optical laws like Beer-Lambert's and Kirchhoff's.

Main Methods:

• Utilized ergodic Markov chains to model photon behavior within nanophotonic systems.
• Focused on the steady-state distribution of photons rather than long-run emission angles.
• Applied the method to model luminescent solar concentrators (LSCs) using semiconductor nanocrystals.

Main Results:

• The ergodic Markov chain method successfully reproduces Beer-Lambert's Law and Kirchhoff's Law.
• The model quantifies deviations from these laws when their underlying assumptions are not met.
• Demonstrated the method's applicability to complex systems like semiconductor nanocrystal-based LSCs.

Conclusions:

• Ergodic Markov chains provide a powerful framework for understanding steady-state photon distributions in nanophotonics.
• This approach offers deeper insights into macroscopic optical responses under illumination.
• The method serves as a valuable tool for analyzing optical phenomena and designing nanophotonic devices.