Physically meaningful Monte Carlo approach to the four-flux solution of a dense multilayered system.

Abstract

Due to the complexity of the radiative transfer equation, light transport problems are commonly solved using either models under restrictive assumptions, e.g., N-flux models where infinite lateral extension is assumed, or numerical methods. While the latter can be applied to more general cases, it is difficult to relate their parameters to the physical properties of the systems under study. Hence in this contribution we present, first, a review of a four-flux formalism to study the light transport problem in a plane-parallel system together with a derivation of equations to evaluate the different contributions to the total absorptance and, second, as a complementary tool, a Monte Carlo algorithm with a direct correspondence between its inputs and the properties of the system. The combination of the four-flux model and the Monte Carlo approach provides (i) all convergence warranties since the formalism has been established as a limit and (ii) new added capabilities, i.e., both temporal (transient states) and spatial (arbitrarily inhomogeneous media) resolution. The support between the theoretical model and the numerical tool is reciprocal since the model is utilized to set a Monte Carlo discretization criterion, while the Monte Carlo approach is used to validate the aforementioned model. This reinforces the parallel approach used in this work. Furthermore, we provide some examples to show its capabilities and potential, e.g., the study of the temporal distribution of a delta-like pulse of light.