Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with unmatched positives/negatives refractive indexes

The exact homogenized probability density function, for a photon making a step of length $s$ has been analytically derived for a binary (isotropic-Poisson) statistical mixture with unmatched refractive indexes. The companions, exact, homogenized probability density function for a photon to change direction (``scatter'') with an angle $\vartheta$, and the homogenized albedo, have also been obtained analytically. These functions also hold even in the case of negative refractive indexes and allow one to reduce hundreds of MC simulations of photon propagation in complex binary (isotropic-Poisson) statistical mixtures, to only one MC simulation, for an equivalent homogeneous medium. Note, that this is not an approximate approach, but a mathematically equivalent and exact result. Additionally, some tutorial examples of homogenized MC simulations are also given.