Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture

Area of Science:

• Physics
• Computational Science
• Optics

Background:

• Monte Carlo (MC) simulations are crucial for modeling photon propagation in various scientific fields.
• Implementing MC simulations for statistical mixtures is often highly complex.
• Current methods require extensive computational resources for accurate results.

Purpose of the Study:

• To propose a novel approach for simplifying MC simulations of photon propagation in statistical mixtures.
• To derive an exact analytical expression for the single step function (SSF) in binary statistical mixtures.
• To reduce the computational complexity and number of simulations required.

Main Methods:

• Derivation of the exact analytical expression for the probability density function of photons' random steps (SSF).
• Focus on a binary (isotropic-Poisson) statistical mixture as an explanatory example.
• Development of an equivalent homogeneous medium representation.

Main Results:

• The derived SSF analytically describes photon random steps in a binary statistical mixture.
• The approach transforms the complex mixture into an equivalent homogeneous medium.
• This significantly reduces the number of required MC simulations from hundreds to one.

Conclusions:

• The new analytical SSF offers a substantial simplification for MC simulations in statistical mixtures.
• This method enhances the efficiency and accessibility of MC simulations in optics and beyond.
• The derived SSF for binary mixtures is a novel contribution to computational physics.