Stochastic radiative transfer in random media: Pure absorbing cases

Area of Science:

• Physics
• Applied Mathematics
• Optical Engineering

Background:

• Stochastic radiation transport is crucial for understanding wave propagation in complex media.
• Previous models often simplify the statistical properties of random media.

Purpose of the Study:

• To investigate the influence of stochasticity in random media on one-dimensional radiation transport.
• To develop a statistical model for ensemble-averaged transmission in binary random mixtures.

Main Methods:

• Derivation of a statistical model based on the cumulative probability density function (PDF) of optical depth.
• Numerical simulation using Monte Carlo calculations for Markovian and non-Markovian mixtures.
• Analysis of the impact of mixing statistics, particle size, and mixed configuration.

Main Results:

• Mixing statistics critically affect ensemble-averaged intensities, particularly at small optical depths.
• The cumulative PDF's distribution explains sensitivity to chord length distribution and variances.
• Particle size significantly influences transport when correlation length nears the photon mean free path.

Conclusions:

• The study provides a robust model for radiation transport in random media.
• Understanding mixing statistics is essential for accurate prediction of transmission.
• The findings have implications for designing systems involving wave propagation through heterogeneous materials.