Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with...

Area of Science:

• Computational Physics
• Photonics and Optics
• Applied Mathematics

Background:

• Photon propagation in complex media often requires computationally intensive Monte Carlo simulations.
• Existing models for binary mixtures with unmatched refractive indexes can be simplified.
• Homogenization techniques aim to represent complex media as simpler, equivalent homogeneous ones.

Purpose of the Study:

• To analytically derive the exact homogenized probability density function (PDF) for photon steps in binary mixtures.
• To obtain exact, homogenized PDFs for photon scattering angles (polar and azimuthal) and homogenized albedo.
• To demonstrate the reduction in computational cost for photon propagation simulations.

Main Methods:

• Analytical derivation of probability density functions for photon propagation.
• Development of exact homogenized functions for scattering events and albedo in binary mixtures.
• Application to mixtures with unmatched and negative refractive indexes.

Main Results:

• The exact homogenized probability density function for photon step length was derived.
• Exact, homogenized PDFs for scattering angles (polar ϑ, azimuthal φ) and albedo were obtained.
• These functions are applicable to binary mixtures with unmatched and negative refractive indexes.

Conclusions:

• The derived analytical functions provide a mathematically equivalent and exact method for simulating photon propagation.
• Significant reduction in Monte Carlo simulations (from hundreds to one) is achievable for complex binary mixtures.
• The approach offers a powerful tool for efficiently studying photon transport in various optical media.