Circular Bessel statistics: derivation and application to wave propagation in random media

Area of Science:

• Wave physics
• Statistical optics
• Random media theory

Background:

• Traditional Gaussian statistics fail to describe wave phenomena in Anderson localization and weakly scattering regimes.
• The breakdown occurs when wave fields cannot be treated as sums of independent random phasors.
• A need exists for a unified statistical model applicable across diverse scattering conditions.

Purpose of the Study:

• To introduce a novel family of circular Bessel probability density functions.
• To provide a unified statistical framework for wave propagation in any random medium.
• To extend the applicability of statistical models beyond the limitations of Gaussian distributions.

Main Methods:

• Development of circular Bessel probability density functions.
• Modeling wave fields as random phasor sums with a variable number of contributors.
• Numerical simulations of electromagnetic wave propagation in two-dimensional random media.

Main Results:

• Circular Bessel statistics accurately describe wave intensity, amplitude, and field statistics in random media.
• These statistics are valid in regimes where Gaussian models fail, including Anderson localization and weak scattering.
• Numerical simulations confirm the efficacy of the proposed density functions.

Conclusions:

• Circular Bessel statistics offer a comprehensive model for wave propagation in all random media scattering regimes.
• This framework supports advancements in random media characterization and imaging through scattering.
• Applications include the design of novel random lasers and improved understanding of wave-matter interactions.