Stochastic Dynamics of Incoherent Branched Flow

TL;DR

This paper develops a stochastic theory for incoherent branched flow in weakly disordered media, revealing how coherence and interference influence flow formation and providing a framework for future nonlinear media studies.

Contribution

It introduces a comprehensive stochastic model for incoherent branched flow, extending understanding beyond coherent wave systems with closed-form equations and validated simulations.

Findings

Derived equations for intensity correlation and scintillation index.

Quantitative agreement between theory and simulations.

Highlighted the role of coherence in branched flow dynamics.

Abstract

Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent experiments have reported the observation of optical branched flow by using an incoherent light source, thus revealing the key role of coherent phase-sensitive effects in the development of incoherent branched flow. By considering the paraxial wave equation as a generic representative model, we elaborate a stochastic theory of both coherent and incoherent branched flow. We derive closed-form equations that determine the evolution of the intensity correlation function, as well as the value and the propagation distance of the maximum of the scintillation index, which characterize the dynamical formation of incoherent branched flow. We report accurate numerical simulations that are found in quantitative agreement with the theory without free parameters. Our theory highlights the important impact of coherence and interference on branched flow, thereby providing a framework for exploring branched flow in nonlinear media, in relation with the formation of freak waves in oceans.