Speckle formation of light propagation in random media. The Gaussian conjecture

A widely accepted conjecture in the physical literature states that classical wave-fields propagating in random media over large distances eventually follow a complex circular Gaussian distribution. In this limit, the wave intensity becomes exponentially distributed, which corroborates the speckle patterns of laser light observed in experiments. This talk reports on recent result settling the conjecture in the weak-coupling, paraxial regime of wave propagation, which is accurate and routinely used in the application of laser light propagation in turbulent atmospheres. The limiting macroscopic Gaussian wave-field is fully characterized by a correlation function solution of an anomalous diffusion equation. Numerical simulations illustrate the theoretical findings.  This is joint work with Anjali Nair.