# Loss of phase and universality of stochastic interactions between laser beams

## TL;DR

This paper demonstrates that nonlinear propagation causes laser beams to lose initial phase information, leading to universal interaction statistics that can be modeled without precise phase knowledge.

## Contribution

It reveals the loss of phase and universality in laser beam interactions due to nonlinear propagation, introducing a polynomial-chaos approach for statistical modeling.

## Key findings

- Phase information is lost over long distances in nonlinear propagation.
- Interaction outcomes become statistically universal, independent of initial phases.
- Polynomial-chaos method efficiently predicts interaction statistics.

## Abstract

We show that all laser beams gradually lose their initial phase information in nonlinear propagation. Therefore, if two beams travel a sufficiently long distance before interacting, it is not possible to predict whether they would intersect in- or out-of-phase. Hence, if the underlying propagation model is non-integrable, deterministic predictions and control of the interaction outcome become impossible. Because the relative phase between the two beams becomes uniformly distributed in $[0,2\pi]$, however, the statistics of the interaction outcome are universal, and can be efficiently computed using a polynomial-chaos approach, even when the distributions of the noise sources are unknown.