# Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

## TL;DR

This paper explores how nonlinearity influences the formation of caustics and rogue waves across different wave systems, demonstrating experimentally and through simulations that small phase fluctuations can produce strong caustics in nonlinear regimes.

## Contribution

It provides the first experimental and simulation evidence that nonlinearity significantly enhances caustic formation from small phase fluctuations in wave systems.

## Key findings

- Nonlinear propagation amplifies small phase fluctuations into strong caustics.
- Experimental and simulation results align with nonlinear Schrödinger equation predictions.
- Nonlinearity's role is crucial in understanding rogue wave phenomena in various physical systems.

## Abstract

Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean floor can generate random caustics and focus the energy of tsunami waves. Caustics share many similarities to rogue waves, as they both exhibit heavy-tailed distribution, i.e. an overpopulation of large events. Linear Schr\"odinger-type equations are usually used to explain the wave dynamics of caustics. However, in that the wave amplitude increases dramatically in caustics, nonlinearity is inevitable in many systems. In this Letter, we investigate the effect of nonlinearity on the formation of optical caustics. We show experimentally that, in contrast to linear systems, even small phase fluctuations can generate strong caustics upon nonlinear propagation. We simulated our experiment based on the nonlinear Schr\"odinger equation (NLSE) with Kerr-type nonlinearity, which describes the wave dynamics not only in optics, but also in some other physical systems such as oceans. Therefore, our results may also aid our understanding of ocean phenomena.