# Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics

## TL;DR

This paper demonstrates that time-delayed feedback can induce and control the spontaneous formation of two-dimensional rogue waves in broad-area nonlinear optical systems, revealing a universal instability mechanism.

## Contribution

It introduces a novel mechanism for rogue wave generation via time-delayed feedback in optical systems, applicable to both Lugiato-Lefever and laser models.

## Key findings

- Rogue waves are induced by delayed feedback in optical systems.
- The probability distribution of pulse heights shows long-tailed behavior.
- The phenomenon is universal across different optical models.

## Abstract

We demonstrate a way to generate a two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution which is often considered as a signature of the presence of rogue waves appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is an universal phenomenon.