Extended and confined rogue wave states in non-instantaneous Kerr resonators

We present a numerical study of an optical cavity filled with a non-instantaneous Kerr medium and driven by a coherently injected beam. We provide evidence of exploding localized structures at the output of this simple optical device. This phenomenon arises from the interaction between self-pulsating and modulational instabilities within the system. The exploding dissipative structure manifests as a localized mixed mode that exhibits an irregular temporal evolution. A statistical analysis reveals a connection between this phenomenon and the formation of rogue waves in both one- and two-dimensional configurations. We show that rogue wave states can either extend to fill the entire cavity length (1D) or transverse plane (2D) or remain confined to a specific region. Finally, we report the emergence of a localized state that exhibits spatiotemporal complexity and generates rogue waves in this system.