Dissipative topological light bullets in graphene-based active random metamaterials

We predict a type of three-dimensional spatiotemporal solitons, or light bullets, in an active metamaterial of randomly dispersed graphene nanoflakes embedded within an optically pumped gain medium (rhodamine 6G). Adopting a generalized nonlinear Schrödinger equation governing optical propagation in such a system, we find that, depending on the external pumping conditions and graphene flake density, these spatiotemporal solitons appear in a wide variety of shapes ranging from inverted toplike objects to vortex tori, supported by the complex nonlinearity of the metamaterial. We uncover their domain of existence by tuning the gain coefficient of rhodamine 6G, finding fundamental and vortex light bullets with distinct topological charges. We further discover that the spatiotemporal profiles and instability gain of the bullets unambiguously correspond to the graphene nanoflakes' volume density and gain coefficient of the active component. Our results provide a route towards the manipulation of three-dimensional spatiotemporal solitons in an easy-to-fabricate metamaterial.