Fractal polariton topological insulator

We introduce higher-order polariton topological insulator (HOTI) realized with a fractal array of microcavity pillars arranged into Sierpiński gasket-like geometry. This system, exhibiting self-similarity in different generations, can support localized modes in either the external or multiple internal corners, depending on the controllable distortion introduced into first-generation structure. Nonlinear corner modes can be selectively excited in this dissipative system using resonant optical pumping. Strong polariton-polariton interactions lead to tilt of the resonance curves and bistability as the pump amplitude increases, allowing control over corner state profiles. Linear stability analysis illustrates dynamical stability of such states. Our results show how nontrivial topology manifests itself in self-similar, <i>aperiodic</i> structures and indicate that fractal geometry may bring qualitatively new localization scenarios in polariton HOTIs.