Bounds on the Topological Charge of Photonic Systems

Topology has become a central concept in understanding physical phenomena, leading to important advances in condensed matter and photonics. Recent work has established a universal upper bound on the energy gap of Chern insulators in electronic systems, revealing a fundamental connection between topology, quantum geometry, and optical absorption. Here, we generalize this framework to photonic systems, deriving rigorous upper bounds on gap Chern numbers without requiring explicit topological analysis. Our approach enables the estimation of the topological charge of band gaps in both dispersive and nondispersive regimes.