An Operator-Based Approach to Topological Photonics - Band Structures and Bloch Eigenstates Not Required

Explore an innovative operator-based approach to topological photonics in this 40-minute lecture by Alexander Cerjan from PCS Institute for Basic Science. Delve into a mathematical framework for determining a photonic structure's topology directly from its real-space description, bypassing the need for band structure or Bloch eigenstate calculations. Discover how this method, based on the photonic system's spectral localizer, yields local invariants protected by local gaps for every symmetry class. Learn about the emergence of non-trivial topology and boundary-localized resonances in photonic crystals lacking complete band gaps. Examine the extension of this approach to nonlinear systems, introducing quantitative definitions of topological nonlinear modes and topological dynamics. Gain insights into the exciting field of topological structures in photonics and their potential applications in linear and non-linear devices.