Abstract

The scattering matrix is a crucial characterization of a physical system. The authors present here a systematic topological theory of scattering matrices, focusing on their singular values and vectors. They identify topological characteristics such as winding number, Berry phase, and skew polarization. The theory uncovers the topological nature of coherent perfect absorption and introduces coherent perfect extinction, where a coherent wave is completely extinguished through interference. These findings advance the understanding of scattering and have implications for novel wave devices.