Complex energy structures of exceptional point pairs in two level systems

Abstract: We investigate the topological properties of multiple exceptional points in non-Hermitian two-level systems, emphasizing vorticity as a topological invariant arising from complex energy structures. We categorize EP pairs as fundamental building blocks of larger EP assemblies, distinguishing two types: type-I pairs with opposite vorticities and type-II pairs with identical vorticities. By analyzing the branch cut formation in a two-dimensional parameter space, we reveal the distinct topological features of each EP pair type. Furthermore, we extend our analysis to configurations with multiple EPs, demonstrating the cumulative vorticity and topological implications. To illustrate these theoretical structures, we model complex energy bands within a two-dimensional photonic crystal composed of lossy materials, identifying various EP pairs and their branch cuts. These findings contribute to the understanding of topological characteristics in non-Hermitian systems.