Phase of Topological Lattice with Leaky Guided Mode Resonance

Abstract

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk–edge correspondence and symmetry-related topological invariants has been extended to non-Hermitian systems. Correspondingly, the value of geometric phases, such as the Pancharatnam–Berry or Zak phases, under the adiabatic quantum deformation process in the presence of non-Hermitian conditions, are now of significant interest. Here, we explicitly calculate the Zak phases of one-dimensional topological nanobeams that sustain guided-mode resonances, which lead to energy leakage to a continuum state. The retrieved Zak phases show as zero for trivial and as π for nontrivial photonic crystals, respectively, which ensures bulk–edge correspondence is still valid for certain non-Hermitian conditions.