Methodology for Topological Interface Engineering in 2D Photonic Crystals

Abstract: Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic topological interfaces in two-dimensional photonic crystals. We introduce an iterative band connection algorithm that preserves mode symmetry and present a general framework for band symmetry recognition, essential for identifying Z2 topological phases. Design strategies for unit cell geometries are developed to achieve targeted band inversions, overlapping bandgaps, and tailored dispersions. Furthermore, the approach can be readily adapted to specific material platforms and operating wavelengths, including the telecommunication range, by appropriately scaling the lattice parameter as long as absorption remains low. We investigate the trade-off between bandgap size and band flatness, identifying exceptions governed by lattice geometry. Additionally, we demonstrate how photonic crystal periodicity influences the stability of topological modes and enhances unidirectional energy transport.