# Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals

## TL;DR

This paper experimentally demonstrates second-order topological insulator phases in 2D dielectric photonic crystals, visualizing edge and corner states, and introduces a new topological invariant for characterizing these phases, expanding the potential for hierarchical light manipulation.

## Contribution

The study shows HOTIs can be realized without negative coupling in dielectric PCs, using a novel bulk polarization-based topological invariant, broadening the scope of topological photonics.

## Key findings

- Visualization of topological edge and corner states in dielectric PCs
- Introduction of a new bulk polarization-based topological invariant
- Realization of HOTIs without negative coupling

## Abstract

The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been investigated as a novel topological phase of matter beyond the conventional bulk-boundary correspondence. Previous studies of HOTIs have been mainly focused on the topological multipole systems with negative coupling between lattice sites. Here we experimentally demonstrate that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals (PCs). We visualize both one-dimensional topological edge states and zero-dimensional topological corner states by using near-field scanning technique. To characterize the topological properties of PCs, we define a novel topological invariant based on the bulk polarizations. Our findings open new research frontiers for searching HOTIs in dielectric PCs and provide a new mechanism for light-manipulating in a hierarchical way.