Demonstration of higher-order topological States in photonic kagome lattice with next-nearest-neighbour coupling

In this paper, we investigate topological states in a two-dimensional distorted Kagome lattice with next- nearest-neighbour (NNN) coupling. We show that introducing NNN coupling leads to the emergence of a new type of higher-order corner states in a non-trivial topological phase. Using near-field scanning technique, we verify our theoretical predictions in the microwave frequency range and demonstrate field profiles for both conventional and new type of corner states. The experimental results are in perfect agreement with numerical simulations of finite structure.