Dual Band Second‐Order Topological Corner States in 2D Valley‐Hall Hexagonal Photonic Crystals

Abstract

Second‐order topological corner states are of great importance in the field of topological photonics. In particular, for realizing disorder‐immune coherent nanosources based on nonlinear processes one needs multiband topological corner states. This work reports dual band second‐order topological corner states in the structure of valley‐Hall hexagonal photonic crystals. When the ratio between the radii of dielectric cylinders in the unit cells continuously increases, bulk gap opening, appearance of edge states, edge gap opening, and generation of second‐order corner states successively occur in the first and third bandgaps. By changing the structural parameters, the eigenfrequencies of the corner states in both edge gaps can be flexibly adjusted. Compared with square‐lattice valley‐Hall systems, large difference of eigenfrequencies of corner states in dual bandgaps can be obtained with hexagonal photonic crystals, which is the key advantage of the proposed systems for applications in nonlinear coherent generations such as second‐harmonic generation. The numerical results show that the dual band second‐order corner states clearly exhibit robustness against structural defects, significantly distinguished from the defect states. The results presented in this work pave the way toward topologically protected coherent nanosources by nonlinear frequency conversion which are robust against structural disorder or defects.

Simultaneous Appearance of Different Topological Phases in a Single Photonic System: Coexisting Phases Characterized by Bulk Polarization and Valley‐Chern Number Enabling Dual‐Band Second‐Order Topological States

“…[ 3–9 ] The successful transferring of topological concepts from condensed matter physics [ 10 ] to photonics [ 11,12 ] has provided a new way of robust manipulation of light against structural disorders or defects using the photonic quantum Hall effect [ 13,14 ] and photonic quantum spin‐ [ 15,16 ] and valley‐Hall effects, [ 17–20 ] paving the way toward important applications such as topological lasers [ 4,6,8,21 ] and topological edge solitons. [ 22,23 ] The recently proposed multiband topological states [ 5,23–27 ] can be applied for topological nonlinear frequency conversion. [ 28–30 ]…”