Hybrid-orbital topological disclination states and wave propagation in defect-induced confined Mie resonance photonic crystals

Topological disclinations (TDs), derived from the cut-and-glue process in topological crystalline insulators, have been effectively employed to localize fractional charges in classical wave systems. However, most existing strategies primarily focus on TD modes within the lowest band gap, neglecting the higher-orbital states. As the bands become entangled, higher band gaps are too narrow to support distinguished TD modes from bulk modes. In this work, we successfully demonstrate TD modes within the $s$-, $p$-, $d$-, and higher-orbital band gaps. In addition, we build photonic waveguides under the interplay between valley-Hall topology and TD defects. Unlike the traditional topological edge states confined on the outer boundary of the model, this TD-induced optical paths can hold hybrid-orbital topological waveguides within the sample. Furthermore, a wave propagation network is achieved by interconnecting different TD states, enabling more versatile wave transmission modes across various band gaps. This study paves the way for the manipulation of TD states and waveguides within hybrid-orbital band gaps in photonic crystals, offering promising applications in the design and fabrication of multimode optical devices, such as beam splitters and embedded topological cavities.