The coupled cavity-waveguide approach provides a flexible platform to design integrated photonic devices that are widely applied in optical communications and information processing. Topological photonic crystals that can excite the nontrivial edge state (ES) and corner state (CS), have unprecedented capability in manipulating electromagnetic (EM) waves, leading to a variety of unusual functionalities that are impossible to achieve with conventional cavity-waveguide systems. In this paper, two-dimensional photonic crystals consisting of a topological ES waveguide, a...