Multiplexing Two Types of High-Order Topological Corner States in Kagome Lattice Photonic Crystals.

Topological corner states with wavelength-selective excitation and directional routing enable on-chip wavelength-dependent beam splitters (WDBSs) for multiplexing technology. In this work, we employ two types of topological corner states to implement WDBS in kagome lattice photonic crystals. A tight-binding model incorporating both nearest-neighbor and next-nearest-neighbor couplings is applied to describe the bulk and corner states in the second-order topological photonic crystal. A 120-degree-turning interface is constructed that supports two types of corner states, where the type-I corner state is even mode originating from nearest-neighbor coupling and the type-II state is odd mode originating from next-nearest-neighbor coupling. The spatial Fourier transformation of eigenstates indicates that the type-I mode supports propagating waves along 30-degree channel and is inhibited along the 90-degree channel, and vice versa for type II. With different resonant wavelengths, the two types of corner states have direction-wavelength locking mechanisms, enabling us to propose a 1 × 2 channel WDBS. Such WDBS design has achieved a low-crosstalk multiplexing based on the directionality of corner states. This finding provides guidance for multiplexing different types of topological photonic states, which is conducive to promoting the design of on-chip wavelength/mode-division multiplexers with topological protection.