Dirac tuning and boundary-induced topological robust transmission in symmetric honeycomb optical waveguide networks

Topological valley Hall photonic structures enable low-loss, robust light propagation without external excitation, emerging as a critical frontier for integrated photonic chips. Here we propose multi-connected honeycomb optical waveguide networks (OWNs), and analytically derive its dispersion relation. We systematically demonstrate that the degeneracy of -point Dirac cones is governed by the parity of waveguide length ratios. Odd length ratios enable robust formation of frequency-locked -point Dirac cones, which exhibit outstanding frequency stability and defect immunity and further give rise to a distinctive pseudo-diffusive transport response. In contrast, K-point Dirac cones exhibit unprecedented tunability, where their quantity and frequency positions can be flexibly regulated by varying the length ratios. These tailored Dirac modes efficiently excite boundary-induced topological edge states, realizing unidirectional boundary transmission. Defect simulations confirm that the excited edge states maintain robust propagation against local defects at both structure boundaries and interior domains. Different from conventional symmetry-breaking schemes relying on sublattice parameter modulation, our strategy constructs topological domain interfaces purely via finite-lattice boundary configuration differences, fundamentally eliminating fabrication errors and extra optical losses introduced by traditional designs. This work deepens the physical understanding of Dirac dispersion engineering, offering a novel paradigm for low-loss integrated topological photonic devices.