We investigate topological interface states (TISs) in inversion- or mirror-symmetric one-dimensional photonic crystals (PCs) composed of \(\varvec{n}\) dielectric materials, where each unit cell has equal optical thickness ( \(\varvec{\lambda /6}\) for ternary and \(\varvec{\lambda /8}\) for quaternary PCs). Contrary to conventional assumptions that differing outer layers are required for TIS emergence, our results reveal that this is not universally necessary: ternary PCs with identical outer layers and a distinct central material fail to support TISs, while quaternary PCs can exhibit TISs even when the first and last layers are the same, provided that the internal layers differ significantly. This demonstrates that internal structural asymmetry, rather than boundary conditions alone, governs the existence of TISs. Zak phase analysis confirms their topological origin, and we further show that higher refractive index contrast leads to wider bandgaps. These findings establish new design principles for achieving robust and tunable topological states in terahertz photonics and integrated optical applications.
