Manipulation of photonic topological edge and corner states via trivial claddings

Crystalline symmetry offers a powerful tool to realize photonic topological phases, in which additional trivial claddings are typically required to confine topological boundary states. However, the utility of the trivial cladding in manipulating topological waves is often overlooked. Here, we demonstrate two topologically distinct kagome photonic crystals (KPCs) based on different crystalline symmetries: \mathbit{C}\mathbf{6}- symmetric KPCs exhibit a quantum spin Hall phase, while \mathbit{C}\mathbf{3}-symmetric KPCs serve as trivial cladding. By tuning the geometric parameter of the trivial cladding, we observe that a pair of topological interface states featured with pseudospin-momentum locking undergoes a phase transition, accompanied by the appearance and disappearance of corner states in a finite hexagonal supercell. Such a geometry-induced band inversion is characterized by a sign change in the Dirac mass of the topological interface states and holds potential for applications such as rainbow trapping. Furthermore, we experimentally demonstrate the corner states, which is a hallmark of higher-order topology, also depend critically on the trivial cladding. Our work highlights the crucial role of trivial claddings on the formation of topological boundary states, and offers a novel approach for their manipulation.

💡 Research Summary

In this work the authors investigate how a trivial (non‑topological) cladding can be used not merely as a passive boundary that prevents radiation loss, but as an active element that controls the properties of topological edge and corner states in kagome photonic crystals (KPCs). Three primitive cell configurations are defined: a C₆‑symmetric “H‑KPC” that realizes a photonic analogue of the quantum spin Hall (QSH) phase, and two C₃‑symmetric “U‑KPC” and “D‑KPC” structures that are topologically trivial in the C₆ sense. Because all three share the same bulk band structure, the H‑KPC and D‑KPC can be juxtaposed to form a domain wall while keeping the band gaps aligned.

The D‑KPC serves as the cladding. By continuously varying its rod radius parameter d, the authors tune the frequency splitting between the odd‑parity and even‑parity interface modes, which is equivalent to changing the Dirac mass term of the one‑dimensional massive Dirac equation that describes the edge. At a critical value d_c≈0.38 a the mass changes sign, closing the edge gap and reopening it with opposite sign – a clear topological phase transition of the interface states. This transition is directly observed in both simulations and microwave experiments through Fourier‑transformed field scans, and the pseudospin‑momentum locking is visualized by phase vortices and opposite Poynting‑vector circulations for opposite wavevectors.

Exploiting the tunable dispersion, the authors design a graded structure in which d varies slowly along the interface. The resulting spatial variation of the group velocity causes different frequency components of a broadband excitation to slow down and stop at distinct positions, realizing a “topological rainbow trapping” effect. Unlike previous schemes that rely on a single edge band, here both the upper and lower edge branches are tunable, extending the operational bandwidth.

Beyond edge physics, the study examines higher‑order topology. A finite hexagonal supercell is built with an H‑KPC core surrounded by D‑KPC cladding. Six corner states appear inside the edge gap; they split into two sets of three due to finite‑size effects and the C₃ symmetry of the cladding. Calculations of corner charge reveal a mismatch between core and cladding (Q_core≈0.5 e, Q_clad≈0), confirming that the corner modes stem from higher‑order topology. By varying d, the edge gap closes and reopens, and the corner states merge with the edge continuum or disappear entirely, despite the bulk topology of the core remaining unchanged. This behavior maps onto a Su‑Schrieffer‑Heeger (SSH) chain formed by the interface: increasing d strengthens intra‑cell hopping (trivial SSH phase) while decreasing d enhances inter‑cell hopping (non‑trivial SSH phase), thereby controlling the presence of end‑states that manifest as corner modes in the 2‑D structure.

Experimental verification includes bulk, edge, and corner pump‑probe measurements on half‑hexagonal samples to avoid whispering‑gallery modes. The measured transmission spectra match the simulated eigen‑frequencies, confirming the existence and tunability of all three types of states.

Overall, the paper demonstrates three key advances: (1) trivial cladding can be engineered to flip the Dirac mass of topological edge states, inducing a controllable edge‑state topological transition; (2) higher‑order corner states are not immutable but can be switched on or off by the same cladding geometry, revealing a direct link between edge‑state SSH physics and 2‑D higher‑order topology; (3) the geometry‑controlled edge dispersion enables practical functionalities such as broadband topological rainbow trapping. The work opens pathways for more sophisticated photonic devices where boundary materials are deliberately designed to manipulate topological wave phenomena, suggesting future extensions to dielectric‑constant modulation, nonlinear effects, and three‑dimensional photonic crystals.