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Topologically protected waveguides have attracted growing interest due to their robustness against disorder and defects. In parallel, the advent of non-Hermitian physics—with its inherent gain-and-loss mechanisms—has introduced new tools for manipulating wave localization and transport. However, most attempts to combine non-Hermitian effects with topological systems impose the non-Hermitian skin effect (NHSE) uniformly on all modes, lacking selectivity for topological states.
In this work, we propose a scheme that realizes a topologically selective NHSE by combining sub-symmetry-protected boundary modes with long-range, non-reciprocal couplings. In a modified Su–Schrieffer–Heeger (SSH) chain, we analytically demonstrate that even in a spectrum densely populated with bulk states, a robust zero-energy edge mode can be preserved while the NHSE is selectively applied to the trivial bulk modes, achieving spatial separation between topological and bulk states. By tuning the long-range couplings, we observe a non-Hermitian phase transition in the complex energy spectrum: it evolves from a closed loop (circle), to an arc, and then to a loop with reversed winding direction. These transitions correspond to a leftward NHSE, the disappearance of the NHSE, and a rightward NHSE, respectively. Calculating the generalized Brillouin zone (GBZ), we confirm this transition by observing the GBZ crossing the unit circle, indicating a change in the NHSE direction.
We further extend our model to a two-dimensional higher-order SSH lattice, where selective non-Hermitian modulation enables clear spatial separation between topological corner states and bulk modes. To quantify this, we compute the local density of states (LDOS) in the complex energy plane for site 0 (a topologically localized corner) and site 288 (a region exhibiting NHSE). The LDOS comparison reveals that the topological states are primarily localized at site 0, while bulk states affected by NHSE accumulate at site 288.
To validate the theoretical predictions, we perform finite-element simulations of optical resonator arrays employing whispering-gallery modes. By tuning the coupling distances and incorporating gain/loss through refractive index engineering, we replicate the modified SSH model and confirm the selective localization of topological and bulk modes.
Our results demonstrate a robust method for the selective excitation and spatial control of topological states in non-Hermitian systems, providing a foundation for future low-crosstalk, high-stability topological photonic devices. -
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