Self-healing effect (SHE) was first demonstrated in conventional diffraction-free systems [3], where light fields recover their spatial profiles after encountering an obstacle because the diffracted fields decrease inversely with propagation distance z. Longhi later extended this concept to non-Hermitian systems, where the lattice typically exhibits the non-Hermitian skin effect (NHSE) [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], predicting infinitely many self-healing skin modes that are exponentially localized at the lattice boundary [19]. This extension builds on key principles of non-Hermitian physics [20,21,22,23,24,25], including biorthogonal eigenstates [21, 26, 27] and non-Bloch Band theory [28,29,30,31,32]. The exploration of non-Hermitian phenomena has been experimentally realized in various platforms, including photonics [2, 33,34,35,36,37,38,39,40], electrical circuits [41, 42], ultracold atoms [43, 44], acoustic systems [45,46,47,48] and mechanical lattices [49, 50].
A key characteristic of non-Hermitian systems is their high spectral sensitivity to boundary conditions [30, 51]. The boundary modification enabling transition between periodic boundary conditions (PBC) and open boundary conditions (OBC) in non-Hermitian systems reshapes the entire spectral and spatial characteristics of skin modes [52,53,54,55,56]. Unlike in Hermitian lattices, where defects induce localized states around the perturbation [57], recent studies have further shown that by engineering edge terms under OBC, one can selectively excite the quasi-edge states under semi-infinite boundary conditions [19, 58], and realize counter skin effect [59]. However, in systems under OBC, the response of the energy spectrum to boundary perturbations and the feasible experimental routes for achieving SHE remain unclear.
Here, we propose and demonstrate skin mode tunability (SMT), a mechanism for tuning the spectrum of skin modes by applying boundary modifications at the edge opposite to their localization. While skin modes exhibit strong spatial confinement under OBC, the biorthogonal nature of non-Hermitian systems enables precise spectral tuning through remote end perturbations. By adjusting boundary potentials, a specific skin mode can be spectrally isolated from the other states, turning it into a self-healing state (SHS). Unlike typical skin modes, the SHS reconstructs its profile after encountering an obstacle, as it acquires the largest imaginary energy and thus dominates during propagation. This mechanism enables the realization of SHE for skin modes, and we further propose and numerically demonstrate an experimentally feasible implementation using photonic Floquet lattices with currently accessible parameters.