A new study shows that the spatial distribution of non-reciprocity can reshape the eigenmodes of a given system into an arbitrary spatial pattern while leaving the energy spectrum completely unchanged. The theoretical framework, validated by a programmable electrical circuit and simulated coupled resonant optical waveguides, offers a new degree of design freedom for reconfigurable lasers, sensors, and other wave-control devices.
Non-Hermitian systems, open systems that exchange energy with their surroundings, can display a striking non-Hermitian skin effect, in which wave functions that would otherwise be extended instead accumulate at the boundary. In a study published in Optics and Photonics Research , researchers from Fudan University and Southeast University extend this effect, showing that tailoring the spatial distribution of non-reciprocal coupling unlocks a substantially larger design space than previously recognized. The team proved that for a one-dimensional finite lattice with only nearest-neighbor coupling, the energy spectrum depends only on the product of the forward and backward hopping amplitudes at each bond. Consequently, the spatial distribution of non-reciprocity can be freely redesigned, through a deterministic similarity transformation equivalent to an imaginary gauge field, allowing the spatial profile of every eigenmode to be reshaped without altering the energy spectrum or the topological protection of edge states. They term this approach non-Hermitian reshaping engineering (NHRE).
Key highlights include:
Theoretical framework: A one-dimensional model demonstrates that arbitrary spatial distributions of non-reciprocity can reshape eigenmode profiles while leaving the energy spectrum entirely unchanged.
Unified framework: The framework recovers the conventional non-Hermitian skin effect and the previously reported topological mode "morphing" as special cases and further extends them to truly arbitrary mode reshaping.
Higher-dimensional extension: The framework can be extended to reshape a topological corner mode in a two-dimensional lattice into the letters "FDU" without altering its energy or topological protection, highlighting the substantial design freedom afforded by this approach.
Circuit demonstration: A programmable 20-node electrical circuit with tunable non-reciprocal coupling confirms that eigenmode profiles are reshaped as designed, while resonant frequencies remain fixed.
Photonic validation: Simulations of coupled ring-resonator optical waveguides reproduce the same spectrum-preserving reshaping at optical frequencies, pointing toward reconfigurable topological lasers.
By decoupling the spatial shape of a wave function from its energy spectrum and topology, non-Hermitian reshaping engineering establishes a new design paradigm for reconfigurable photonic, electronic, and other wave-based devices.
Citation: Rong Z, Chen Y, Bai Y, Cui T, Zhou L, et al . Arbitrary eigenmode reshaping induced by distributed non-reciprocity in non-Hermitian systems. Opt. Photonics Res. 2026(1):0004, https://doi.org/10.55092/opr20260004.
Optics and Photonics Research
Experimental study
Not applicable
Arbitrary eigenmode reshaping induced by distributed non-reciprocity in non-Hermitian systems
30-Jun-2026