Arbitrary Eigenmode Reshaping Induced by Distributed Non-Reciprocity in Non-Hermitian Systems

Periodic non-reciprocal systems have attracted significant attention for their striking non-Hermitian skin effect (NHSE) and the development of a comprehensive non-Bloch theory. In contrast, aperiodic non-reciprocal systems have been rarely explored, owing to the intrinsic complexity induced by spatial non-uniformity and absence of predictable physical behavior. Here, we establish a theoretical framework to analyze aperiodic non-reciprocal systems and reveal that the spatially varying non-reciprocal coupling is a powerful and deterministic knob to control the wave-functions of eigenmodes. By tailoring the non-reciprocity distribution, we combine theory and proof-of-concept electric-circuit experiments to demonstrate that the eigenmodes of a non-Hermitian system can be reshaped into arbitrary spatial profiles without altering their spectral distribution, a phenomenon termed as the non-Hermitian reshaping effect (NHRE). In the special case of a uniform non-reciprocity distribution, NHRE reduces to the conventional NHSE. This concept can be generalized to arbitrary higher-dimensional systems and to high-frequency regimes, offering an efficient route to mode modulation and deepening our understanding of non-Hermitian physics.