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

Arbitrary Eigenmode Reshaping Induced by Distributed Non-Reciprocity in Non-Hermitian Systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Arbitrary Eigenmode Reshaping Induced by Distributed Non-Reciprocity in Non-Hermitian Systems Shaojie Ma, Zhaomin Rong, Yanan Bai, Lei Zhou, Yu Chen, Shuo Liu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8381307/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract 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. Physical sciences/Physics/Quantum physics/Quantum mechanics Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Physics/Optical physics/Nanophotonics and plasmonics Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological insulators Full Text Additional Declarations There is NO Competing Interest. Supplementary Files NHRESINC.pdf SI for "Arbitrary Eigenmode Reshaping Induced by Distributed Non-Reciprocity in Non-Hermitian Systems" Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8381307","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":570484969,"identity":"2d63cf78-6795-4628-a0a3-b940497fb023","order_by":0,"name":"Shaojie 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