{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T20:13:12Z","timestamp":1780603992811,"version":"3.54.1"},"reference-count":103,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T00:00:00Z","timestamp":1653350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","award":["D95F21002140006"],"award-info":[{"award-number":["D95F21002140006"]}]},{"name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","award":["FA9550-21-1-0347"],"award-info":[{"award-number":["FA9550-21-1-0347"]}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"publisher","award":["D95F21002140006"],"award-info":[{"award-number":["D95F21002140006"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"publisher","award":["FA9550-21-1-0347"],"award-info":[{"award-number":["FA9550-21-1-0347"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 \u00d7 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.<\/jats:p>","DOI":"10.3390\/s22113977","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T00:14:14Z","timestamp":1653437654000},"page":"3977","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":85,"title":["Non-Hermitian Sensing in Photonics and Electronics: A Review"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0612-7742","authenticated-orcid":false,"given":"Martino","family":"De Carlo","sequence":"first","affiliation":[{"name":"Photonics Research Group, Department of Electrical and Information Engineering, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"De Leonardis","sequence":"additional","affiliation":[{"name":"Photonics Research Group, Department of Electrical and Information Engineering, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard A.","family":"Soref","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Massachusetts at Boston, Boston, MA 02125, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luigi","family":"Colatorti","sequence":"additional","affiliation":[{"name":"Photonics Research Group, Department of Electrical and Information Engineering, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0802-4464","authenticated-orcid":false,"given":"Vittorio M. N.","family":"Passaro","sequence":"additional","affiliation":[{"name":"Photonics Research Group, Department of Electrical and Information Engineering, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,24]]},"reference":[{"key":"ref_1","unstructured":"Landau, L., and Lifshitz, E. (1965). Quantum Mechanics, Non-Relativistic Theory, Pergamon-Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1063\/1.1705118","article-title":"Results on Certain Non-Hermitian Hamiltonians","volume":"8","author":"Wong","year":"1967","journal-title":"J. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5243","DOI":"10.1103\/PhysRevLett.80.5243","article-title":"Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry","volume":"80","author":"Bender","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1038\/s42005-019-0130-z","article-title":"The Dawn of Non-Hermitian Optics","volume":"2","author":"Khajavikhan","year":"2019","journal-title":"Commun. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"222001","DOI":"10.1088\/1361-6455\/aae42f","article-title":"Parity-Time Symmetry in Optical Microcavity Systems","volume":"51","author":"Wen","year":"2018","journal-title":"J. Phys. B At. Mol. Opt. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1093\/nsr\/nwy011","article-title":"Parity\u2013Time Symmetric Photonics","volume":"5","author":"Zhao","year":"2018","journal-title":"Natl. Sci. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1038\/s41563-019-0304-9","article-title":"Parity\u2013Time Symmetry and Exceptional Points in Photonics","volume":"18","author":"Rotter","year":"2019","journal-title":"Nat. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"eaar7709","DOI":"10.1126\/science.aar7709","article-title":"Exceptional Points in Optics and Photonics","volume":"363","author":"Miri","year":"2019","journal-title":"Science"},{"key":"ref_9","first-page":"031042","article-title":"PT-Symmetric Acoustics","volume":"4","author":"Zhu","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5905","DOI":"10.1038\/ncomms6905","article-title":"An Invisible Acoustic Sensor Based on Parity-Time Symmetry","volume":"6","author":"Fleury","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_11","first-page":"021007","article-title":"Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization","volume":"6","author":"Ding","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"040101","DOI":"10.1103\/PhysRevA.84.040101","article-title":"Experimental Study of Active LRC circuits with PT symmetries","volume":"84","author":"Schindler","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"444029","DOI":"10.1088\/1751-8113\/45\/44\/444029","article-title":"PT-Symmetric Electronics","volume":"45","author":"Schindler","year":"2012","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"053824","DOI":"10.1103\/PhysRevA.87.053824","article-title":"Effective Spontaneous PT-Symmetry Breaking in Hybridized Metamaterials","volume":"87","author":"Kang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"033834","DOI":"10.1103\/PhysRevA.94.033834","article-title":"Chiral Exceptional Points in Metasurfaces","volume":"94","author":"Kang","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"085004","DOI":"10.1088\/1367-2630\/18\/8\/085004","article-title":"Effective PT-Symmetric Metasurfaces for Subwavelength Amplified Sensing","volume":"18","author":"Xiao","year":"2016","journal-title":"New J. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"023903","DOI":"10.1103\/PhysRevLett.113.023903","article-title":"Negative Refraction and Planar Focusing Based on Parity-Time Symmetric Metasurfaces","volume":"113","author":"Fleury","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"214411","DOI":"10.1103\/PhysRevB.95.214411","article-title":"Topological Properties of a Coupled Spin-Photon System Induced by Damping","volume":"95","author":"Harder","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1038\/s41467-017-01634-w","article-title":"Observation of the Exceptional Point in Cavity Magnon-Polaritons","volume":"8","author":"Zhang","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"013852","DOI":"10.1103\/PhysRevA.92.013852","article-title":"Mechanical PT symmetry in Coupled Optomechanical Systems","volume":"92","author":"Xu","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1364\/PRJ.396115","article-title":"Review of Exceptional Point-Based Sensors","volume":"8","author":"Wiersig","year":"2020","journal-title":"Photonics Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1038\/nphys4323","article-title":"Non-Hermitian Physics and PT Symmetry","volume":"14","author":"Makris","year":"2018","journal-title":"Nat. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"015005","DOI":"10.1103\/RevModPhys.93.015005","article-title":"Exceptional Topology of Non-Hermitian Systems","volume":"93","author":"Bergholtz","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"L171","DOI":"10.1088\/0305-4470\/38\/9\/L03","article-title":"Physical Realization of PT-Symmetric Potential Scattering in a Planar Slab Waveguide","volume":"38","author":"Ruschhaupt","year":"2005","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2632","DOI":"10.1364\/OL.32.002632","article-title":"Theory of Coupled Optical PT-Symmetric Structures","volume":"32","author":"Makris","year":"2007","journal-title":"Opt. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"053810","DOI":"10.1103\/PhysRevA.88.053810","article-title":"Antisymmetric PT-Photonic Structures with Balanced Positive- and Negative-Index Materials","volume":"88","author":"Ge","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"053845","DOI":"10.1103\/PhysRevA.96.053845","article-title":"Anti-PT Symmetry in Dissipatively Coupled Optical Systems","volume":"96","author":"Yang","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"103904","DOI":"10.1103\/PhysRevLett.100.103904","article-title":"Beam Dynamics in PT Symmetric Optical Lattices","volume":"100","author":"Makris","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"080402","DOI":"10.1103\/PhysRevLett.101.080402","article-title":"Visualization of Branch Points InPT-Symmetric Waveguides","volume":"101","author":"Klaiman","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1038\/nphys1515","article-title":"Observation of Parity\u2013Time Symmetry in Optics","volume":"6","author":"Makris","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1126\/science.1258480","article-title":"Parity-Time\u2013Symmetric Microring Lasers","volume":"346","author":"Hodaei","year":"2014","journal-title":"Science"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1126\/science.1258479","article-title":"Single-Mode Laser by Parity-Time Symmetry Breaking","volume":"346","author":"Feng","year":"2014","journal-title":"Science"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1103\/PhysRevA.82.043803","article-title":"Unidirectional Nonlinear PT-Symmetric Optical Structures","volume":"82","author":"Ramezani","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1038\/nphys2927","article-title":"Parity\u2013Time-Symmetric Whispering-Gallery Microcavities","volume":"10","author":"Peng","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1038\/nphoton.2014.133","article-title":"Parity\u2013Time Symmetry and Variable Optical Isolation in Active\u2013Passive-Coupled Microresonators","volume":"8","author":"Chang","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1038\/nature18605","article-title":"Dynamically Encircling an Exceptional Point for Asymmetric Mode Switching","volume":"537","author":"Doppler","year":"2016","journal-title":"Nature"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1038\/s41377-019-0200-8","article-title":"Dynamically Encircling an Exceptional Point in Anti-Parity-Time Symmetric Systems: Asymmetric Mode Switching for Symmetry-Broken Modes","volume":"8","author":"Zhang","year":"2019","journal-title":"Light Sci. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6845","DOI":"10.1073\/pnas.1603318113","article-title":"Chiral Modes and Directional Lasing at Exceptional Points","volume":"113","author":"Peng","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"B1","DOI":"10.1364\/PRJ.5.0000B1","article-title":"Unidirectional Lasing in Semiconductor Microring Lasers at an Exceptional Point","volume":"5","author":"Longhi","year":"2017","journal-title":"Photonics Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"213901","DOI":"10.1103\/PhysRevLett.106.213901","article-title":"Unidirectional Invisibility Induced ByPT-Symmetric Periodic Structures","volume":"106","author":"Lin","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1038\/nmat3495","article-title":"Experimental Demonstration of a Unidirectional Reflectionless Parity-Time Metamaterial at Optical Frequencies","volume":"12","author":"Feng","year":"2012","journal-title":"Nat. Mater."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"031801","DOI":"10.1103\/PhysRevA.82.031801","article-title":"PT-Symmetric Laser Absorber","volume":"82","author":"Longhi","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"093902","DOI":"10.1103\/PhysRevLett.106.093902","article-title":"PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems","volume":"106","author":"Chong","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"143903","DOI":"10.1103\/PhysRevLett.112.143903","article-title":"Experimental Demonstration of a Coherent Perfect Absorber with PT Phase Transition","volume":"112","author":"Sun","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1126\/science.abj1028","article-title":"Coherent Perfect Absorption at an Exceptional Point","volume":"373","author":"Wang","year":"2021","journal-title":"Science"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1038\/s41567-019-0746-7","article-title":"Electromagnetically Induced Transparency at a Chiral Exceptional Point","volume":"16","author":"Wang","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1126\/science.aaf8533","article-title":"Orbital Angular Momentum Microlaser","volume":"353","author":"Miao","year":"2016","journal-title":"Science"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1002\/lpor.201500227","article-title":"Nonlinear Switching and Solitons in PT-symmetric Photonic Systems","volume":"10","author":"Suchkov","year":"2016","journal-title":"Laser Photonics Rev."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Kumar, P., Saravi, S., Pertsch, T., Setzpfandt, F., and Sukhorukov, A.A. (2022). Nonlinear Quantum Spectroscopy with Parity-Time Symmetric Integrated Circuits. arXiv.","DOI":"10.1364\/PRJ.450410"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2178","DOI":"10.1109\/JLT.2019.2899486","article-title":"Generalized Modeling of Optomechanical Forces Applied to PT-Symmetric Optical Microscale Resonators","volume":"37","author":"Lamberti","year":"2019","journal-title":"J. Lightwave Technol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1515\/nanoph-2021-0721","article-title":"Topological Optomechanical Amplifier in Synthetic PT-Symmetry","volume":"11","author":"Zhang","year":"2022","journal-title":"Nanophotonics"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"22614","DOI":"10.1364\/OE.423426","article-title":"Exceptional Point Magneto-Optic Isolators","volume":"29","author":"Grede","year":"2021","journal-title":"Opt. Express"},{"key":"ref_53","unstructured":"Haus, H. (1984). Waves and Fields in Optoelectronics, Prentice-Hall."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"065501","DOI":"10.1088\/2040-8978\/16\/6\/065501","article-title":"Quasi PT-Symmetry in Passive Photonic Lattices","volume":"16","author":"Ornigotti","year":"2014","journal-title":"J. Opt."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1038\/s42005-018-0087-3","article-title":"Observation of Slowly Decaying Eigenmodes without Exceptional Points in Floquet Dissipative Synthetic Circuits","volume":"1","author":"Harter","year":"2018","journal-title":"Commun. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"100052","DOI":"10.1016\/j.rio.2020.100052","article-title":"(INVITED) Exceptional Points of Parity-Time- and Anti-Parity-Time-Symmetric Devices for Refractive Index and Absorption-Based Sensing","volume":"2","year":"2021","journal-title":"Results Opt."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1364\/OPTICA.5.001342","article-title":"Fluctuations and Noise-Limited Sensing near the Exceptional Point of Parity-Time-Symmetric Resonator Systems","volume":"5","author":"Mortensen","year":"2018","journal-title":"Optica"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1515\/nanoph-2019-0036","article-title":"On the Time Evolution at a Fluctuating Exceptional Point","volume":"8","author":"Wolff","year":"2019","journal-title":"Nanophotonics"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"023805","DOI":"10.1103\/PhysRevA.98.023805","article-title":"No Exceptional Precision of Exceptional-Point Sensors","volume":"98","author":"Langbein","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"4320","DOI":"10.1038\/s41467-018-06477-7","article-title":"Fundamental Limits and Non-Reciprocal Approaches in Non-Hermitian Quantum Sensing","volume":"9","author":"Lau","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"180501","DOI":"10.1103\/PhysRevLett.123.180501","article-title":"Quantum Noise Theory of Exceptional Point Amplifying Sensors","volume":"123","author":"Zhang","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1038\/s41467-020-15341-6","article-title":"Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope","volume":"11","author":"Wang","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_63","first-page":"15","article-title":"Diabolical Points in the Spectra of Triangles. Proceedings of the Royal Society of London A","volume":"392","author":"Berry","year":"1984","journal-title":"Math. Phys. Sci."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"153902","DOI":"10.1103\/PhysRevLett.122.153902","article-title":"Sensing with Exceptional Surfaces in Order to Combine Sensitivity with Robustness","volume":"122","author":"Zhong","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1364\/OPTICA.6.000190","article-title":"Exceptional Surfaces in PT-Symmetric Non-Hermitian Photonic Systems","volume":"6","author":"Zhou","year":"2019","journal-title":"Optica"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"033505","DOI":"10.1103\/PhysRevA.104.033505","article-title":"Exceptional-Surface-Enhanced Rotation Sensing with Robustness in a Whispering-Gallery-Mode Microresonator","volume":"104","author":"Li","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"5954","DOI":"10.1109\/JLT.2021.3091333","article-title":"Design of an Exceptional-Surface-Enhanced Silicon-On-Insulator Optical Accelerometer","volume":"39","author":"Soref","year":"2021","journal-title":"J. Lightwave Technol."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"2000569","DOI":"10.1002\/lpor.202000569","article-title":"Experimental Realization of Sensitivity Enhancement and Suppression with Exceptional Surfaces","volume":"15","author":"Qin","year":"2021","journal-title":"Laser Photonics Rev."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1038\/s41467-022-27990-w","article-title":"Chiral and Degenerate Perfect Absorption on Exceptional Surfaces","volume":"13","author":"Soleymani","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1364\/JOSAA.11.000963","article-title":"Coupled-Mode Theory for Optical Waveguides: An Overview","volume":"11","author":"Huang","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1021\/acsphotonics.0c01053","article-title":"Antiparity-Time Symmetry in Passive Nanophotonics","volume":"7","author":"Fan","year":"2020","journal-title":"ACS Photonics"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/50.588673","article-title":"Microring Resonator Channel Dropping Filters","volume":"15","author":"Little","year":"1997","journal-title":"J. Lightwave Technol."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1038\/s41586-019-1780-4","article-title":"Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity","volume":"576","author":"Hokmabadi","year":"2019","journal-title":"Nature"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"18823","DOI":"10.1109\/JSEN.2021.3092058","article-title":"Enhancement of Sensitivity Near Exceptional Point by Constructing Nonreciprocal Fiber Cavity Assisted by Isolator and Erbium-Doped Fiber","volume":"21","author":"Liu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"30340","DOI":"10.1364\/OE.397853","article-title":"Nonlinear Transition between PT-Symmetric and PT-Broken Modes in Coupled Fiber Lasers","volume":"28","author":"Suchkov","year":"2020","journal-title":"Opt. Express"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1038\/s41467-018-04690-y","article-title":"Observation of an Anti-PT-Symmetric Exceptional Point and Energy-Difference Conserving Dynamics in Electrical Circuit Resonators","volume":"9","author":"Choi","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1038\/s41928-019-0284-4","article-title":"Sensitive Readout of Implana Microsensors Using a Wireless System Locked to an Exceptional Point","volume":"2","author":"Dong","year":"2019","journal-title":"Nat. Electron."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1364\/OL.42.001556","article-title":"Ultrasensitive Micro-Scale Parity-Time-Symmetric Ring Laser Gyroscope","volume":"42","author":"Ren","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"714","DOI":"10.3367\/UFNe.0184.201407g.0775","article-title":"Sagnac Effect in Ring Lasers and Ring Resonators. How Does the Refractive Index of the Optical Medium Influence the Sensitivity to Rotation?","volume":"57","author":"Malykin","year":"2014","journal-title":"Phys.-Uspekhi"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"3261","DOI":"10.1109\/JLT.2018.2837754","article-title":"Design Rules of a Microscale PT-Symmetric Optical Gyroscope Using Group IV Platform","volume":"36","author":"Passaro","year":"2018","journal-title":"J. Lightwave Technol."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"3956","DOI":"10.1364\/OL.44.003956","article-title":"High-Sensitivity Real-Splitting Anti-PT-Symmetric Microscale Optical Gyroscope","volume":"44","author":"Lamberti","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"106983","DOI":"10.1016\/j.optlaseng.2022.106983","article-title":"Design of a Resonator-Bus-Resonator Anti-Parity-Time-Symmetric Integrated Optical Gyroscope","volume":"153","author":"Lamberti","year":"2022","journal-title":"Opt. Lasers Eng."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1038\/s41586-019-1777-z","article-title":"Observation of the Exceptional-Point-Enhanced Sagnac Effect","volume":"576","author":"Lai","year":"2019","journal-title":"Nature"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"203901","DOI":"10.1103\/PhysRevLett.112.203901","article-title":"Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Microcavity Sensors for Single-Particle Detection","volume":"112","author":"Wiersig","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1038\/nature23281","article-title":"Exceptional Points Enhance Sensing in an Optical Microcavity","volume":"548","author":"Chen","year":"2017","journal-title":"Nature"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"134503","DOI":"10.1063\/5.0020944","article-title":"Real Frequency Splitting Indirectly Coupled Anti-Parity-Time Symmetric Nanoparticle Sensor","volume":"128","author":"Li","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"7594","DOI":"10.1021\/acs.nanolett.0c03119","article-title":"Breaking Anti-PT Symmetry by Spinning a Resonator","volume":"20","author":"Zhang","year":"2020","journal-title":"Nano Lett."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"A23","DOI":"10.1364\/PRJ.6.000A23","article-title":"Parity-Time-Symmetric Whispering-Gallery Mode Nanoparticle Sensor","volume":"6","author":"Chen","year":"2018","journal-title":"Photonics Res."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"103106","DOI":"10.1063\/5.0082364","article-title":"Enhanced Nanoparticle Sensing by Mode Intensity in a Non-Reciprocally Coupled Microcavity","volume":"131","author":"Jiang","year":"2022","journal-title":"J. Appl. Phys."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1038\/nature23280","article-title":"Enhanced Sensitivity at Higher-Order Exceptional Points","volume":"548","author":"Hodaei","year":"2017","journal-title":"Nature"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1038\/s41467-018-04251-3","article-title":"Exceptional Point Engineered Glass Slide for Microscopic Thermal Mapping","volume":"9","author":"Zhao","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"024002","DOI":"10.1103\/PhysRevApplied.12.024002","article-title":"Exceptional Point Enhances Sensitivity of Optomechanical Mass Sensors","volume":"12","author":"Djorwe","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"214415","DOI":"10.1103\/PhysRevB.99.214415","article-title":"Exceptional Magnetic Sensitivity of PT-Symmetric Cavity Magnon Polaritons","volume":"99","author":"Cao","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1038\/s41567-020-0796-x","article-title":"Symmetry-Breaking-Induced Plasmonic Exceptional Points and Nanoscale Sensing","volume":"16","author":"Park","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"205102","DOI":"10.1088\/1361-6463\/ab761d","article-title":"Ultrahigh Sensitivity Stress Sensing Method near the Exceptional Point of Parity-Time Symmetric Systems","volume":"53","author":"Xing","year":"2020","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"1900278","DOI":"10.1002\/lpor.201900278","article-title":"Chip-Based Optical Isolator and Nonreciprocal Parity-Time Symmetry Induced by Stimulated Brillouin Scattering","volume":"14","author":"Ma","year":"2020","journal-title":"Laser Photonics Rev."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Liu, Y., Yan, P., Liu, F., Jian, A., and Sang, S. (2021). Biosensing Near the Exceptional Point Based on Resonant Optical Tunneling Effect. Micromachines, 12.","DOI":"10.3390\/mi12040426"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"254001","DOI":"10.1088\/1361-6463\/abf167","article-title":"Gas Sensing near Exceptional Points","volume":"54","author":"Nie","year":"2021","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1038\/s41928-018-0072-6","article-title":"Generalized Parity\u2013Time Symmetry Condition for Enhanced Sensor Telemetry","volume":"1","author":"Chen","year":"2018","journal-title":"Nat. Electron."},{"key":"ref_100","unstructured":"Kononchuk, R., Cai, J., Ellis, F., Thevamaran, R., and Kottos, T. (2022). Enhanced Signal-to-Noise Performance of EP-Based Electromechanical Accelerometers. arXiv."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"213901","DOI":"10.1103\/PhysRevLett.123.213901","article-title":"Enhanced Sensing and Nondegraded Thermal Noise Performance Based on PT-Symmetric Electronic Circuits with a Sixth-Order Exceptional Point","volume":"123","author":"Xiao","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"063008","DOI":"10.1088\/1367-2630\/abfc69","article-title":"Ultra-Sensitive Passive Wireless Sensor Exploiting High-Order Exceptional Point for Weakly Coupling Detection","volume":"23","author":"Zeng","year":"2021","journal-title":"New J. Phys."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"044049","DOI":"10.1103\/PhysRevApplied.11.044049","article-title":"Noninvasive Glucose Sensor Based on Parity-Time Symmetry","volume":"11","author":"Zhang","year":"2019","journal-title":"Phys. Rev. Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/11\/3977\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:17:47Z","timestamp":1760138267000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/11\/3977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,24]]},"references-count":103,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["s22113977"],"URL":"https:\/\/doi.org\/10.3390\/s22113977","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,24]]}}}