From biological ecosystems to spin glasses,connectivity plays a crucial role in determining the function,dynamics,and resiliency of a network.In the realm of non-Hermitian physics,the possibility of complex and asymmetric exchange interactions(丨Kij丨≠丨Kji丨)between a network of oscillators has been theoretically shown to lead to novel behaviors like delocalization,skin effect,and bulk-boundary correspondence.An archetypical lattice exhibiting the aforementioned properties is that proposed by Hatano and Nelson in a series of papers in late 1990s.While the ramifications of these theoretical works in optics have been recently pursued in synthetic dimensions,the Hatano-Nelson model has yet to be realized in real space.What makes the implementation of these lattices challenging is the difficulty in establishing the required asymmetric exchange interactions in optical platforms.In this work,by using active optical oscillators featuring non-Hermiticity and nonlinearity,we introduce an anisotropic exchange between the resonant elements in a lattice,an aspect that enables us to observe the non-Hermitian skin effect,phase locking,and near-field beam steering in a Hatano-Nelson laser array.Our work opens up new regimes of phase-locking in lasers while shedding light on the fundamental physics of non-Hermitian systems.

Yuzhou G.N.Liu;Yunxuan Wei;Omid Hemmatyar;Georgios G.Pyrialakos;Pawel S.Jung;Demetrios N.Christodoulides;Mercedeh Khajavikhan

Ming Hsieh Department of Electrical and Computer Engineering,University of Southern California,Los Angeles,CA 90089,USA;CREOL,The College of Optics&Photonics,University of Central Florida,Orlando,FL 32816-2700,USA;Faculty of Physics,Warsaw University of Technology,Koszykowa 75,00-662 Warsaw,Poland;Department of Physics&Astronomy,Dornsife College of Letters,Arts,&Sciences,University of Southern California,Los Angeles,CA 90089,USA

光：科学与应用（英文版）

[1]Yuzhou G.N.Liu;Yunxuan Wei;Omid Hemmatyar;Georgios G.Pyrialakos;Pawel S.Jung;Demetrios N.Christodoulides;Mercedeh Khajavikhan-.Complex skin modes in non-Hermitian coupled laser arrays)[J].光：科学与应用（英文版）,2022(12):3002-3007

resiliency,Kij,Kji,Hatano,ramifications

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