Eran Lustig

All Publications

• Photonic topological insulator induced by a dislocation in three dimensions. Nature Lustig, E., Maczewsky, L. J., Beck, J., Biesenthal, T., Heinrich, M., Yang, Z., Plotnik, Y., Szameit, A., Segev, M. 2022; 609 (7929): 931-935

  Abstract

  The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2-4 and are emerging as a promising tool for robust lasers5, quantum devices6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and  acoustic waves10-13, where the topological protection in the latter  is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14-17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.

  View details for DOI 10.1038/s41586-022-05129-7

  View details for PubMedID 36171384

• Amplified emission and lasing in photonic time crystals SCIENCE Lyubarov, M., Lumer, Y., Dikopoltsev, A., Lustig, E., Sharabi, Y., Segev, M. 2022; 377 (6604): 425-+

  Abstract

  Photonic time crystals (PTCs), materials with a dielectric permittivity that is modulated periodically in time, offer new concepts in light manipulation. We study theoretically the emission of light from a radiation source placed inside a PTC and find that radiation corresponding to the momentum bandgap is exponentially amplified, whether initiated by a macroscopic source, an atom, or vacuum fluctuations, drawing the amplification energy from the modulation. The radiation linewidth becomes narrower with time, eventually becoming monochromatic in the middle of the bandgap, which enables us to propose the concept of nonresonant tunable PTC laser. Finally, we find that the spontaneous decay rate of an atom embedded in a PTC vanishes at the band edge because of the low density of photonic states.

  View details for DOI 10.1126/science.abo3324

  View details for Web of Science ID 000830834600039

  View details for PubMedID 35679355

• Spatiotemporal photonic crystals OPTICA Sharabi, Y., Lustig, E., Dikopoltsev, A., Lumer, Y., Segev, M. 2022; 9 (6): 585-592

  View details for DOI 10.1364/OPTICA.455672

  View details for Web of Science ID 000814087500001

• Light emission by free electrons in photonic time-crystals PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Dikopoltsev, A., Sharabi, Y., Lyubarov, M., Lumer, Y., Tsesses, S., Lustig, E., Kaminer, I., Segev, M. 2022; 119 (6)

  Abstract

  Photonic time-crystals (PTCs) are spatially homogeneous media whose electromagnetic susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by momentum gaps (rather than energy bands and energy gaps, as in photonic crystals). Here, we present a study on the emission of radiation by free electrons in PTCs. We show that a free electron moving in a PTC spontaneously emits radiation, and when associated with momentum-gap modes, the electron emission process is exponentially amplified by the modulation of the refractive index. Moreover, under strong electron-photon coupling, the quantum formulation reveals that the spontaneous emission into the PTC bandgap experiences destructive quantum interference with the emission of the electron into the PTC band modes, leading to suppression of the interdependent emission. Free-electron physics in PTCs offers a platform for studying a plethora of exciting phenomena, such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons.

  View details for DOI 10.1073/pnas.2119705119

  View details for Web of Science ID 000758487100016

  View details for PubMedID 35131857

  View details for PubMedCentralID PMC8833186

• Topological insulator vertical-cavity laser array SCIENCE Dikopoltsev, A., Harder, T. H., Lustig, E., Egorov, O. A., Beierlein, J., Wolf, A., Lumer, Y., Emmerling, M., Schneider, C., Hoefling, S., Segev, M., Klembt, S. 2021; 373 (6562): 1514-+

  Abstract

  Topological insulator lasers are arrays of semiconductor lasers that exploit fundamental features of topology to force all emitters to act as a single coherent laser. In this study, we demonstrate a topological insulator vertical-cavity surface-emitting laser (VCSEL) array. Each VCSEL emits vertically, but the in-plane coupling between emitters in the topological-crystalline platform facilitates coherent emission of the whole array. Our topological VCSEL array emits at a single frequency and displays interference, highlighting that the emitters are mutually coherent. Our experiments exemplify the power of topological transport of light: The light spends most of its time oscillating vertically, but the small in-plane coupling is sufficient to force the array of individual emitters to act as a single laser.

  View details for DOI 10.1126/science.abj2232

  View details for Web of Science ID 000698977800051

  View details for PubMedID 34554782

• Synthetic-Space Photonic Topological Insulators Utilizing Dynamically Invariant Structure PHYSICAL REVIEW LETTERS Nemirovsky, L., Cohen, M., Lumer, Y., Lustig, E., Segev, M. 2021; 127 (9): 093901

  Abstract

  Synthetic-space topological insulators are topological systems with at least one spatial dimension replaced by a periodic arrangement of modes, in the form of a ladder of energy levels, cavity modes, or some other sequence of modes. Such systems can significantly enrich the physics of topological insulators, in facilitating higher dimensions, nonlocal coupling, and more. Thus far, all synthetic-space topological insulators relied on active modulation to facilitate transport in the synthetic dimensions. Here, we propose dynamically invariant synthetic-space photonic topological insulators: a two-dimensional evolution-invariant photonic structure exhibiting topological properties in synthetic dimensions. This nonmagnetic structure is static, lacking any kind of modulation in the evolution coordinate, yet it displays an effective magnetic field in synthetic space, characterized by a Chern number of one. We study the evolution of topological states along the edge, and on the interface between two such structures with opposite synthetic-space chirality, and demonstrate their robust unidirectional propagation in the presence of defects and disorder. Such topological structures can be realized in photonics and cold atoms and provide a fundamentally new mechanism for topological insulators.

  View details for DOI 10.1103/PhysRevLett.127.093901

  View details for Web of Science ID 000688556600003

  View details for PubMedID 34506166

• Topological photonics in synthetic dimensions ADVANCES IN OPTICS AND PHOTONICS Lustig, E., Segev, M. 2021; 13 (2): 426-461

  View details for DOI 10.1364/AOP.418074

  View details for Web of Science ID 000668556700003

• Disordered Photonic Time Crystals PHYSICAL REVIEW LETTERS Sharabi, Y., Lustig, E., Segev, M. 2021; 126 (16): 163902

  Abstract

  We study the propagation of electromagnetic waves in disordered photonic time crystals: spatially homogenous media whose refractive index changes randomly in time. We find that the group velocity of a pulse propagating in such media decreases exponentially, eventually coming to a complete stop, while experiencing exponential growth in intensity. These effects greatly depend on the Floquet band structure of the photonic time crystal, with the strongest sensitivity to disorder occurring in superluminal modes. Finally, we analyze the ensemble statistics and find them to coincide with those of Anderson localization, exhibiting single parameter scaling.

  View details for DOI 10.1103/PhysRevLett.126.163902

  View details for Web of Science ID 000652829700007

  View details for PubMedID 33961479

• Anomalous Floquet Thouless pumping Pan, Y., Dikopoltsev, A., Lustig, E., Cheng, Q., Segev, M., IEEE IEEE. 2021

  View details for Web of Science ID 000831479801391

• Towards photonic time-crystals: observation of a femtosecond time-boundary in the refractive index Lustig, E., Saha, S., Bordo, E., DeVault, C., Chowdhury, S. N., Sharabi, Y., Boltasseva, A., Cohen, O., Shalaev, V. M., Segev, M., IEEE IEEE. 2021

  View details for Web of Science ID 000831479800277

• Light emission by free electrons in photonic time-crystals Dikopoltsev, A., Sharabi, Y., Lyubarov, M., Lumer, Y., Tsesses, S., Lustig, E., Kaminer, I., Segev, M., IEEE IEEE. 2021

  View details for Web of Science ID 000831479801191

• Topological insulator vertically-emitting laser array Dikopoltsev, A., Harder, T. H., Lustig, E., Egorov, O. A., Beierlein, J., Wolf, A., Lumer, Y., Emmerling, M., Schneider, C., Hofling, S., Segev, M., Klembt, S., IEEE IEEE. 2021

  View details for Web of Science ID 000831479803059

• Identifying Topological Phase Transitions in Experiments Using Manifold Learning PHYSICAL REVIEW LETTERS Lustig, E., Yair, O., Talmon, R., Segev, M. 2020; 125 (12): 127401

  Abstract

  We demonstrate the identification of topological phase transitions from experimental data using diffusion maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system undergoing a topological phase transition and demonstrate the ability of this approach to identify topological phase transitions even when the data originates from a small part of the system, and does not even include edge states.

  View details for DOI 10.1103/PhysRevLett.125.127401

  View details for Web of Science ID 000568998900011

  View details for PubMedID 33016717

• Photonic Floquet topological insulators in a fractal lattice. Light, science & applications Yang, Z., Lustig, E., Lumer, Y., Segev, M. 2020; 9 (1): 128

  Abstract

  We present Floquet fractal topological insulators: photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides. The helical modulation induces an artificial gauge field and leads to a trivial-to-topological phase transition. The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1. We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder. In a similar vein, we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation. Finally, we find topological edge states that span the circumference of a hybrid half-fractal, half-honeycomb lattice, passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering, despite the transition from two dimensions to a fractal dimension. Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.

  View details for DOI 10.1038/s41377-020-00354-z

  View details for PubMedID 34282112

• Photonic Floquet topological insulators in a fractal lattice. Light, science & applications Yang, Z., Lustig, E., Lumer, Y., Segev, M. 2020; 9: 128

  Abstract

  We present Floquet fractal topological insulators: photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides. The helical modulation induces an artificial gauge field and leads to a trivial-to-topological phase transition. The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1. We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder. In a similar vein, we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation. Finally, we find topological edge states that span the circumference of a hybrid half-fractal, half-honeycomb lattice, passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering, despite the transition from two dimensions to a fractal dimension. Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.

  View details for DOI 10.1038/s41377-020-00354-z

  View details for PubMedID 32704361

  View details for PubMedCentralID PMC7371641

• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions PHYSICAL REVIEW X Yang, Z., Lustig, E., Harari, G., Plotnik, Y., Lumer, Y., Bandres, M. A., Segev, M. 2020; 10 (1)

  View details for DOI 10.1103/PhysRevX.10.011059

  View details for Web of Science ID 000518536800001

• Topological evolution-invariant photonic structures in synthetic dimensions Nemirovsky, L., Cohen, M., Lumer, Y., Lustig, E., Segev, M., IEEE IEEE. 2020

  View details for Web of Science ID 000612090003300

• Topological insulator VCSEL array Dikopoltsev, A., Harder, T. H., Lustig, E., Egorov, O. A., Beierlein, J., Emmerling, M., Schneider, C., Hoefling, S., Segev, M., Klembt, S., IEEE IEEE. 2020

  View details for Web of Science ID 000612090001484

• Spatiotemporal Photonic Crystals Sharabi, Y., Lustig, E., Dikopoltsev, A., Lumer, Y., Segev, M., IEEE IEEE. 2020

  View details for Web of Science ID 000612090001012

• Experimentally Realizing Photonic Topological Edge States in 3D Lustig, E., Maczewsky, L., Biesenthal, T., Yang, Z., Plotnik, Y., Szameit, A., Segev, M., IEEE IEEE. 2020

  View details for Web of Science ID 000612090003053

• Photonic topological insulator in synthetic dimensions NATURE Lustig, E., Weimann, S., Plotnik, Y., Lumer, Y., Bandres, M. A., Szameit, A., Segev, M. 2019; 567 (7748): 356-+

  Abstract

  Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections. These phases have been demonstrated for electronic systems, electromagnetic waves1-5, cold atoms6,7, acoustics8 and even mechanics9, and their potential applications include spintronics, quantum computing and highly efficient lasers10-12. Typically, the model describing topological insulators is a spatial lattice in two or three dimensions. However, topological edge states have also been observed in a lattice with one spatial dimension and one synthetic dimension (corresponding to the spin modes of an ultracold atom13-15), and atomic modes have been used as synthetic dimensions to demonstrate lattice models and physical phenomena that are not accessible to experiments in spatial lattices13,16,17. In photonics, topological lattices with synthetic dimensions have been proposed for the study of physical phenomena in high dimensions and interacting photons18-22, but so far photonic topological insulators in synthetic dimensions have not been observed. Here we demonstrate experimentally a photonic topological insulator in synthetic dimensions. We fabricate a photonic lattice in which photons are subjected to an effective magnetic field in a space with one spatial dimension and one synthetic modal dimension. Our scheme supports topological edge states in this spatial-modal lattice, resulting in a robust topological state that extends over the bulk of a two-dimensional real-space lattice. Our system can be used to increase the dimensionality of a photonic lattice and induce long-range coupling by design, leading to lattice models that can be used to study unexplored physical phenomena.

  View details for DOI 10.1038/s41586-019-0943-7

  View details for Web of Science ID 000462010000049

  View details for PubMedID 30778196

• 3D Parity Time symmetry in 2D photonic lattices utilizing artificial gauge fields in synthetic dimensions Lustig, E., Plotnik, Y., Yang, Z., Segev, M., IEEE IEEE. 2019

  View details for Web of Science ID 000482226303067

• Light Propagation in Temporally Disordered Media Sharabi, Y., Lustig, E., Segev, M., IEEE IEEE. 2019

  View details for Web of Science ID 000482226302418

• Mode-locked Topological Laser in Synthetic Dimensions Yang, Z., Lustig, E., Harari, G., Plotnik, Y., Bandres, M., Segev, M., IEEE IEEE. 2019

  View details for Web of Science ID 000482226300247

• Magnetic Gauge Field for Photons in Synthetic Dimensions by a Propagation-Invariant Photonic Structure Nemirovsky, L., Cohen, M., Lustig, E., Segev, M., IEEE IEEE. 2019

  View details for Web of Science ID 000482226302239

• Topological aspects of photonic time crystals OPTICA Lustig, E., Sharabi, Y., Segev, M. 2018; 5 (11): 1390-1395

  View details for DOI 10.1364/OPTICA.5.001390

  View details for Web of Science ID 000450664900004

• Classifying Photonic Topological Phases Using Manifold Learning Yair, O., Lustig, E., Talmon, R., Segev, M., IEEE IEEE. 2018

  View details for Web of Science ID 000526031000288

• Experimental Realization of Photonic Topological Insulators in Synthetic Dimensions Lustig, E., Weimann, S., Plotnik, Y., Bandres, M. A., Szameit, A., Segev, M., IEEE IEEE. 2018

  View details for Web of Science ID 000526031000290

• Topology of Photonic Time-Crystals Lustig, E., Sharabi, Y., Segev, M., IEEE IEEE. 2018

  View details for Web of Science ID 000526031000383

• Curved-space topological phases in photonic lattices PHYSICAL REVIEW A Lustig, E., Cohen, M., Bekenstein, R., Harari, G., Bandres, M. A., Segev, M. 2017; 96 (4)

  View details for DOI 10.1103/PhysRevA.96.041804

  View details for Web of Science ID 000413761800002

• Extending edge modes with non-Hermitian forcing Sheinfux, H., Lustig, E., Lumer, Y., Pltonik, Y., Segev, M., IEEE IEEE. 2017

  View details for Web of Science ID 000427296200247

• Topologically protected photonic propagation in the bulk Lustig, E., Weimann, S., Plotnik, Y., Lumer, Y., Bandres, M. A., Szameit, A., Segev, M., IEEE IEEE. 2017

  View details for Web of Science ID 000427296200346

• Dynamic Localization by Curved Space Cohen, M., Lustig, E., Bekenstein, R., Sheinfux, H., Lumer, Y., Segev, M., IEEE IEEE. 2016

  View details for Web of Science ID 000391286400358

• Photonic Topological Dynamics induced by Curved Surfaces Lustig, E., Cohen, M., Bekenstein, R., Bandres, M. A., Harari, G., Segev, M., IEEE IEEE. 2016

  View details for Web of Science ID 000391286400338