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Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science , this issue p. eaar4003 , p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. These attributes make topological insulator systems ideal candidates for enabling applications in quantum computation and spintronics. We propose a concept that exploits topological effects in a unique way: the topological insulator laser. These are lasers whose lasing mode exhibits topologically protected transport without magnetic fields. The underlying topological properties lead to a highly efficient laser, robust to defects and disorder, with single-mode lasing even at very high gain values. The topological insulator laser alters current understanding of the interplay between disorder and lasing, and at the same time opens exciting possibilities in topological physics, such as topologically protected transport in systems with gain. On the technological side, the topological insulator laser provides a route to arrays of semiconductor lasers that operate as one single-mode high-power laser coupled efficiently into an output port.

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.Topological photonics: fractal latticesPhotonic topological insulators are currently a subject of great interest because they support edge states that can propagate without being affected by defects and disorder. All topological insulators discovered thus far have a bulk surrounded by edges. Now, Zhaoju Yang and coworkers from Technion in Israel, found theoretically that photonic topological insulators can also exist in fractal lattices, comprising only edges—with no bulk at all. They studied fractal lattices structured as Sierpinski gasket composed of an array of evanescently coupled helical waveguides. Despite the lack periodicity in such structures, tight-binding simulations and quasienergy analysis predict the existence of topological edge states, residing either on outer or on inner edges, exhibiting a Chern number of 1 and displaying scattering-free propagation. The fractal symmetries of such lattices are found to be crucial for the existence of the topological properties. Such fractal lattices could be fabricated by femtosecond laser writing technology.

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 waves 1 – 5 , cold atoms 6 , 7 , acoustics 8 and even mechanics 9 , and their potential applications include spintronics, quantum computing and highly efficient lasers 10 – 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 atom 13 – 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 lattices 13 , 16 , 17 . In photonics, topological lattices with synthetic dimensions have been proposed for the study of physical phenomena in high dimensions and interacting photons 18 – 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. A spatially oscillating two-dimensional waveguide array is used to realize a photonic topological insulator in synthetic dimensions with modal-space edge states, unidirectionality and robust topological protection.

Artificial gauge fields enable uncharged particles to behave as if affected by external fields. Generated by geometry or modulation, artificial gauge fields are instrumental in realizing topological physics in photonics, cold atoms and acoustics. Here, we experimentally demonstrate waveguiding by artificial gauge fields. We construct artificial gauge fields by using waveguide arrays with non-trivial trajectories. Tilting the arrays results in gauge fields that are different in the core and cladding, shifting their dispersion curves, thereby confining the light to the core. In a more advanced setting, we demonstrate waveguiding in a medium with the same gauge and dispersion everywhere, where the only difference between the core and the cladding is a phase shift in the dynamics of the gauge fields, which facilitates waveguiding via bound states in the continuum. Waveguiding and bound states in the continuum via artificial gauge fields relate to a plethora of systems, ranging from photonics and microwaves to cold atoms and acoustics.Optical guiding by a synthetic gauge field is experimentally demonstrated through an array of evanescently coupled identical waveguides, opening the door to applications of artificial gauge fields in optical, microwave and acoustic systems and in cold atoms.

Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed—because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene—a photonic honeycomb lattice—to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems. The propagation of light in photonic crystals with a honeycomb structure mirrors the behaviour of charges in graphene, therefore allowing for the investigation of electronic properties that cannot otherwise be accessed in graphene itself. This approach is now used to predict unexpected edge states that localize in the bearded edges of hexagonal lattices.

We propose a system that exploits the fundamental features of topological photonics and synthetic dimensions to force many semiconductor laser resonators to synchronize, mutually lock, and under suitable modulation emit a train of transform-limited mode-locked pulses. These lasers exploit the Floquet topological edge states in a 1D array of ring resonators, which corresponds to a 2D topological system with one spatial dimension and one synthetic frequency dimension. We show that the lasing state of the multielement laser system possesses the distinct characteristics of spatial topological edge states while exhibiting topologically protected transport. The topological synthetic-space edge mode imposes a constant-phase difference between the multifrequency modes on the edges, and together with modulation of the individual elements forces the ensemble of resonators to mode lock and emit short pulses, robust to disorder in the multiresonator system. Our results offer a proof-of-concept mechanism to actively mode lock a laser diode array of many lasing elements, which is otherwise extremely difficult due to the presence of many spatial modes of the array. The topological synthetic-space concepts proposed here offer an avenue to overcome this major technological challenge and open new opportunities in laser physics.

Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation, as they have been enablers of topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms, and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields. We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission. We identify total internal reflection (TIR) and complete transmission and demonstrate the concept in experiments. In addition, we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces. As an example, we propose a scheme to make a gauge imaging system—a device that can reconstruct (image) the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.Photonics: Manipulating light with artificial fieldsArtificial gauge fields are a technique to engineer the potential landscape such that neutral particles mimic the dynamics of charged particles driven by external fields. Researchers in Israel and Germany, led by Mordechai Segev at Technion Israel Institute of Technology, and Georg von Freymann from the University of Kaiserslautern, Germany, and their students Moshe-Ishay Cohen and Christina Joerg, studied theoretically and experimentally what happens when waves are incident at the interface between two photonic systems made from the same material, with the only thing making them different being their artificial gauge fields. The team formulated the generalized laws of refraction and reflection at such “gauge interfaces”, and demonstrated the concepts with micro-printed waveguides arrays with different tilt angles. The research demonstrates that several interfaces between regions with differing gauge fields could be used to develop novel photonic devices.

A multistep thermochemical etching procedure was applied to very large Nd3+:YAG rods to increase their fracture strength. The strengthening procedure combined selection of high-quality material, fine centerless grinding, thermochemical etching, and (after completion of the lapping, polishing and AR coating) an additional hot thermochemical etching, with rod ends protected with poly-tetra-fluoro-ethylene (Teflon) caps. The final cleaning step, not previously reported, is essential in removing fracture causing contaminations on the rod surface. A unique thermal load-to-fracture technique was applied on test rods to measure their fracture strength. The rods were thermally loaded up to fracture by means of optical pumping in a specially designed laser pump chamber. The results thus obtained were analyzed by Weibull distribution statistics appropriate to these tests. The strengthened laser rods of this study sustained a maximum pump power density of Iℓmax = 500 W cm−1. This value is higher by a factor of four over untreated rods and also higher than any previously published data for such large rods. High-power diode-pumped laser heads were operated with the strengthened crystalline and polycrystalline Nd:YAG rods, yielded output power of ~ 3 kW, when pumped with 7 kW. Such performance was routinely achieved without any instance of rod fracture. Reliability of the strengthening procedure was further demonstrated by the failure-free operation of an azimuthally polarized high-power master-oscillator power-amplifier system (composed of oscillator, preamplifier, and six power amplifiers), emitting an output power in excess of 10 kW.

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.

An experimental realization of a photonic topological insulator is reported that consists of helical waveguides arranged in a honeycomb lattice; the helicity provides a symmetry-breaking effect, leading to optical states that are topologically protected against scattering by disorder. A photonic topological insulator One of the hottest fields of condensed-matter research is that of topological insulators. They exist in electronic states that are robust against disorder owing to the topological protection provided by the underlying electronic structure. Their potential practical importance lies in their ability to control and manipulate electron waves without scattering. An interesting question is whether it would be possible to make a topological insulator for light. The answer is yes, and here Mordechai Segev and colleagues demonstrate the first experimental realization of a photonic topological insulator, which consists of helical waveguides arranged in a honeycomb lattice. The helicity is crucial, providing a symmetry breaking effect leading to topological insulator properties. The authors demonstrate one-way edge states that are protected from scattering. Topological insulators are a new phase of matter 1 , with the striking property that conduction of electrons occurs only on their surfaces 1 , 2 , 3 . In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 . One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties 11 , 12 , 14 . Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect 15 , by placing a gyromagnetic photonic crystal in an external magnetic field 5 . But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism—one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently 6 , 7 , 8 , 9 , 10 . One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states 10 . This is in the spirit of the proposed Floquet topological insulators 16 , 17 , 18 , 19 , in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides 20 arranged in a graphene-like honeycomb lattice 21 , 22 , 23 , 24 , 25 , 26 . Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate ( z ) acts as ‘time’ 27 . Thus the helicity of the waveguides breaks z -reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.