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Optical modulators are at the heart of optical communication links. Ideally, they should feature low loss, low drive voltage, large bandwidth, high linearity, compact footprint and low manufacturing cost. Unfortunately, these criteria have been achieved only on separate occasions. Based on a silicon and lithium niobate hybrid integration platform, we demonstrate Mach–Zehnder modulators that simultaneously fulfil these criteria. The presented device exhibits an insertion loss of 2.5 dB, voltage–length product of 2.2 V cm in single-drive push–pull operation, high linearity, electro-optic bandwidth of at least 70 GHz and modulation rates up to 112 Gbit s−1. The high-performance modulator is realized by seamless integration of a high-contrast waveguide based on lithium niobate—a popular modulator material—with compact, low-loss silicon circuitry. The hybrid platform demonstrated here allows for the combination of ‘best-in-breed’ active and passive components, opening up new avenues for future high-speed, energy-efficient and cost-effective optical communication networks.Low-loss, high-speed and efficient optical modulators on a silicon platform are demonstrated.

Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization 1 , where increasing the randomness induces a metal–insulator transition. The introduction of topology in condensed-matter physics 2 – 4 lead to the discovery of topological phase transitions and materials as topological insulators 5 . Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy 6 and new topological phases 7 – 9 . Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition 10 . Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal–insulator), a topological and parity–time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops 11 . Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.  A triple phase transition, where changing a single parameter simultaneously gives rise to metal–insulator, topological and a parity–time symmetry-breaking phase transitions, is observed in non-Hermitian Floquet quasicrystals.

Microcavity-based frequency combs, or ‘microcombs’1,2, have enabled many fundamental breakthroughs3–21 through the discovery of temporal cavity-solitons. These self-localized waves, described by the Lugiato–Lefever equation22, are sustained by a background of radiation usually containing 95% of the total power23. Simple methods for their efficient generation and control are currently being investigated to finally establish microcombs as out-of-the-lab tools24. Here, we demonstrate microcomb laser cavity-solitons. Laser cavity-solitons are intrinsically background-free and have underpinned key breakthroughs in semiconductor lasers22,25–28. By merging their properties with the physics of multimode systems29, we provide a new paradigm for soliton generation and control in microcavities. We demonstrate 50-nm-wide bright soliton combs induced at average powers more than one order of magnitude lower than the Lugiato–Lefever soliton power threshold22, measuring a mode efficiency of 75% versus the theoretical limit of 5% for bright Lugiato–Lefever solitons23. Finally, we can tune the repetition rate by well over a megahertz without any active feedback.By nesting a Kerr microresonator in a fibre loop with gain, 50-nm-wide bright microcavity-based soliton combs with a mode efficiency of 75% can be induced at average powers more than one order of magnitude lower than the Lugiato–Lefever soliton power threshold, facilitating real-world applications.

Tuning optical microcavities to exceptional points enhances their ability to sense nanoscale objects, owing to the topological features of exceptional points. Exceptional points, exceptional optics Recent insights into open (non-Hermitian) physical systems have led to a new range of optical systems in which, counter-intuitively, loss is introduced. By careful tuning of loss and gain, certain degeneracies called 'exceptional points' emerge, which have intriguing properties that can be harnessed, for example, in new types of lasers, one-way optical waveguides and topological effects. Two papers in this issue demonstrate the high sensitivity of such non-Hermitian degeneracies to external perturbations, which can be used for precision sensing and detection. Weijian Chen et al . report sensing of nanoparticles with exceptional points generated in a silicon dioxide micro-toroid resonator. Hossein Hodaei et al . generated a higher-order exceptional point by coupling three micro-rings made from a semiconductor laser material. This third-order exceptional point has an even higher, cube-root (rather than square-root) dependence on perturbations. The two papers together provide a new route to ultraprecise chip-based sensing systems. Sensors play an important part in many aspects of daily life such as infrared sensors in home security systems, particle sensors for environmental monitoring and motion sensors in mobile phones. High-quality optical microcavities are prime candidates for sensing applications because of their ability to enhance light–matter interactions in a very confined volume. Examples of such devices include mechanical transducers 1 , magnetometers 2 , single-particle absorption spectrometers 3 , and microcavity sensors for sizing single particles 4 and detecting nanometre-scale objects such as single nanoparticles and atomic ions 5 , 6 , 7 . Traditionally, a very small perturbation near an optical microcavity introduces either a change in the linewidth or a frequency shift or splitting of a resonance that is proportional to the strength of the perturbation. Here we demonstrate an alternative sensing scheme, by which the sensitivity of microcavities can be enhanced when operated at non-Hermitian spectral degeneracies known as exceptional points 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 . In our experiments, we use two nanoscale scatterers to tune a whispering-gallery-mode micro-toroid cavity, in which light propagates along a concave surface by continuous total internal reflection, in a precise and controlled manner to exceptional points 12 , 13 . A target nanoscale object that subsequently enters the evanescent field of the cavity perturbs the system from its exceptional point, leading to frequency splitting. Owing to the complex-square-root topology near an exceptional point, this frequency splitting scales as the square root of the perturbation strength and is therefore larger (for sufficiently small perturbations) than the splitting observed in traditional non-exceptional-point sensing schemes. Our demonstration of exceptional-point-enhanced sensitivity paves the way for sensors with unprecedented sensitivity.

The hallmark property of two-dimensional topological insulators is robustness of quantized electronic transport of charge and energy against disorder in the underlying lattice 1 . That robustness arises from the fact that, in the topological bandgap, such transport can occur only along the edge states, which are immune to backscattering owing to topological protection. However, for sufficiently strong disorder, this bandgap closes and the system as a whole becomes topologically trivial: all states are localized and all transport vanishes in accordance with Anderson localization 2 , 3 . The recent suggestion 4 that the reverse transition can occur was therefore surprising. In so-called topological Anderson insulators, it has been predicted 4 that the emergence of protected edge states and quantized transport can be induced, rather than inhibited, by the addition of sufficient disorder to a topologically trivial insulator. Here we report the experimental demonstration of a photonic topological Anderson insulator. Our experiments are carried out in an array of helical evanescently coupled waveguides in a honeycomb geometry with detuned sublattices. Adding on-site disorder in the form of random variations in the refractive index of the waveguides drives the system from a trivial phase into a topological one. This manifestation of topological Anderson insulator physics shows experimentally that disorder can enhance transport rather than arrest it. A counter-intuitive state—known as a topological Anderson insulator—in which strong disorder leads to the formation of topologically protected rather than trivial states is realized in a photonic system.

Engineering light-matter interactions using non-Hermiticity, particularly through spectral degeneracies known as exceptional points (EPs), is an emerging field with potential applications in areas such as cavity quantum electrodynamics, spectral filtering, sensing, and thermal imaging. However, tuning and stabilizing a system to a discrete EP in parameter space is a challenging task. Here, we circumvent this challenge by operating a waveguide-coupled resonator on a surface of EPs, known as an exceptional surface (ES). We achieve this by terminating only one end of the waveguide with a tuneable symmetric reflector to induce a nonreciprocal coupling between the frequency-degenerate clockwise and counterclockwise resonator modes. By operating the system at critical coupling on the ES, we demonstrate chiral and degenerate perfect absorption with squared-Lorentzian lineshape. We expect our approach to be useful for studying quantum processes at EPs and to serve as a bridge between non-Hermitian physics and other fields that rely on radiation engineering. Robust engineering of non-Hermitian light-matter coupling will be crucial for future optical device design. Here the authors present a photonic system that operates on an exceptional surface, demonstrating chiral and degenerate absorption with super-Lorentzian lineshape.

The generation of ultra-low-noise microwave and mmWave in miniaturized, chip-based platforms can transform communication, radar and sensing systems 1 – 3 . Optical frequency division that leverages optical references and optical frequency combs has emerged as a powerful technique to generate microwaves with superior spectral purity than any other approaches 4 – 7 . Here we demonstrate a miniaturized optical frequency division system that can potentially transfer the approach to a complementary metal-oxide-semiconductor-compatible integrated photonic platform. Phase stability is provided by a large mode volume, planar-waveguide-based optical reference coil cavity 8 , 9 and is divided down from optical to mmWave frequency by using soliton microcombs generated in a waveguide-coupled microresonator 10 – 12 . Besides achieving record-low phase noise for integrated photonic mmWave oscillators, these devices can be heterogeneously integrated with semiconductor lasers, amplifiers and photodiodes, holding the potential of large-volume, low-cost manufacturing for fundamental and mass-market applications 13 . A miniaturized optical frequency division system that could transfer the generation of microwaves, with superior spectral purity, to a complementary metal-oxide-semiconductor-compatible integrated photonic platform is demonstrated showing potential for large-volume, low-cost manufacturing for many applications.

Signal processing is of critical importance for various science and technology fields. Analog optical processing can provide an effective solution to perform large-scale and real-time data processing, superior to its digital counterparts, which have the disadvantages of low operation speed and large energy consumption. As an important branch of modern optics, Fourier optics exhibits great potential for analog optical image processing, for instance for edge detection. While these operations have been commonly explored to manipulate the spatial content of an image, mathematical operations that act directly over the angular spectrum of an image have not been pursued. Here, we demonstrate manipulation of the angular spectrum of an image, and in particular its differentiation, using dielectric metasurfaces operating across the whole visible spectrum. We experimentally show that this technique can be used to enhance desired portions of the angular spectrum of an image. Our approach can be extended to develop more general angular spectrum analog meta-processors, and may open opportunities for optical analog data processing and biological imaging. Metasurfaces processing incoming images have been proposed in the context of real space operations. Here, the authors demonstrate mathematical operations, such as differentiation, on the angular spectrum of an image using metasurfaces, which can be used to enhance spectral features of an image.

The optical microresonator-based frequency comb (microcomb) provides a versatile platform for nonlinear physics studies and has wide applications ranging from metrology to spectroscopy. The deterministic quantum regime is an unexplored aspect of microcombs, in which unconditional entanglements among hundreds of equidistant frequency modes can serve as critical ingredients to scalable universal quantum computing and quantum networking. Here, we demonstrate a deterministic quantum microcomb in a silica microresonator on a silicon chip. 40 continuous-variable quantum modes, in the form of 20 simultaneously two-mode squeezed comb pairs, are observed within 1 THz optical span at telecommunication wavelengths. A maximum raw squeezing of 1.6 dB is attained. A high-resolution spectroscopy measurement is developed to characterize the frequency equidistance of quantum microcombs. Our demonstration offers the possibility to leverage deterministically generated, frequency multiplexed quantum states and integrated photonics to open up new avenues in fields of spectroscopy, quantum metrology, and scalable, continuous-variable-based quantum information processing. Microcombs operating in the deterministic quantum regime could lead to new applications. Here, the authors demonstrate a quantum microcomb consisting of 20 two-mode squeezed comb pairs, in an optical microresonator on a silicon chip.

Parity–time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals. Topologically protected bound states in parity–time-symmetric non-Hermitian photonic lattices are theoretically predicted and experimentally demonstrated.