Nonlinear Optics: feature issue introduction.

This joint issue of Optics Express and Optical Materials Express showcases 29 articles that report the latest advancements in nonlinear optics. These articles include contributions from authors who participated in the Optica Nonlinear Optics Topical Meeting, which took place in Honolulu, Hawaii, from July 10th to July 14th, 2023. The conference was organized by Optica (formerly known as OSA). As an introduction, the editors provide a summary of these articles, which cover a broad range of topics in nonlinear optics, spanning from fundamental nonlinear optical concepts to novel nonlinear effects, and from innovative nonlinear materials to topics such as ultrafast optics, machine learning empowered nonlinear optics, and unconventional applications. This diverse array of contributions reflects the dynamic and interdisciplinary nature of contemporary research in the field of nonlinear optics while showcasing some of the most recent developments.

Non-centrosymmetric topological phase probed by non-linear Hall effect.

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe5, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe5 and provide a platform to probe and control local quantum geometry via crystal symmetries.

A hybrid topological quantum state in an elemental solid.

Topology1-3 and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a 'hybrid' topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4.

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

SLAM medical imaging enabled by pre-chirp and gain jointly managed Yb-fiber laser.

We demonstrate a pre-chirp and gain jointly managed Yb-fiber laser that drives simultaneous label-free autofluorescence-multiharmonic (SLAM) medical imaging. We show that a gain managed Yb-fiber amplifier produces high-quality compressed pulses when the seeding pulses exhibit proper negative pre-chirp. The resulting laser source can generate 43-MHz, 34-fs pulses centered at 1110 nm with more than 90-nJ energy. We apply this ultrafast source to SLAM imaging of cellular and extracellular components in various human tissues of intestinal adenocarcinoma, lung adenocarcinoma, and liver.

High power optical frequency comb with 10-19 frequency instability.

Optical frequency combs with more than 10 W have paved the way for extreme ultraviolet combs generation by interaction with inert gases, leading to extreme nonlinear spectroscopy and the ultraviolet nuclear clock. Recently, the demand for an ultra-long-distance time and frequency space transfer via optical dual-comb proposes a new challenge for high power frequency comb in respect of power scaling and optical frequency stability. Here we present a frequency comb based on fiber chirped pulse amplification (CPA), which can offer more than 20 W output power. We further characterize the amplifier branch noise contribution by comparing two methods of locking to an optical reference and measure the out-of-loop frequency instability by heterodyning two identical high-power combs. Thanks to the low noise CPA, reasonable locking method, and optical path-controlled amplifiers, the out-of-loop beat note between two combs demonstrates the unprecedented frequency stability of 4.35 × 10-17 at 1s and 6.54 × 10-19 at 1000 s.

Intertwining of Magnetism and Charge Ordering in Kagome FeGe.

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of the charge ordering and the associated structural distortion remains elusive. We discuss the structural and electronic properties of FeGe. Our proposed ground state phase accurately captures atomic topographies acquired by scanning tunneling microscopy. We show that the 2 × 2 × 1 CDW likely results from the Fermi surface nesting of hexagonal-prism-shaped kagome states. FeGe is found to exhibit distortions in the positions of the Ge atoms instead of the Fe atoms in the kagome layers. Using in-depth first-principles calculations and analytical modeling, we demonstrate that this unconventional distortion is driven by the intertwining of magnetic exchange coupling and CDW interactions in this kagome material. The movement of Ge atoms from their pristine positions also enhances the magnetic moment of the Fe kagome layers. Our study indicates that magnetic kagome lattices provide a material candidate for exploring the effects of strong electronic correlations on the ground state and their implications for transport, magnetic, and optical responses in materials.

Causal structure of interacting Weyl fermions in condensed matter systems.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

High-power, high-repetition-rate tunable longwave mid-IR sources based on DFG in the OPA regime.

We demonstrate high-power longwave mid-IR ultrafast sources based on a high-power Er-fiber laser system at 1.55 µm with a 32-MHz repetition rate. Compared with previous 1.03-µm-driven difference frequency generation (DFG), our current configuration allows tighter focusing in the GaSe crystal thanks to an increased damage threshold at 1.55 µm. Consequently, the 1.55-µm-driven DFG can operate in the regime of optical parametric amplification (OPA), in which the mid-IR power grows exponentially with respect to the square root of the pumping power. We experimentally demonstrate this operation regime and achieve broadband mid-IR pulses that are tunable in the 7.7-17.3 µm range with a maximum average power of 58.3 mW, which is also confirmed by our numerical simulation.

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+ δ Te2.

Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Cr1+ δ Te2 is a self-intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real-space Berry curvature effects, similar considerations of momentum-space Berry curvature are lacking. Here, the electronic structure and transport properties of epitaxial Cr1+ δ Te2 thin films are systematically investigated over a range of doping, δ (0.33 - 0.71). Spectroscopic experiments reveal the presence of a characteristic semi-metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi-metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum-space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets.

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6 Sn6 . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6 Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Application of Multiphoton Microscopic Imaging in Study of Gastric Cancer.

Multiphoton microscopy (MPM) imaging relies on the nonlinear interaction between ultrashort optical pulses and the samples to achieve image contrast. Featuring larger penetration depth, less phototoxicity, 3-dimensional sectioning capability, no need for labeling, MPM become a powerful medical imaging technique that can identify structural characteristics of tissues at the cellular and subcellular levels. In this review paper, we introduce the working principle of MPM imaging, present the current results of MPM imaging applied to the study of gastric tumors, and discuss the future prospects of this interdisciplinary research field.

On the frequency spanning of SPM-enabled spectral broadening: analytical solutions.

We present an analytical treatment of ultra-short pulses propagating in an optical fiber in the strong nonlinearity regime, in which the interaction between self-phase modulation (SPM) and group-velocity dispersion (GVD) substantially broadens the input spectrum. Supported by excellent agreement with the simulation results, these analytical solutions provide a convenient and reasonable accurate estimation of the peak position of the outermost spectral lobes as well as the full width at half maximum of the broadened spectrum. We show that our unified solutions are valid for either Gaussian pulse or hyperbolic secant pulse propagating inside an optical fiber with positive or negative GVD. Our findings shed light on the optimization of SPM-enabled spectral broadening in various applications.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe.

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

Embryonic ethanol exposure induces ectopic Hcrt and MCH neurons outside hypothalamus in rats and zebrafish: Role in ethanol-induced behavioural disturbances.

Embryonic exposure to ethanol increases the risk for alcohol use disorder in humans and stimulates alcohol-related behaviours in different animal models. Evidence in rats and zebrafish suggests that this phenomenon induced by ethanol at low-moderate concentrations involves a stimulatory effect on neurogenesis and density of hypothalamic neurons expressing the peptides, hypocretin/orexin (Hcrt) and melanin-concentrating hormone (MCH), known to promote alcohol consumption. Building on our report in zebrafish showing that ethanol induces ectopic expression of Hcrt neurons outside the hypothalamus, we investigated here whether embryonic ethanol exposure also induces ectopic peptide neurons in rats similar to zebrafish and affects their morphological characteristics and if these ectopic neurons are functional and have a role in the ethanol-induced disturbances in behaviour. We demonstrate in rats that ethanol at a low-moderate dose, in addition to increasing Hcrt and MCH neurons in the lateral hypothalamus where they are normally concentrated, induces ectopic expression of these peptide neurons further anterior in the nucleus accumbens core and ventromedial caudate putamen where they have not been previously observed and causes morphological changes relative to normally located hypothalamic neurons. Similar to rats, embryonic ethanol exposure at a low-moderate dose in zebrafish induces ectopic Hcrt neurons anterior to the hypothalamus and alters their morphology. Notably, laser ablation of these ectopic Hcrt neurons blocks the behavioural effects induced by ethanol exposure, including increased anxiety and locomotor activity. These findings suggest that the ectopic peptide neurons are functional and contribute to the ethanol-induced behavioural disturbances related to the overconsumption of alcohol.

Observation of a linked-loop quantum state in a topological magnet.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state1-13. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids5, magnets6,7, the quantum Hall effect3,8, topological insulators9,10, Weyl semimetals11-13 and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet14-20. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

Fibroblast growth factor 2: Role in prenatal alcohol-induced stimulation of hypothalamic peptide neurons.

Prenatal alcohol exposure (PAE) increases alcohol consumption and risk for alcohol use disorder. This phenomenon in rodents is suggested to involve a stimulatory effect of PAE, in female more than male offspring, on neurogenesis and density of neurons expressing neuropeptides in lateral hypothalamus (LH), including melanin-concentrating hormone (MCH), known to promote alcohol intake. With evidence suggesting a role for fibroblast growth factor 2 (FGF2) and its receptor FGFR1 in stimulating neurogenesis and alcohol drinking, we investigated here whether the FGF2-FGFR1 system is involved in the PAE-induced increase in MCH neurons, in postnatal offspring of pregnant rats given ethanol orally (embryonic day 10-15) at a low-moderate (2 g/kg/day) or high (5 g/kg/day) dose. Our results demonstrate that PAE at the low-moderate but not high dose stimulates FGF2 and FGFR1 gene expression and increases the density of MCH neurons co-expressing FGF2, only in females, but FGFR1 in both sexes. PAE induces this effect in the dorsal but not ventral area of the LH. Further analysis of FGF2 and FGFR1 transcripts within individual MCH neurons reveals an intracellular, sex-dependent effect, with PAE increasing FGF2 transcripts positively related to FGFR1 in the nucleus as well as cytoplasm of females but transcripts only in the cytoplasm of males. Peripheral injection of FGF2 itself (80 µg/kg, s.c.) in pregnant rats mimics these effects of PAE. Together, these results support the involvement of the FGF2-FGFR1 system in mediating the PAE-induced, sex dependent increase in density of MCH neurons, possibly contributing to increased alcohol consumption in the offspring.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt.

MnBi2Te4 (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi2Te3 phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.