Nonlinear Optics with 2D Layered Materials

Boosting classical and quantum nonlinear processes in ultrathin van der Waals materials

Understanding and controlling nonlinear processes is crucial for engineering light-matter interaction and generating non-classical light. A significant challenge in ultra-thin nonlinear materials is the marked diminution of the nonlinear conversion efficiency due to the reduced light-matter interaction length and, in many cases, the centrosymmetric crystalline structures. Here we relax these limitations and report a giant boost of classical and quantum nonlinear processes in ultrathin van der Waals materials. Specifically, with a metal-nonlinear material heterostructure we enhance classical second-harmonic generation in h-BN flakes by two orders of magnitude. Moreover, we have engineered a metal-SiO2-nonlinear material heterostructure resulting in a remarkable two orders of magnitude augmentation of the quantum spontaneous parametric down-conversion (SPDC) in NbOCl2 flakes. Notably, we demonstrate SPDC in a 16 nm-thick NbOCl2 flake integrated into the proposed structure. These findings simplify on-chip quantum state engineering and accelerate the use of van der Waals materials in nonlinear optoelectronics.

Artificially Engineered Nonlinear Circular Dichroism with Chiral Nanoscrolling of 2D Materials

Nonlinear chiroptical response, particularly nonlinear circular dichroism (CD), holds significant potential for advancing nanotechnology, biophotonics, and molecular imaging. While conventional approaches rely on intrinsic chiral materials, we demonstrate a novel strategy to engineer this effect by transforming achiral two-dimensional (2D) transition-metal dichalcogenides (TMDs) into chiral nanostructures. By scrolling monolayer TMDs into geometrically chiral nanoscrolls, we achieve pronounced nonlinear CD (up to 0.8), evidenced by circular-polarization-dependent second-harmonic generation (SHG). Notably, the SHG-CD degree is tailored by controlling the nanoscrolls' scrolling axes, demonstrating, for the first time, programmable chirality-dependent nonlinear responses in TMD nanoscrolls. Furthermore, the confined electromagnetic fields within the scrolled geometry amplify the SHG intensity by up to 100-fold compared to monolayers. This chiral nanoscrolling is anticipated to enable innovative functionalities in the realm of compact nonlinear light sources and modulators, heralding a new era of advanced photonic applications.

Broadband and efficient third-harmonic generation from black phosphorus-hybrid plasmonic metasurfaces in the mid-infrared

Black phosphorus (BP), with a mid-infrared (MIR) bandgap of 0.34 eV, presents itself as a promising material for MIR nonlinear optical applications. We report the realization of MIR third-harmonic generation (THG) in both BP and BP-hybrid plasmonic metasurfaces (BPM). BP exhibits a high third-order nonlinear susceptibility ([Formula: see text]) exceeding 10-18 m2/V2 in the MIR region with a maximum value of 1.55 × 10-17 m2/V2 at 5000 nm. The BP flake achieves a THG conversion efficiency of 1.4 × 10-5, surpassing that of other 2D materials by over one order of magnitude. To further enhance this nonlinear performance, a BPM is designed and fabricated to achieve a two-order-of-magnitude enhancement in THG, leading to a record conversion efficiency of 6.5 × 10-4, exceeding the performance of previously reported metasurfaces by more than one order of magnitude. These findings establish BP as a promising platform for next-generation MIR nonlinear optical devices.

Leveraging Strong Electric Field Gradients at Anapole Resonances for Enhanced Second Harmonic Generation from Molybdenum Disulfide Disks

Van der Waals layered materials are emerging as promising nanophotonic platforms for realizing linear and nonlinear optical devices. In particular, the high refractive indices of transition metal dichalcogenides, combined with their strong layer dependent optical properties offer interesting possibilities for designing photonic functionalities. In this study, the resonant enhancement of second harmonic generation (SHG) using molybdenum disulfide (MoS2) disks on a silicon substrate with an intermediate silicon dioxide (SiO2) layer is demonstrated. The resonant enhancement observed here is attributed to the combined interaction of the anapole scattering modes supported within the disk and Fabry-Perot (FP) modes within the multilayer stack. For a fixed MoS2 disk dimensions, an optimized SiO2 layer thickness results in constructive interference between the anapole and FP modes, thereby enhancing the fundamental field within the disk. Utilizing this resonance mechanism, SHG enhancements as high as 160 and 85-times are experimentally demonstrated when compared with unpatterned multilayer and monolayer MoS2 flakes respectively. These are the highest reported enhancement values for the widely used 2H-polytype MoS2. A significant enhancement in SHG is observed here for 2H-MoS2 despite the alternating sheet dipoles canceling the far-field emission owing to the strong electric field gradient setup within the disk at the anapole resonance.

Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides

Materials capable of light upconversion-transforming low-energy photons into higher-energy ones-are pivotal in advancing optoelectronics, energy solutions, and photocatalysis. However, the discovery in various materials pays little attention on few-layer transition metal dichalcogenides, primarily due to their indirect bandgaps and weaker light-matter interactions. Here, we report a pronounced light upconversion in few-layer transition metal dichalcogenides through upconversion photoluminescence spectroscopy. Our joint theory-experiment study attributes the upconversion photoluminescence to a resonant exciton-exciton annihilation involving a pair of dark excitons with opposite momenta, followed by the spontaneous emission of upconverted bright excitons, which can have a high upconversion efficiency. Additionally, the upconversion photoluminescence is generic in MoS2, MoSe2, WS2, and WSe2, showing a high tuneability from green to ultraviolet light (2.34-3.1 eV). The findings pave the way for further exploration of light upconversion regarding fundamental properties and device applications in two-dimensional semiconductors.

Origin of Nonlinear Circular Photocurrent in 2D Semiconductor MoS_{2}

Nonlinear photogalvanic effects in two-dimensional materials, particularly the nonlinear circular photocurrents (NCPs) that belong to the helicity-dependent spin photocurrents, have sparked enormous research interest. Although notable progress has been witnessed, the underling origin of NCPs remains elusive. Here, we present systematic photocurrent characteristics, symmetry analysis and theoretical calculations to uncover the physical origin of NCPs in MoS_{2}, a prototypical 2D semiconductor. Our results show that the NCP responses in 2D semiconductor MoS_{2} result from the circular photon drag effect (CPDE), rather than the generally believed circular photogalvanic effect. Furthermore, we demonstrate that the NCPs are highly tunable with electrostatic doping and increase progressively with MoS_{2} thickness, evidencing the interlayer constructive nature of CPDE responses. Our Letter unravels the critical role of the previously overlooked CPDE contribution to NCPs, revolutionizing previous understanding and thus providing deep insights into further fundamental studies and technological advances in nonlinear photovoltaic and opto-spintronic devices.

Scalable Manufacturing of Low-Symmetry Plasmonic Nanospindle Arrays with Tunable Surface Lattice Resonance

Geometry-dependent plasmonic surface lattice resonances (SLRs) have garnered great interest across a range of applications, including nanolasers, sensors, photocatalysis, and nonlinear optics. However, the rational fabrication of high-quality, low-symmetry, plasmonic nanoparticle arrays over large areas remains challenging. Herein, we report a versatile strategy for the scalable fabrication of centimeter-scale plasmonic nanospindle (NS) arrays with high positional and orientational precision. Our approach combines solvent-assisted soft lithography with in situ reduction of metal precursors, enabling the cost-effective production of large-area and well-ordered NS arrays without the need of specialized equipment. The Au NS arrays exhibit superior SLRs with a ultranarrow line width of 3.9 nm and a quality factor (Q-factor) of 309. The aspect ratio and lattice geometry of the NSs can be precisely tuned by applying mechanical strain to the stretchable elastomeric template, thus, allowing us to customize the SLR performance across the near-infrared spectrum. This technique enables the precise engineering of anisotropic nanoparticle arrays in a standard chemistry laboratory, opening new possibilities for advanced plasmonic devices.

Ferroelectricity and Nonlinear Optical Responses in Two-Dimensional Distorted MX2Y (M = Cu, Ag, Au; X = Chalcogens; Y = Halogen) Monolayers

Two-dimensional (2D) materials with spontaneous polarization can exhibit large second-order nonlinear optical (NLO) effects. Here, we present a series of stable distorted MX2Y monolayers by using first-principles calculations and lattice vibration analysis. The structural distortion leads to a lower polar symmetry, giving rise to intrinsic ferroelectricity with a Curie point up to room temperature. We show that the bulk photovoltaic effect (BPVE) in polar MX2Y monolayers has an enhanced shift current, an order of magnitude larger than that in the undistorted nonpolar counterparts. Meanwhile, the second harmonic generation (SHG) susceptibility reaches up to the order of 106 pm2/V, superior to that of 2D conventional materials such as MoS2, h-BN, and GeS. Our study advances the research in 2D ferroelectric materials and would stimulate more efforts in developing optoelectronic devices based on NLO effects.

Fabrication of Dual-Functional MXene@NiCo2S4 Composites with Enhanced Nonlinear Optical and Electrochemical Properties

The design and synthesis of multifunctional nanomaterials have attracted considerable attention for expanding the range of practical applications. Herein, a metal-organic framework (MOFs)-derived NiCo2S4 attached to MXene is rationally designed and constructed for an optical limiter and supercapacitor. The MOF-derived NiCo2S4 enhances the tendency of hydroxyl groups on the MXene surface to attract metal ions, resulting in the formation of sulfur vacancies. Moreover, MXene offers a high specific surface area to facilitate the rapid complexation of charge carriers. The resultant MXene@NiCo2S4 (MX@NCS) exhibits markedly enhanced nonlinear optical (NLO) and electrochemical properties through synergistic interactions between the components. The NLO properties can be further optimized by adjusting the amount of MX@NCS powder dispersed in methyl methacrylate (MX@NCS)2-6/PMMA) by using the Z-scan technique. Specifically, the (MX@NCS)4/PMMA exhibits the strongest reverse saturable absorption (RSA) and self-defocusing effects at 100 µJ with β = 3.87 × 102 cm·GW-1 and γ = -5.94 × 10-4 cm2·GW-1. Concurrently, the constructed supercapacitor shows a superior energy density of 51.21 Wh·kg-1 at a power density of 863.65 W·kg-1. Notably, the present study indicates a novel strategy to explore the application of materials in the development of efficient optical limiter and supercapacitor technologies.

Tunable polarization entangled photon-pair source in rhombohedral boron nitride

Entangled photon-pair sources are pivotal in various quantum applications. Miniaturizing the quantum devices to meet the requirement in limited space applications drives the search for ultracompact entangled photon-pair sources. The rise of two-dimensional (2D) semiconductors has been demonstrated as ultracompact entangled photon-pair sources. However, the photon-pair generation rate and purity are relatively low, and the strong photoluminescence in 2D semiconductors also makes the operational wavelength range limited. Here, we use the spontaneous parametric down conversion (SPDC) of rhombohedral boron nitride (rBN) as a polarization entangled photon-pair source. We have achieved a generation rate of more than 120 hertz (a record-high SPDC coincidence rate with 2D materials) and a high-purity photon-pair generation with a coincidence-to-accidental ratio of above 200. Tunable Bell state generation is also demonstrated by simply rotating the pump polarization, with a fidelity up to 0.93. Our results suggest rBN as an ideal candidate for on-chip integrated quantum devices.

Nonlinear optics of graphitic carbon allotropes: from 0D to 3D

The dimensionality of materials fundamentally influences their electronic and optical properties, presenting a complex interplay with nonlinear optical (NLO) characteristics that remains largely unexplored. In this review, we focus on the influence of dimensionality on the NLO properties of graphitic allotropes, ranging from 0D fullerenes, 1D carbon nanotubes, and 2D graphene, to 3D graphite, all of which share a consistent sp2 hybridized chemical bonding structure. We examine the distinct physical and NLO properties across these dimensions, underscoring the profound impact of dimensionality. Notably, dimension-specific physical phenomena, such as Luttinger liquid in 1D and Landau quantization in 2D, play a significant role in shaping NLO phenomena. Finally, we explore the promising potential of NLO properties in systems with mixed dimensionalities, setting the stage for future breakthroughs and innovative applications.

Nanoscale thickness Octave-spanning coherent supercontinuum light generation

Coherent broadband light generation has attracted massive attention due to its numerous applications ranging from metrology, sensing, and imaging to communication. In general, spectral broadening is realized via third-order and higher-order nonlinear optical processes (e.g., self-phase modulation, Raman transition, four-wave mixing, multiwave mixing), which are typically weak and thus require a long interaction length and the phase matching condition to enhance the efficient nonlinear light-matter interaction for broad-spectrum generation. Here, for the first time, we report octave-spanning coherent light generation at the nanometer scale enabled by a phase-matching-free frequency down-conversion process. Up to octave-spanning coherent light generation with a -40dB spectral width covering from ~565 to 1906 nm is demonstrated in discreate manner via difference-frequency generation, a second-order nonlinear process in gallium selenide and niobium oxide diiodide crystals at the 100-nanometer scale. Compared with conventional coherent broadband light sources based on bulk materials, our demonstration is ~5 orders of magnitude thinner and requires ~3 orders of magnitude lower excitation power. Our results open a new way to possibly create compact, versatile and integrated ultra-broadband light sources.

Experimental Realization of Fluoroborophene

Borophene, an anisotropic metallic Dirac material exhibits superlative physical and chemical properties. While the lack of bandgap restricts its electronic chip applications, insufficient charge carrier density and electrochemical/catalytically active sites, restricts its energy storage and catalysis applications. Fluorination of borophene can induce bandgap and yield local electron injection within its crystallographic lattice. Herein, a facile synthesis of fluoroborophene with tunable fluorine content through potassium fluoride-assisted solvothermal-sonochemical combinatorial approach is reported. Fluoroborophene monolayers with lateral dimension 50 nm-5 µm are synthesized having controlled fluorine content (12-35%). Fluoroborophene exhibits inter-twinned crystallographic structure, with fluorination-tunable visible-range bandgap ≈1.5-2.5 eV, and density functional theory calculations also corroborate it. Fluoroborophene is explored for electrocatalytic oxygen evolution reaction in an alkaline medium and bestow a good stability. Tunable bandgap, electrophilicity and molecular anchoring capability of fluoroborophene will open opportunities for novel electronic/optoelectronic/spintronic chips, energy storage devices, and in numerous catalytic applications.

Advancing Two-Photon Photodynamic Therapy Over NIR-II Excitable Conjugated Microporous Polymer with NIR-I Emission

The availability of second near-infrared (NIR-II) excitable two-photon photosensitizers with NIR-I emission for efficient photodynamic therapy (PDT) is limited by challenges in molecular design. In this study, a NIR-II light-excitable two-photon conjugated microporous polymer (Tph-Dbd) with emission in the NIR-I region is developed. The large conjugated system and delocalized electronic structures endow Tph-Dbd with a large two-photon absorption cross-section under NIR-II light excitation. Moreover, the efficient electron acceptor and donor units within the π-conjugated backbones result in NIR-I emission for high signal-to-background ratio imaging, as well as separated highest occupied molecular orbital and lowest unoccupied molecular orbital distributions for excellent singlet oxygen generation ability. The excellent NIR-II excitable two-photon absorption activity, NIR-I emission, good biocompatibility, and high photostability allow Tph-Dbd to be used for efficient in vitro fluorescence imaging guided PDT. Moreover, the impressive photothermal effect of Tph-Dbd can overcome the limitations of PDT in the treatment of hypoxic tumors. This study highlights a strategy for designing NIR-II excitable two-photon photosensitizers for advanced PDT.

Phase Engineering of Giant Second Harmonic Generation in Bi2O2Se

2D materials with remarkable second-harmonic generation (SHG) hold promise for future on-chip nonlinear optics. Relevant materials with both giant SHG response and environmental stability are long-sought targets. Here, the enormous SHG from the phase engineering of a high-performance semiconductor, Bi2O2Se (BOS), under uniaxial strain, is demonstrated. SHG signals captured in strained 20 nm-BOS films exceed those of NbOI2 and NbOCl2 of similar thickness by a factor of 10, and are four orders of magnitude higher than monolayer-MoS2, resulting in a significant second-order nonlinear susceptibility on the order of 1 nm V-1. Intriguingly, the strain enables continuous adjustment of the ferroelectric phase transition across room temperature. An exceptionally large tunability of SHG, approximately six orders of magnitude, is achieved through strain modulation. This colossal SHG, originating from the geometric phase of Bloch wave functions and coupled with sensitive strain tunability in this air-stable 2D semiconductor, opens new possibilities for designing chip-scale, switchable nonlinear optical devices.

3D Nanofabrication via Directed Material Assembly: Mechanism, Method, and Future

Fabrication of complex three-dimensional (3D) structures at nanoscale is the core of nanotechnology, as it enables the creation of various micro-/nano-devices such as micro-robots, metamaterials, sensors, photonic devices, etc. Among most 3D nanofabrication strategies, the guided material assembly, an efficient bottom-up approach capable of directly constructing designed structures from precise integration of material building blocks, possesses compelling advantages in diverse material compatibility, sufficient driving forces, facile processing steps, and nanoscale resolution. In this review, we focus on assembly-based fabrication methods capable of creating complex 3D nanostructures (instead of periodic or 2.5D-only structures). Recent advances are classified based on the different assembly mechanisms, i.e., assembly driven by chemical reactions, physical interactions, and the synergy of multiple microscopic interactions. The design principles of representative fabrication strategies with an emphasis on their respective advantages, e.g., structural design flexibility, material compatibility, resolution, or applications are analyzed. In the summary and outlook, existing challenges, as well as possible paths to solutions for future development are reviewed. We believe that with recent advances in assembly-based nanofabrication strategies, 3D nanofabrication has achieved tremendous progress in resolution, material generality, and manufacturing cost, for it to make a greater impact in the near future.

Polarization entanglement enabled by orthogonally stacked van der Waals NbOCl2 crystals

Polarization entanglement holds significant importance for photonic quantum technologies. Recently emerging subwavelength nonlinear quantum light sources, e.g., GaP and LiNbO3 thin films, benefiting from the relaxed phase-matching constraints and volume confinement, have shown intriguing properties, such as high-dimensional hyperentanglement and robust entanglement anti-degradation. Van der Waals (vdW) NbOCl2 crystal, with strong optical nonlinearities, has emerged as a potential candidate for ultrathin quantum light sources. However, polarization entanglement is inaccessible in the NbOCl2 crystal due to its unfavorable nonlinear susceptibility tensor. Here, by leveraging the twist-stacking degree of freedom inherently in vdW systems, we showcase the preparation of polarization entanglement and quantum Bell states.

Programmable nonlinear optical neuromorphic computing with bare 2D material MoS2

Nonlinear optical responses in two-dimensional (2D) materials can build free-space optical neuromorphic computing systems. Ensuring the high performance and the tunability of the system is essential to encode diverse functions. However, common strategies, including the integration of external electrode arrays or photonic structures with 2D materials, and barely patterned 2D materials, exhibit a contradiction between performance and tunability. Because the unique band dispersions of 2D materials can provide hidden paths to boost nonlinear responses independently, here we introduced a new free-space optical computing concept within a bare molybdenum disulfide array. This system can preserve high modulation performance with fast speed, low energy consumption, and high signal-to-noise ratio. Due to the freedom from the restrictions of fixed photonic structures, the tunability is also enhanced through the synergistic encodings of the 2D cells and the excitation pulses. The computing mechanism of transition from two-photon absorption to synergistic excited states absorption intrinsically improved the modulation capability of nonlinear optical responses, revealed from the relative transmittance modulated by a pump-probe-control strategy. Optical artificial neural network (ANN) and digital processing were demonstrated, revealing the feasibility of the free-space optical computing based on bare 2D materials toward neuromorphic applications.

Dimension-Dependent Nonlinear Optical Properties of Stanene Nanosheets

Stanene (Sn)-based materials, with a graphene-like hexagonal structure, are now attracting considerable interest for potential applications in photoelectricity. However, the nonlinear optical properties of stanene remain largely unexplored. In this work, we prepared different sizes of stanene by liquid phase exfoliation and differential centrifugation methods, including two-dimensional (2D) Sn nanosheets (NSs) and zero-dimensional (0D) Sn nanodots (NDs). Z-scan measurements reveal that 2D Sn NSs exhibited high saturable absorption behavior, while the 0D Sn NDs led to reverse saturable absorption. Femtosecond ultrafast transient absorption spectra revealed that the reverse saturable absorption of Sn NDs is derived from a stronger excited state absorption and faster exciton relaxation dynamics. This research expands the potential applications of stanene in laser shielding and other ultrafast photonics technologies.

Substrate Interference and Strain in the Second-Harmonic Generation from MoSe2 Monolayers

Nonlinear optical materials of atomic thickness, such as non-centrosymmetric 2H transition metal dichalcogenide monolayers, have a second-order nonlinear susceptibility (χ(2)) whose intensity can be tuned by strain. However, whether χ(2) is enhanced or reduced by tensile strain is a subject of conflicting reports. Here, we grow high-quality MoSe2 monolayers under controlled biaxial strain created by two different substrates and study their linear and nonlinear optical responses with a combination of experimental and theoretical approaches. Up to a 15-fold overall enhancement in second-harmonic generation (SHG) intensity is observed from MoSe2 monolayers grown on SiO2 when compared to its value on a Si3N4 substrate. By considering an interference contribution from different dielectrics and their thicknesses, a factor of 2 enhancement of χ(2) was attributed to the biaxial strain: substrate interference and strain are independent handles to engineer the SHG strength of non-centrosymmetric 2D materials.

Theoretical Prediction of Monolayer BeP2O4H4 with Excellent Nonlinear-Optical Properties in Deep-Ultraviolet Range

Most 2D nonlinear optical (NLO) materials do not have an ultrawide bandgap, therefore, they are unsuitable for working in the deep-ultraviolet spectral range (< 200 nm). Herein, the theoretical prediction of an excellent monolayer BeP2O4H4 (ML-BPOH) is reported. DFT analyses suggest a low cleavage energy (≈45 meV per atom) from a naturally existed bulk-BPOH material, indicating feasible exfoliation. This novel 2D material exhibits excellent properties including an ultrawide bandgap (Eg) of 7.84 eV, and a strong second-order nonlinear susceptibility (d b u l k e f f $d_{bulk}^{eff}$ = 0.43 pm V-1), which is comparable to that of benchmark bulk-KBBF crystal (d16 = 0.45 pm V-1). The wide bandgap and large SHG effect of ML-BPOH are mainly derived from the (PO2H2)- tetrahedron. Notably, ML-BPOH exhibits an outstanding 50% variation in dsheet under minor stress stimuli (±3%) due to rotation of structurally rigid (PO2H2)- tetrahedron. This indicates significant potential for application in material deformation monitoring.

Critical-Layered MoS2 for the Enhancement of Supercontinuum Generation in Photonic Crystal Fibre

Supercontinuum generation (SCG) from silica-based photonic crystal fibers (PCFs) is of highly technological significance from microscopy to metrology, but has been hindered by silica's relatively low intrinsic optical nonlinearity. The prevailing approaches of filling PCF with nonlinear gases or liquids can endow fibre with enhanced optical nonlinearity and boosted SCG efficiency, yet these hybrids are easily plagued by fusion complexity, environmental incompatibility or transmission mode instability. Here this work presents a strategy of embedding solid-state 2D MoS2 atomic layers into the air-holes of PCF to efficiently enhance SCG. This work demonstrates a 4.8 times enhancement of the nonlinear coefficient and a 70% reduction of the threshold power for SCG with one octave spanning in the MoS2-PCF hybrid. Furthermore, this work finds that the SCG enhancement is highly layer-dependent, which only manifests for a real 2D regime within the thickness of five atomic layers. Theoretical calculations reveal that the critical thickness arises from the trade-off among the layer-dependent enhancement of the nonlinear coefficient, leakage of fundamental mode and redshift of zero-dispersion wavelength. This work provides significant advances toward efficient SCG, and highlights the importance of matching an appropriate atomic layer number in the design of functional 2D material optical fibers.

Large-Area Epitaxial Growth of Transition Metal Dichalcogenides

Over the past decade, research on atomically thin two-dimensional (2D) transition metal dichalcogenides (TMDs) has expanded rapidly due to their unique properties such as high carrier mobility, significant excitonic effects, and strong spin-orbit couplings. Considerable attention from both scientific and industrial communities has fully fueled the exploration of TMDs toward practical applications. Proposed scenarios, such as ultrascaled transistors, on-chip photonics, flexible optoelectronics, and efficient electrocatalysis, critically depend on the scalable production of large-area TMD films. Correspondingly, substantial efforts have been devoted to refining the synthesizing methodology of 2D TMDs, which brought the field to a stage that necessitates a comprehensive summary. In this Review, we give a systematic overview of the basic designs and significant advancements in large-area epitaxial growth of TMDs. We first sketch out their fundamental structures and diverse properties. Subsequent discussion encompasses the state-of-the-art wafer-scale production designs, single-crystal epitaxial strategies, and techniques for structure modification and postprocessing. Additionally, we highlight the future directions for application-driven material fabrication and persistent challenges, aiming to inspire ongoing exploration along a revolution in the modern semiconductor industry.

Nonlinear physics of moiré superlattices

Nonlinear physics is one of the most important research fields in modern physics and materials science. It offers an unprecedented paradigm for exploring many fascinating physical phenomena and realizing diverse cutting-edge applications inconceivable in the framework of linear processes. Here we review the recent theoretical and experimental progress concerning the nonlinear physics of synthetic quantum moiré superlattices. We focus on the emerging nonlinear electronic, optical and optoelectronic properties of moiré superlattices, including but not limited to the nonlinear anomalous Hall effect, dynamically twistable harmonic generation, nonlinear optical chirality, ultralow-power-threshold optical solitons and spontaneous photogalvanic effect. We also present our perspectives on the future opportunities and challenges in this rapidly progressing field, and highlight the implications for advances in both fundamental physics and technological innovations.

Strong chiroptical nonlinearity in coherently stacked boron nitride nanotubes

Nanomaterials with a large chiroptical response and high structural stability are desirable for advanced miniaturized optical and optoelectronic applications. One-dimensional (1D) nanotubes are robust crystals with inherent and continuously tunable chiral geometries. However, their chiroptical response is typically weak and hard to control, due to the diverse structures of the coaxial tubes. Here we demonstrate that as-grown multiwalled boron nitride nanotubes (BNNTs), featuring coherent-stacking structures including near monochirality, homo-handedness and unipolarity among the component tubes, exhibit a scalable nonlinear chiroptical response. This intrinsic architecture produces a strong nonlinear optical response in individual multiwalled BNNTs, enabling second-harmonic generation (SHG) with a conversion efficiency up to 0.01% and output power at the microwatt level-both excellent figures of merit in the 1D nanomaterials family. We further show that the rich chirality of the nanotubes introduces a controllable nonlinear geometric phase, producing a chirality-dependent SHG circular dichroism with values of -0.7 to +0.7. We envision that our 1D chiral platform will enable novel functions in compact nonlinear light sources and modulators.

Enhanced vertical second harmonic generation from layered GaSe coupled to photonic crystal circular Bragg resonators

Two-dimensional (2D) layered materials without centrosymmetry, such as GaSe, have emerged as promising novel optical materials due to large second-order nonlinear susceptibilities. However, their nonlinear responses are severely limited by the short interaction between the 2D materials and light, which should be improved by coupling them with photonic structures with strong field confinement. Here, we theoretically design photonic crystal circular Bragg gratings (CBG) based on hole gratings with a quality factor as high as Q = 8 × 103, a mode volume as small as V = 1.18 (λ/n)3, and vertical emission of light field in silicon nitride thin film platform. Experimentally, we achieved a Q value up to nearly 4 × 103, resulting in a 1,200-fold enhancement of second harmonic generation from GaSe flakes with a thickness of 50 nm coupling to the CBG structures under continuous-wave excitation. Our work endows silicon-based photonic platforms with significant second-order nonlinear effect, which is potentially applied in on-chip quantum light sources and nonlinear frequency conversion.

Probing Dark Excitons in Monolayer MoS_{2} by Nonlinear Two-Photon Spectroscopy

We report a new dark exciton in monolayer MoS_{2} using second harmonic generation spectroscopy. Hereby, the spectrally dependent second harmonic generation intensity splits into two branches, and an anticrossing is observed at ∼25  meV blue detuned from the bright neutral exciton. These observations are indicative of coherent quantum interference arising from strong two-photon light-matter interaction with an excitonic state that is dark for single photon interaction. The existence of the dark state is supported by engineering its relaxation to bright localized excitons, mediated by vibrational modes of a proximal nanobeam cavity. We show that two-photon light-matter interaction involving dark states has the potential to control relaxation pathways induced by nanostructuring the local environment. Moreover, our results indicate that dark excitons have significant potential for nonlinear quantum devices based on their nontrivial excitonic photophysics.

Application of the Knife-Edge Technique on Transition Metal Dichalcogenide Monolayers for Resolution Assessment of Nonlinear Microscopy Modalities

We report application of the knife-edge technique at the sharp edges of WS2 and MoS2 monolayer flakes for lateral and axial resolution assessment in all three modalities of nonlinear laser scanning microscopy: two-photon excited fluorescence (TPEF), second- and third-harmonic generation (SHG, THG) imaging. This technique provides a high signal-to-noise ratio, no photobleaching effect and shows good agreement with standard resolution measurement techniques. Furthermore, we assessed both the lateral resolution in TPEF imaging modality and the axial resolution in SHG and THG imaging modality directly via the full-width at half maximum parameter of the corresponding Gaussian distribution. We comprehensively analyzed the factors influencing the resolution, such as the numerical aperture, the excitation wavelength and the refractive index of the embedding medium for the different imaging modalities. Glycerin was identified as the optimal embedding medium for achieving resolutions closest to the theoretical limit. The proposed use of WS2 and MoS2 monolayer flakes emerged as promising tools for characterization of nonlinear imaging systems.

Giant nonlinear optical wave mixing in a van der Waals correlated insulator

Optical nonlinearities are one of the most fascinating properties of two-dimensional (2D) materials. While tremendous efforts have been made to find and optimize the second-order optical nonlinearity in enormous 2D materials, opportunities to explore higher-order ones are elusive because of the much lower efficiency. Here, we report the giant high odd-order optical nonlinearities in centrosymmetric correlated van der Waals insulator manganese phosphorus triselenide. When illuminated by two near-infrared femtosecond lasers, the sample generates a series of profound four- and six-wave mixing outputs. The near-infrared third-order nonlinear susceptibility reaches near the highest record values of 2D materials. Comparative measurements to other prototypical nonlinear optical materials [lithium niobate, gallium(II) selenide, and tungsten disulfide] reveal its extraordinary wave mixing efficiency. The wave mixing processes are further used for nonlinear optical waveguide with multicolor emission. Our work highlights the promising prospect for future research of the nonlinear light-matter interactions in the correlated 2D system and for potential nonlinear photonic applications.

Quasi-BICs enhanced second harmonic generation from WSe2 monolayer

Quasi-bound states in the continuum (quasi-BICs) offer unique advantages in enhancing nonlinear optical processes and advancing the development of active optical devices. Here, the tunable robust quasi-BICs resonances are experimentally achieved through the engineering of multiple-hole Si-metasurface. Notably, the quasi-BICs mode exhibits flat bands with minimal dispersion at a wide range of incident angles, as demonstrated by the angle-resolved spectroscopy measurements. Furthermore, we demonstrate a giant second-harmonic generation (SHG) enhancement by coupling a WSe2 monolayer to the quasi-BICs hosted in the metasurface. Leveraging the strong local electric field and high state density of the observed quasi-BICs, the SHG from the WSe2 monolayer can be enhanced by more than two orders of magnitude. Our work paves the way for effectively enhancing nonlinear optical processes in two dimensional (2D) materials within the framework of silicon photonics and is expected to be applied in nonlinear optical devices.

Tailoring of the polarization-resolved second harmonic generation in two-dimensional semiconductors

Second harmonic generation is a non-linear optical phenomenon in which coherent radiation with frequency ω interacts with a non-centrosymmetric material and produces coherent radiation at frequency 2ω. Owing to the exciting physical phenomena that take place during the non-linear optical excitation at the nanoscale, there is currently extensive research in the non-linear optical responses of nanomaterials, particularly in low-dimensional materials. Here, we review recent advancements in the polarization-resolved second harmonic generation propertied from atomically thin two-dimensional (2D) crystals and present a unified theoretical framework to account for their nonlinear optical response. Two major classes of 2D materials are particularly investigated, namely metal chalcogenides and perovskites. The first attempts to tune and control the second harmonic generation properties of such materials via the application of specific nanophotonic schemes are additionally demonstrated and discussed. Besides presenting recent advances in the field, this work also delineates existing limitations and highlights emerging possibilities and future prospects in this field.

Intense second-harmonic generation in two-dimensional PtSe2

Platinum diselenide (PtSe2), classified as a noble metal dichalcogenide, has garnered substantial interest owing to its layer-dependent band structure, remarkable air-stability, and high charge-carrier mobilities. These properties make it highly promising for a wide array of applications in next-generation electronic and optoelectronic devices, as well as sensors. Additionally, two-dimensional (2D) PtSe2 demonstrates significant potential as a saturable absorber due to its exceptional nonlinear optical response across an ultrabroad spectra range, presenting exciting opportunities in ultrafast and nonlinear photonics. In this work, we explore the second-order nonlinear optical characteristics of 2D PtSe2 by analyzing its second-harmonic generation (SHG) excited by a pulsed laser at 1064 nm. Our investigation unveils a layer-dependent SHG response in PtSe2, with prominent SHG intensity observed in few-layer PtSe2. The distinct six-fold polarization dependence pattern observed in the SHG intensity reflects the inherent threefold rotational symmetry inherent to the PtSe2 crystal structure. Remarkably, the SHG intensity of 4-layer PtSe2 surpasses that of mechanically exfoliated monolayer molybdenum disulfide (MoS2) by approximately two orders of magnitude (60-fold), underscoring its exceptional second-order nonlinear optical response. Combined with its ultrahigh air-stability, these distinctive nonlinear optical characteristics position two-dimensional PtSe2 as a promising candidate for ultrathin nonlinear nanophotonic devices.

Anisotropic van der Waals Tellurene-Based Multifunctional, Polarization-Sensitive, In-Line Optical Device

Polarization plays a paramount role in scaling the optical network capacity. Anisotropic two-dimensional (2D) materials offer opportunities to exploit optical polarization-sensitive responses in various photonic and optoelectronic applications. However, the exploration of optical anisotropy in fiber in-line devices, critical for ultrafast pulse generation and modulation, remains limited. In this study, we present a fiber-integrated device based on a single-crystalline tellurene nanosheet. Benefiting from the chiral-chain crystal lattice and distinct optical dichroism of tellurene, multifunctional optical devices possessing diverse excellent properties can be achieved. By inserting the in-line device into a 1.5 μm fiber laser cavity, we generated both linearly polarized and dual-wavelength mode-locking pulses with a degree of polarization of 98% and exceptional long-term stability. Through a twisted configuration of two tellurene nanosheets, we realized an all-optical switching operation with a fast response. The multifunctional device also serves as a broadband photodetector. Notably, bipolar polarization encoding communication at 1550 nm can be achieved without any external voltage. The device's multifunctionality and stability in ambient environments established a promising prototype for integrating polarization as an additional physical dimension in fiber optical networks, encompassing diverse applications in light generation, modulation, and detection.

Interfacial epitaxy of multilayer rhombohedral transition-metal dichalcogenide single crystals

Rhombohedral-stacked transition-metal dichalcogenides (3R-TMDs), which are distinct from their hexagonal counterparts, exhibit higher carrier mobility, sliding ferroelectricity, and coherently enhanced nonlinear optical responses. However, surface epitaxial growth of large multilayer 3R-TMD single crystals is difficult. We report an interfacial epitaxy methodology for their growth of several compositions, including molybdenum disulfide (MoS2), molybdenum diselenide, tungsten disulfide, tungsten diselenide, niobium disulfide, niobium diselenide, and molybdenum sulfoselenide. Feeding of metals and chalcogens continuously to the interface between a single-crystal Ni substrate and grown layers ensured consistent 3R stacking sequence and controlled thickness from a few to 15,000 layers. Comprehensive characterizations confirmed the large-scale uniformity, high crystallinity, and phase purity of these films. The as-grown 3R-MoS2 exhibited room-temperature mobilities up to 155 and 190 square centimeters per volt second for bi- and trilayers, respectively. Optical difference frequency generation with thick 3R-MoS2 showed markedly enhanced nonlinear response under a quasi-phase matching condition (five orders of magnitude greater than monolayers).

Strain distribution in WS2 monolayers detected through polarization-resolved second harmonic generation

Two-dimensional (2D) graphene and graphene-related materials (GRMs) show great promise for future electronic devices. GRMs exhibit distinct properties under the influence of the substrate that serves as support through uneven compression/ elongation of GRMs surface atoms. Strain in GRM monolayers is the most common feature that alters the interatomic distances and band structure, providing a new degree of freedom that allows regulation of their electronic properties and introducing the field of straintronics. Having an all-optical and minimally invasive detection tool that rapidly probes strain in large areas of GRM monolayers, would be of great importance in the research and development of novel 2D devices. Here, we use Polarization-resolved Second Harmonic Generation (P-SHG) optical imaging to identify strain distribution, induced in a single layer of WS2 placed on a pre-patterned Si/SiO2 substrate with cylindrical wells. By fitting the P-SHG data pixel-by-pixel, we produce spatially resolved images of the crystal armchair direction. In regions where the WS2 monolayer conforms to the pattern topography, a distinct cross-shaped pattern is evident in the armchair image owing to strain. The presence of strain in these regions is independently confirmed using a combination of atomic force microscopy and Raman mapping.

Out-of-plane Emission Dipole of Second Harmonic Generation in Odd- and Even-layered vdWs Janus Nb3SeI7

Integration of atomically thin nonlinear optical (NLO) devices demands an out-of-plane (OP) emission dipole of second harmonic generation (SHG) to enhance the spontaneous emission for nanophotonics. However, the research on van der Waals (vdWs) materials with an OP emission dipole of SHG is still in its infancy. Here, by coupling back focal plane (BFP) imaging with numerical simulations and density functional theory (DFT) calculations, we demonstrate that vdWs Janus Nb3SeI7, ranging from bulk to the monolayer limit, exhibits a dominant OP emission dipole of SHG owing to the breaking of the OP symmetry. Explicitly, even-layered Nb3SeI7 with C6v symmetry is predicted to exhibit a pure OP emission dipole attributed to the only second-order susceptibility coefficient χzxx. Meanwhile, although odd-layered Nb3SeI7 with C3v symmetry has both OP and IP dipole components (χzxx and χyyy), the value of χzxx is 1 order of magnitude greater than that of χyyy, leading to an approximate OP emission dipole of SHG. Moreover, the crystal symmetry and OP emission dipole can be preserved under hydrostatic pressure, accompanied by the enhanced χzxx and the resulting 3-fold increase in SHG intensity. The reported stable OP dipole in 2D vdWs Nb3SeI7 can facilitate the rapid development of chip-integrated NLO devices.

ITO-Induced Nonlinear Optical Response Enhancement of Titanium Nitride Thin Films

A series of TiN/ITO composite films with various thickness of ITO buffer layer were fabricated in this study. The enhancement of optical properties was realized in the composite thin films. The absorption spectra showed that absorption intensity in the near-infrared region was obviously enhanced with the increase of ITO thickness due to the coupling of surface plasma between TiN and ITO. The epsilon-near-zero wavelength of this composite can be tuned from 935 nm to 1895 nm by varying the thickness of ITO thin films. The nonlinear optical property investigated by Z-scan technique showed that the nonlinear absorption coefficient (β = 3.03 × 10-4 cm/W) for the composite was about 14.02 times greater than that of single-layer TiN films. The theoretical calculations performed by finite difference time domain were in good agreement with those of the experiments.

Nonlinear Optical Effects of Hybrid Antimony(III) Halides Induced by Stereoactive 5s2 Lone Pairs and Trimethylammonium Cations

Organic-inorganic hybrid metal halides have unique optical and electronic properties, which are advantageous in the study of nonlinear optical materials. To investigate the effect of stereoactive lone pair electrons and the induction of organic cations on the structure of hybrid antimony(III) halides on nonlinear optics, we synthesize two noncentrosymmetric hybrid antimony(III)-based halide single crystals (TMA)3Sb2X9 (TMA = NH(CH3)3+, X = Cl, Br) by a room-temperature slow evaporation method, and their single-crystal structures, phase transition, X-ray photoelectron spectroscopy, and energy-band structure calculations are studied. More importantly, second-harmonic generation results of (TMA)3Sb2X9 (X = Cl, Br) are about 0.7 and 0.8 × KH2PO4(KDP), respectively. Interestingly, (TMA)3Sb2Cl9 single crystals undergo a reversible structural transition from Pc (No. 7) at room temperature to P21/c (No. 14) at 400 K, while the (TMA)3Sb2Br9 single crystals belong to the noncentrosymmetric space group R3c (No. 161), which clarifies the previous results. This work not only deepens the understanding of the role in lone pair electrons and organic cations in the structural induction in antimony-based halide perovskite materials but also provides guidance for subsequent nonlinear optical explorations.

Extraordinary Enhancement of Nonlinear Optical Interaction in NbOBr2 Microcavities

2D materials are burgeoning as promising candidates for investigating nonlinear optical effects due to high nonlinear susceptibilities, broadband optical response, and tunable nonlinearity. However, most 2D materials suffer from poor nonlinear conversion efficiencies, resulting from reduced light-matter interactions and lack of phase matching at atomic thicknesses. Herein, a new 2D nonlinear material, niobium oxide dibromide (NbOBr2) is reported, featuring strong and anisotropic optical nonlinearities with scalable nonlinear intensity. Furthermore, Fabry-Pérot (F-P) microcavities are constructed by coupling NbOBr2 with air holes in silicon. Remarkable enhancement factors of ≈630 times in second harmonic generation (SHG) and 210 times in third harmonic generation (THG) are achieved on cavity at the resonance wavelength of 1500 nm. Notably, the cavity enhancement effect exhibits strong anisotropic feature tunable with pump wavelength, owing to the robust optical birefringence of NbOBr2. The ratio of the enhancement factor along the b- and c-axis of NbOBr2 reaches 2.43 and 5.27 for SHG and THG at 1500 nm pump, respectively, which leads to an extraordinarily high SHG anisotropic ratio of 17.82 and a 10° rotation of THG polarization. The research presents a feasible and practical strategy for developing high-efficiency and low-power-pumped on-chip nonlinear optical devices with tunable anisotropy.

Strong nonlinear optical processes with extraordinary polarization anisotropy in inversion-symmetry broken two-dimensional PdPSe

Nonlinear optical activities, especially second harmonic generation (SHG), are key phenomena in inversion-symmetry-broken two-dimensional (2D) transition metal dichalcogenides (TMDCs). On the other hand, anisotropic nonlinear optical processes are important for unique applications in nano-nonlinear photonic devices with polarization functions, having become one of focused research topics in the field of nonlinear photonics. However, the strong nonlinearity and strong optical anisotropy do not exist simultaneously in common 2D materials. Here, we demonstrate strong second-order and third-order susceptibilities of 64 pm/V and 6.2×10-19 m2/V2, respectively, in the even-layer PdPSe, which has not been discovered in other common TMDCs (e.g., MoS2). Strikingly, it also simultaneously exhibited strong SHG anisotropy with an anisotropic ratio of ~45, which is the largest reported among all 2D materials to date, to the best of our knowledge. In addition, the SHG anisotropy ratio can be harnessed from 0.12 to 45 (375 times) by varying the excitation wavelength due to the dispersion ofχ ( 2 ) values. As an illustrative example, we further demonstrate polarized SHG imaging for potential applications in crystal orientation identification and polarization-dependent spatial encoding. These findings in 2D PdPSe are promising for nonlinear nanophotonic and optoelectronic applications.

Observation of Anisotropic Second Harmonic Generation in Two-Dimensional Niobium Diselenide

The intrinsic anisotropy of NbSe2 provides a favorable prerequisite of second harmonic generation (SHG) and rich possibilities for tailoring its nonlinear optical (NLO) properties. Here we report the highly efficient SHG of mechanically exfoliated NbSe2 flakes. The nonlinear optical response changes with excitation wavelengths, layer thicknesses, and polarizations of the excitation laser. The anisotropic SHG response further exhibits the intrinsic non-centrosymmetric crystal structure and could effectively assign the crystalline orientation of NbSe2 flakes. Interestingly, although NbSe2 flakes with tens of nanometers thickness experience attenuations in SHG performance, more efficient SHG anisotropy ratios were obtained, which are around 4 times higher than that of the 5-layer counterpart. The determined second-order nonlinearities of NbSe2 flakes (monolayer: ∼1.0 × 103 pm/V; 3-layer: ∼73 pm/V) are comparable to those of the commonly reported two-dimensional materials (e.g., MoS2, WSe2, graphene) with the same number of layers and much higher than those of commercial nonlinear optical crystals.

Tunable-bias based optical neural network for reinforcement learning in path planning

Owing to the high integration, reconfiguration and strong robustness, Mach-Zehnder interferometers (MZIs) based optical neural networks (ONNs) have been widely considered. However, there are few works adding bias, which is important for neural networks, into the ONNs and systematically studying its effect. In this article, we propose a tunable-bias based optical neural network (TBONN) with one unitary matrix layer, which can improve the utilization rate of the MZIs, increase the trainable weights of the network and has more powerful representational capacity than traditional ONNs. By systematically studying its underlying mechanism and characteristics, we demonstrate that TBONN can achieve higher performance by adding more optical biases to the same side beside the inputted signals. For the two-dimensional dataset, the average prediction accuracy of TBONN with 2 biases (97.1%) is 5% higher than that of TBONN with 0 biases (92.1%). Additionally, utilizing TBONN, we propose a novel optical deep Q network (ODQN) algorithm to complete path planning tasks. By implementing simulated experiments, our ODQN shows competitive performance compared with the conventional deep Q network, but accelerates the computation speed by 2.5 times and 4.5 times for 2D and 3D grid worlds, respectively. Further, a more noticeable acceleration will be obtained when applying TBONN to more complex tasks. Also, we demonstrate the strong robustness of TBONN and the imprecision elimination method by using on-chip training.

Engineering Symmetry Breaking in Twisted MoS2-MoSe2 Heterostructures for Optimal Thermoelectric Performance

Engineering symmetry breaking in thermoelectric materials holds promise for achieving an optimal thermoelectric efficiency. van der Waals (vdW) layered transition metal dichalcogenides (TMDCs) provide critical opportunities for manipulating the intrinsic symmetry through in-plane symmetry breaking interlayer twists and out-of-plane symmetry breaking heterostructures. Herein, the symmetry-dependent thermoelectric properties of MoS2 and MoSe2 obtained via first-principles calculations are reported, yielding an advanced ZT of 2.96 at 700 K. The underlying mechanisms reveal that the in-plane symmetry breaking results in a lowest thermal conductivity of 1.96 W·m-1·K-1. Additionally, the electric properties can be significantly modulated through band flattening and bandgap alteration, stemming directly from the modified interlayer electronic coupling strength owing to spatial repulsion effects. In addition, out-of-plane symmetry breaking induces band splitting, leading to a decrease in the degeneracy and complex band structures. Consequently, the power factor experiences a notable enhancement from ∼1.32 to 1.71 × 10-2 W·m-1·K-2, which is attributed to the intricate spatial configuration of charge densities and the resulting intensified intralayer electronic coupling. Upon simultaneous implementation of in-plane and out-of-plane symmetry breaking, the TMDCs exhibit an indirect bandgap to direct bandgap transition compared to the pristine structure. This work demonstrates an avenue for optimizing thermoelectric performance of TMDCs through the implementation of symmetry breaking.

Can 2D Semiconductors Be Game-Changers for Nanoelectronics and Photonics?

2D semiconductors have interesting physical and chemical attributes that have led them to become one of the most intensely investigated semiconductor families in recent history. They may play a crucial role in the next technological revolution in electronics as well as optoelectronics or photonics. In this Perspective, we explore the fundamental principles and significant advancements in electronic and photonic devices comprising 2D semiconductors. We focus on strategies aimed at enhancing the performance of conventional devices and exploiting important properties of 2D semiconductors that allow fundamentally interesting device functionalities for future applications. Approaches for the realization of emerging logic transistors and memory devices as well as photovoltaics, photodetectors, electro-optical modulators, and nonlinear optics based on 2D semiconductors are discussed. We also provide a forward-looking perspective on critical remaining challenges and opportunities for basic science and technology level applications of 2D semiconductors.

Optical Second Harmonic Generation of Low-Dimensional Semiconductor Materials

In recent years, the phenomenon of optical second harmonic generation (SHG) has attracted significant attention as a pivotal nonlinear optical effect in research. Notably, in low-dimensional materials (LDMs), SHG detection has become an instrumental tool for elucidating nonlinear optical properties due to their pronounced second-order susceptibility and distinct electronic structure. This review offers an exhaustive overview of the generation process and experimental configurations for SHG in such materials. It underscores the latest advancements in harnessing SHG as a sensitive probe for investigating the nonlinear optical attributes of these materials, with a particular focus on its pivotal role in unveiling electronic structures, bandgap characteristics, and crystal symmetry. By analyzing SHG signals, researchers can glean invaluable insights into the microscopic properties of these materials. Furthermore, this paper delves into the applications of optical SHG in imaging and time-resolved experiments. Finally, future directions and challenges toward the improvement in the NLO in LDMs are discussed to provide an outlook in this rapidly developing field, offering crucial perspectives for the design and optimization of pertinent devices.

Time-Dependent Ultrafast Quadratic Nonlinearity in an Epsilon-Near-Zero Platform

Ultrafast nonlinearity, which results in modulation of the linear optical response, is a basis for the development of time-varying media, in particular those operating in the epsilon-near-zero (ENZ) regime. Here, we demonstrate that the intraband excitation of hot electrons in the ENZ film results in a second-harmonic resonance shift of ∼10 THz (40 nm) and second-harmonic generation (SHG) intensity changes of >100% with only minor (<1%) changes in linear transmission. The modulation is 10-fold enhanced by a plasmonic metasurface coupled to a film, allowing for ultrafast modulation of circularly polarized SHG. The effect is described by the plasma frequency renormalization in the ENZ material and the modification of the electron damping, with a possible influence of the hot-electron dynamics on the quadratic susceptibility. The results elucidate the nature of the second-order nonlinearity in ENZ materials and pave the way to the rational engineering of active nonlinear metamaterials and metasurfaces for time-varying applications.

Two-Dimensional Molybdenum Boride (MBene) Mo4/3B2Tx with Broadband and Termination-Dependent Ultrafast Nonlinear Optical Response

Two-dimensional molybdenum borides (MBenes) comprise a new class of 2D transition metal borides that exhibit potential photonics applications. Recently, the synthesis of individual single-layer Mo4/3B2Tx (T = O, F, OH) MBene sheets has been realized, which attracted considerable attention in optoelectronics. However, there is still a lack of understanding and regulation of the photophysical processes of Mo4/3B2Tx MBene. Here, we demonstrate that Mo4/3B2Tx MBene exhibits a surface termination-dependent electronic structure, carrier dynamics, and nonlinear optical response over a wide wavelength range (500-1550 nm). As prepared 2D Mo4/3B2F2 MBene possesses a semimetal material property that exhibits a shorter intraband scattering process (<100 ps) and a considerable nonlinear optical response at a broadband cover optical communication C band at 1550 nm. These thrilling results are confirmed theoretically and experimentally. The analysis of these results adds to the regulating and understanding of the basic photophysical processes, which is anticipated to be beneficial for the further design of MBene-based photonics and nanoelectronics devices.

Determining by Raman spectroscopy the average thickness and N-layer-specific surface coverages of MoS2 thin films with domains much smaller than the laser spot size

Raman spectroscopy is a widely used technique to characterize nanomaterials because of its convenience, non-destructiveness, and sensitivity to materials change. The primary purpose of this work is to determine via Raman spectroscopy the average thickness of MoS2 thin films synthesized by direct liquid injection pulsed-pressure chemical vapor deposition (DLI-PP-CVD). Such samples are constituted of nanoflakes (with a lateral size of typically 50 nm, i.e., well below the laser spot size), with possibly a distribution of thicknesses and twist angles between stacked layers. As an essential preliminary, we first reassess the applicability of different Raman criteria to determine the thicknesses (or layer number, N) of MoS2 flakes from measurements performed on reference samples, namely well-characterized mechanically exfoliated or standard chemical vapor deposition MoS2 large flakes deposited on 90 ± 6 nm SiO2 on Si substrates. Then, we discuss the applicability of the same criteria for significantly different DLI-PP-CVD MoS2 samples with average thicknesses ranging from sub-monolayer up to three layers. Finally, an original procedure based on the measurement of the intensity of the layer breathing modes is proposed to evaluate the surface coverage for each N (i.e., the ratio between the surface covered by exactly N layers and the total surface) in DLI-PP-CVD MoS2 samples.

Charge transfer excitons and directional fluorescence of in-plane lateral MoSe2-WSe2 heterostructures

In this article, the linear and nonlinear optical properties of in-plane lateral MoSe2-WSe2 heterostructures are theoretically investigated. The polarization-dependent strongest optical absorption in one-photon absorption occurs in charge transfer excited states, where electrons transfer from WSe2 to MoSe2. This phenomenon is supported by the LUMO (lowest unoccupied molecular orbital) and HUMO (highest occupied molecular orbital) imaging obtained through scanning tunneling microscopy. The charge difference density and transition density matrix are used to interpret the electronic transitions, and these interpretations rely on the concept of transition density. The optical properties of two-photon absorption in its nonlinear optical process are significantly different from the excitation in one-photon absorption, where the strongest optical absorption is contributed from direct transition from the ground state to the final state without going through an intermediate excited state, due to the very large difference of permanent dipole moments between the excited and ground states. Our results also reveal directional fluorescence and physical mechanism of in-plane lateral MoSe2-WSe2 heterostructures. Our work can provide insights into the physical mechanism of the optical properties of in-plane lateral MoSe2-WSe2 heterostructures.

pH-Tuned Enantioselectivity Reversal in a Defective Chiral Metal Organic Framework

The introduction of chirality into easy-scalable metal-organic frameworks (MOFs) gives rise to the development of advanced electrochemical sensors. However, integrating chirality by directly connecting metal ions and chiral ligands is unpredictable. Postmodification synthesis is a common method for synthesizing chiral MOFs, but it reduces the size of chiral channels and poses obstacles to the approach of chiral guest molecules. In this work, missing connection defects were introduced into the chiral MOFs through defect engineering strategies, which enhance the recognition of the target enantiomers. pH can tune enantioselectivity reversal in defective chiral MOFs. The chiral MOFs show enantioselectivity for d-Trp at pH = 5 and l-Trp at pH = 8. From the results of zeta potential, regardless of pH 5 or 8, the chiral MOF has a positive potential. The chiral MOFs are positively charged, while tryptophan is negatively charged when pH = 8. The difference in the positive and negative charge interactions between the two amino acids and chiral MOFs leads to chiral recognition. However, the difference in π-π interaction between chiral MOF and Trp enantiomers mainly drives chiral recognition under pH = 5. This study paves a pathway for the synthesis of defective chiral MOFs and highlights the pH-tuned enantioselectivity reversal.