Large nonlinear optical magnetoelectric response in a noncentrosymmetric magnetic Weyl semimetal.

Weyl semimetals resulting from either inversion (P) or time-reversal (T) symmetry breaking have been revealed to show the record-breaking large optical response due to intense Berry curvature of Weyl-node pairs. Different classes of Weyl semimetals with both P and T symmetry breaking potentially exhibit optical magnetoelectric (ME) responses, which are essentially distinct from the previously observed optical responses in conventional Weyl semimetals, leading to the versatile functions such as directional dependence for light propagation and gyrotropic effects. However, such optical ME phenomena of (semi)metallic systems have remained elusive so far. Here, we show the large nonlinear optical ME response in noncentrosymmetric magnetic Weyl semimetal PrAlGe, in which the polar structural asymmetry and ferromagnetic ordering break P and T symmetry. We observe the giant second harmonic generation (SHG) arising from the P symmetry breaking in the paramagnetic phase, being comparable to the largest SHG response reported in Weyl semimetal TaAs. In the ferromagnetically ordered phase, it is found that interference between this nonmagnetic SHG and the magnetically induced SHG emerging due to both P and T symmetry breaking results in the magnetic field switching of SHG intensity. Furthermore, such an interference effect critically depends on the light-propagating direction. The corresponding magnetically induced nonlinear susceptibility is significantly larger than the prototypical ME material, manifesting the existence of the strong nonlinear dynamical ME coupling. The present findings establish the unique optical functionality of P- and T-symmetry broken ME topological semimetals.

Manipulating ultrafast even-order nonlinear chiral responses of L-tryptophan by polarization pulse shaping.

Molecular chirality has long been monitored in the frequency domain in the ultraviolet, visible, and infrared regimes. Recently developed time-domain approaches can detect time-dependent chiral dynamics by enhancing intrinsically weak chiral signals. Even-order nonlinear signals in chiral molecules have gained attention thanks to their existence in the electric dipole approximation, without relying on the weaker higher-order multipole interactions. We illustrate the optimization of temporal polarization pulse-shaping in various frequency ranges (infrared/optical and optical/X ray) to enhance chiral nonlinear signals. These signals can be recast as an overlap integral of matter and field pseudoscalars which contain the relevant chiral information. Simulations are carried out for second- and fourth-order nonlinear spectroscopies in L-tryptophan.

Fluid fibers in true 3D ferroelectric liquids.

We demonstrate an exceptional ability of a high-polarization 3D ferroelectric liquid to form freely suspended fluid fibers at room temperature. Unlike fluid threads in modulated smectics and columnar phases, where translational order is a prerequisite for forming liquid fibers, recently discovered ferroelectric nematic forms fibers with solely orientational molecular order. Additional stabilization mechanisms based on the polar nature of the mesophase are required for this. We propose a model for such a mechanism and show that these fibers demonstrate an exceptional nonlinear optical response and exhibit electric field-driven instabilities.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum.

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n >  10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy.

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

A perfect X-ray beam splitter and its applications to time-domain interferometry and quantum optics exploiting free-electron lasers.

X-ray free-electron lasers (FELs) deliver ultrabright X-ray pulses, but not the sequences of phase-coherent pulses required for time-domain interferometry and control of quantum states. For conventional split-and-delay schemes to produce such sequences, the challenge stems from extreme stability requirements when splitting Ångstrom wavelength beams, where the tiniest path-length differences introduce phase jitter. We describe an FEL mode based on selective electron-bunch degradation and transverse beam shaping in the accelerator, combined with a self-seeded photon emission scheme. Instead of splitting the photon pulses after their generation by the FEL, we split the electron bunch in the accelerator, prior to photon generation, to obtain phase-locked X-ray pulses with subfemtosecond duration. Time-domain interferometry becomes possible, enabling the concomitant program of classical and quantum optics experiments with X-rays. The scheme leads to scientific benefits of cutting-edge FELs with attosecond and/or high-repetition rate capabilities, ranging from the X-ray analog of Fourier transform infrared spectroscopy to damage-free measurements.

Enhanced Green Light Emission from a Silicon-Based Metal-Encapsulated Nanoplasmonic Waveguide.

Integrated silicon plasmonic circuitry is becoming integral for communications and data processing. One key challenge in implementing such optical networks is the realization of optical sources on silicon platforms, due to silicon's indirect bandgap. Here, we present a silicon-based metal-encapsulated nanoplasmonic waveguide geometry that can mitigate this issue and efficiently generate light via third-harmonic generation (THG). Our waveguides are ideal for such applications, having strong power confinement and field enhancement, and an effective use of the nonlinear core area. This unique device was fabricated, and experimental results show efficient THG conversion efficiencies of η = 4.9 × 10-4, within a core footprint of only 0.24 µm2. Notably, this is the highest absolute silicon-based THG conversion efficiency presented to date. Furthermore, the nonlinear emission is not constrained by phase matching. These waveguides are envisioned to have crucial applications in signal generation within integrated nanoplasmonic circuits.

Electro-Induced Phase Transformation of a Conductive Metal-Organic Framework Film for Nonlinear Optical Switching.

Achieving metal-organic frameworks (MOFs) with nonlinear optical (NLO) switching is profoundly important. Herein, the conductive MOFs Cu-TCNQ phase I (Ph-I) and phase II (Ph-II) films were prepared using the liquid-phase-epitaxial layer-by-layer spin-coating method and steam heating method, respectively. Electronic experiments showed that the Ph-II film could be changed into the Ph-I film under an applied electric field. The third-order NLO results revealed that the Ph-I film had a third-order nonlinear reverse saturation absorption (RSA) response and the Ph-II film displayed a third-order nonlinear saturation absorption (SA) response. With increases in the heating time and applied voltage, the third-order NLO response realized the reversible transition between SA and RSA. The theoretical calculations indicated that Ph-I possessed more interlayer charge transfer, resulting in a third-order nonlinear RSA response that was stronger than that of Ph-II. This work applies phase-transformed MOFs to third-order NLO switching and provides new insights into the nonlinear photoelectric applications of MOFs.

Third Harmonic Generation Enhancement and Wavefront Control Using a Local High-Q Metasurface.

High quality factor optical nanostructures provide a great opportunity to enhance nonlinear optical processes such as third harmonic generation. However, the field enhancement in these high quality factor structures is typically accompanied by optical mode nonlocality. As a result, the enhancement of nonlinear processes comes at the cost of their local control as needed for nonlinear wavefront shaping, imaging, and holography. Here we show simultaneous strong enhancement and spatial control over third harmonic generation with a local high-Q metasurface relying on higher-order Mie resonant modes. Our results demonstrate third harmonic generation at an efficiency of up to 3.25 × 10-5, high quality wavefront shaping as illustrated by a third harmonic metalens, and a flatband, angle independent, third harmonic response up to ±11° incident angle. The demonstrated high level of local control and efficient frequency conversion offer promising prospects for realizing novel nonlinear optical devices.

Robust Edge States of Quasi-1D Material Ta2NiSe7 and Applications in Saturable Absorbers.

The helical edge states (ESs) protected by underlying Z2 topology in two-dimensional topological insulators (TIs) arouse upsurges in saturable absorptions thanks to the strong photon-electron coupling in ESs. However, limited TIs demonstrate clear signatures of topological ESs at liquid nitrogen temperatures, hindering the applications of such exotic quantum states. Here, we demonstrate the existence of one-dimensional (1D) ESs at the step edge of the quasi-1D material Ta2NiSe7 at 78 K by scanning tunneling microscopy. Such ESs are rather robust against the irregularity of the edges, suggesting a possible topological origin. The exfoliated Ta2NiSe7 flakes were used as saturable absorbers (SAs) in an Er-doped fiber laser, hosting a mode-locked pulse with a modulation depth of up to 52.6% and a short pulse duration of 225 fs, far outstripping existing TI-based SAs. This work demonstrates the existence of robust 1D ESs and the superior SA performance of Ta2NiSe7.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation.

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

van der Waals Decoration of Ultra-High-Q Silica Microcavities for χ(2)-χ(3) Hybrid Nonlinear Photonics.

Optical nonlinear processes are indispensable in a wide range of applications, including ultrafast lasers, microscopy, and quantum information technologies. Among the diverse nonlinear processes, second-order effects usually overwhelm the higher-order ones, except in centrosymmetric systems, where the second-order susceptibility vanishes to allow the use of the third-order nonlinearity. Here we demonstrate a hybrid photonic platform whereby the balance between second- and third-order susceptibilities can be tuned flexibly. By decorating ultra-high-Q silica microcavities with atomically thin tungsten diselenide, we observe cavity-enhanced second-harmonic generation and sum-frequency generation with continuous-wave excitation at a power level of only a few hundred microwatts. We show that the coexistence of second- and third-order nonlinearities in a single device can be achieved by carefully choosing the size and location of the two-dimensional material. Our approach can be generalized to other types of cavities, unlocking the potential of hybrid systems with controlled nonlinear susceptibilities for novel applications.

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule.

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

Unraveling the structure-property relationship of novel thiophene and furan-fused cyclopentadienyl chromophores for nonlinear optical applications.

Development of organic nonlinear optical materials has become progressively more important due to their emerging applications in new-generation photonic devices. A novel series of chromophores based on innovative thiophene and furan-fused cyclopentadienyl bridge with various powerful donor and acceptor moieties were designed and theoretically investigated for applications in nonlinear optics. To unravel the structure-property relationship between this new push-pull conjugated systems and their nonlinear optical property, multiple methods, including density of states analysis, coupled perturbed Kohn-Sham (CPKS) method, sum-over-states (SOS) model, the two-level model (TSM), hyperpolarizability density analysis, and the (hyper)polarizability contribution decomposition, were performed to comprehensively investigated the nonlinear optical and electronic properties of this new π-system. Due to excellent charge transfer ability of new bridge and distinctive structure of donor and acceptor, the designed chromophores exhibit deep HOMO levels, low excitation energy, high dipole moment difference and large hyperpolarizability, indicating the appealing air-stable property and remarkable electrooptic performance of them. Importantly, THQ-CS-A3 and PA-CS-A3 shows outstanding NLO response properties with ßtot value of 6953.9 × 10-30 and 5066.0 × 10-30 esu in AN, respectively. The influence of the push-pull strength, the heterocycle and the π-conjugation of new bridge on the nonlinear optical properties of this novel powerful systems are clarified. This new series of chromophores exhibit remarkable electro-optical Pockels and optical rectification effect. More interestingly, PA-CS-A3 and THQ-CS-A2 also show appealing SHG effect. This study will help people understand the nature of nonlinear optical properties of innovative heteroarene-fused based cyclopentadienyl chromophores and offer guidance for the rational design of chromophores with outstanding electrooptic (EO) performance in the future.

A Non-π-Conjugated Molecular Crystal with Balanced Second-Harmonic Generation, Bandgap, and Birefringence.

Traditional nonlinear optical (NLO) crystals are exclusively limited to ionic crystals with π-conjugated groups and it is a great challenge to achieve a subtle balance between second-harmonic generation, bandgap, and birefringence for them, especially in the deep-UV spectrum region (Eg  > 6.20 eV). Herein, a non-π-conjugated molecular crystal, NH3 BH3 , which realizes such balance with a large second-harmonic generation response (2.0 × KH2 PO4 at 1064 nm, and 0.45 × ß-BaB2 O4 at 532 nm), deep-UV transparency (Eg > 6.53 eV), and moderate birefringence (Δn = 0.056@550 nm) is reported. As a result, NH3 BH3 exhibits a large quality factor of 0.32, which is evidently larger than those of non-π-conjugated sulfate and phosphate ionic crystals. Using an unpolished NH3 BH3 crystal, effective second-harmonic generation outputs are observed at different wavelengths. These attributes indicate that NH3 BH3 is a promising candidate for deep-UV NLO applications. This work opens up a new door for developing high-performance deep-UV NLO crystals.

Nonlinear Optical Properties of 2D Materials and their Applications.

2D materials are a subject of intense research in recent years owing to their exclusive photoelectric properties. With giant nonlinear susceptibility and perfect phase matching, 2D materials have marvelous nonlinear light-matter interactions. The nonlinear optical properties of 2D materials are of great significance to the design and analysis of applied materials and functional devices. Here, the fundamental of nonlinear optics (NLO) for 2D materials is introduced, and the methods for characterizing and measuring second-order and third-order nonlinear susceptibility of 2D materials are reviewed. Furthermore, the theoretical and experimental values of second-order susceptibility χ(2) and third-order susceptibility χ(3) are tabulated. Several applications and possible future research directions of second-harmonic generation (SHG) and third-harmonic generation (THG) for 2D materials are presented.

Birefringent Dispersion Optimization to Achieve Superior Nonlinear Optical Phase Matching in Deeper Solar-Blind UV Band from KH2PO4 to BeH3PO5.

Nonlinear-optical (NLO) crystals require birefringent phase matching (BPM), particularly in the solar-blind ultraviolet (UV) (200-280 nm) and deep-UV (100-200 nm) regions. Achieving BPM requires optimization of optical dispersion along with having large birefringence. This requirement is especially critical for structures with low optical anisotropy, including classical phosphate UV-NLO crystals like KH2PO4 (KDP). However, there is a scarcity of in-depth theoretical analysis and general design strategies based on structural chemistry to optimize dispersion. This study presents findings from a simplified dielectric model that uncover two vital factors to micro-optimize transparent optical dispersion: effective mass (m*) of excited states and effective number (N*) of photo-responsive states. Smoothing of dispersion occurs as m* increases and N* decreases. First-principles analysis of deep-UV KBe2BO3F2-family structures is used to confirm the conciseness and validity of the model. It further proposes substituting K+ with Be2+ to decrease N* and increase m* while enlarging bandgap. This will lead to improved dispersion and an overall enhancement of KDP's BPM capability. The existing BeH3PO5 (BDP) is predicted to improve the shortest BPM wavelength for second-harmonic generation, from 251 nm in KDP to 201 nm in BDP. BDP's extension into the broader UV solar-blind waveband fully supports the proposed optimization strategy.

Tailoring Broadband Nonlinear Optical Characteristics and Ultrafast Photocarrier Dynamics of Bi2O2S Nanosheets by Defect Engineering.

Low-dimensional bismuth oxychalcogenides have shown promising potential in optoelectronics due to their high stability, photoresponse, and carrier mobility. However, the relevant studies on deep understanding for Bi2O2S is quite limited. Here, comprehensive experimental and computational investigations are conducted in the regulated band structure, nonlinear optical (NLO) characteristics, and carrier dynamics of Bi2O2S nanosheets via defect engineering, taking O vacancy (OV) and substitutional Se doping as examples. As the OV continuously increased to ≈35%, the optical bandgaps progressively narrow from ≈1.21 to ≈0.81 eV and NLO wavelengths are extended to near-infrared regions with enhanced saturable absorption. Simultaneously, the relaxation processes are effectively accelerated from tens of picoseconds to several picoseconds, as the generated defect energy levels can serve as both additional absorption cross-sections and fast relaxation channels supported by theoretical calculations. Furthermore, substitutional Se doping in Bi2O2S nanosheets also modulate their optical properties with the similar trends. As a proof-of-concept, passively mode-locked pulsed lasers in the ≈1.0 µm based on the defect-rich samples (≈35% OV and ≈50% Se-doping) exhibit excellent performance. This work deepens the insight of defect functions on optical properties of Bi2O2S nanosheets and provides new avenues for designing advanced photonic devices based on low-dimensional bismuth oxychalcogenides.

Transformation of SBUs and Synergy of MOF Host-Guest in Single Crystalline State: Ingenious Strategies for Modulating Third-Order NLO Signals.

Central metal exchange can innovatively open the cavity of metal-organic frameworks (MOFs) by alternating the framework topology. Here, the single-crystal-to-single-crystal (SC-SC) transformation is reported from a Co-based MOF {[Co1.25 (HL)0.5 (Pz-NH2 )0.25 (µ3 -O)0.25 (µ2 -OH)0.25 (H2 O)]·0.125 Co·0.125 L·10.25H2 O}n (Co-MOF, L = 5,5'-(1H-2,3,5-triazole-1,4-diyl)diisophthalic acid) into two novel MOF materials, {[Cu1.75 L0.75 (Pz-NH2 )0.125 (µ3 -O)0.125 (µ2 -OH)0.25 (H2 O)0.375 ]•3CH3 CN}n (Cu-MOF) and {[Zn1.75 L0.625 (Pz-NH2 )0.25 (µ3 -O)0.25 (µ2 -O)0.25 (H2 O)1.25 ]•4CH3 CN}n (Zn-MOF), through exchanging the Co2+ in the MOF into Cu2+ or Zn2+ , respectively. The free Co2+ and L4- in the Co-MOF channels fuse with the skeleton during the Co→Cu and Co→Zn exchange processes, leading to the expansion of the channel space and the transformation of the secondary building units (SBUs) to form an adjustable skeleton. The nonlinear optical response results show that the MOFs generated by the exchange of the central metal exhibit different saturable absorption and the self-focusing effect. In addition, loading polypyrrole (PPy) into the MOFs can not only improve the stability of the MOFs but also further optimize the nonlinear optical behavior. This work suggests that SC-SC central metal exchange and the introduction of polymer molecules can tune the nonlinear optical response, which provides a new perspective for the future study of nonlinear optical materials.

Nonlinear Nano-Imaging of Interlayer Coupling in 2D Graphene-Semiconductor Heterostructures.

The emergent electronic, spin, and other quantum properties of 2D heterostructures of graphene and transition metal dichalcogenides are controlled by the underlying interlayer coupling and associated charge and energy transfer dynamics. However, these processes are sensitive to interlayer distance and crystallographic orientation, which are in turn affected by defects, grain boundaries, or other nanoscale heterogeneities. This obfuscates the distinction between interlayer charge and energy transfer. Here, nanoscale imaging in coherent four-wave mixing (FWM) and incoherent two-photon photoluminescence (2PPL) is combined with a tip distance-dependent coupled rate equation model to resolve the underlying intra- and inter-layer dynamics while avoiding the influence of structural heterogeneities in mono- to multi-layer graphene/WSe2 heterostructures. With selective insertion of hBN spacer layers, it is shown that energy, as opposed to charge transfer, dominates the interlayer-coupled optical response. From the distinct nano-FWM and -2PPL tip-sample distance-dependent modification of interlayer and intralayer relaxation by tip-induced enhancement and quenching, an interlayer energy transfer time of τ ET ≈ ( 0 . 35 - 0.15 + 0.65 ) $\tau _{\rm ET} \approx (0.35^{+0.65}_{-0.15})$  ps consistent with recent reports is derived. As a local probe technique, this approach highlights the ability to determine intrinsic sample properties even in the presence of large sample heterogeneity.