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.

Graphene Terahertz Devices for Sensing and Communication

Graphene-based terahertz (THz) devices have emerged as promising platforms for a variety of applications, leveraging graphene's unique optoelectronic properties. This review explores recent advancements in utilizing graphene in THz technology, focusing on two main aspects: THz molecular sensing and THz wave modulation. In molecular sensing, the environment-sensitive THz transmission and emission properties of graphene are utilized for enabling molecular adsorption detection and biomolecular sensing. This capability holds significant potential, from the detection of pesticides to DNA at high sensitivity and selectivity. In THz wave modulation, crucial for next-generation wireless communication systems, graphene demonstrates remarkable potential in absorption modulation when gated. Novel device structures, spectroscopic systems, and metasurface architectures have enabled enhanced absorption and wave modulation. Furthermore, techniques such as spatial phase modulation and polarization manipulation have been explored. From sensing to communication, graphene-based THz devices present a wide array of opportunities for future research and development. Finally, advancements in sensing techniques not only enhance biomolecular analysis but also contribute to optimizing graphene's properties for communication by enabling efficient modulation of electromagnetic waves. Conversely, developments in communication strategies inform and enhance sensing capabilities, establishing a mutually beneficial relationship.

High-Order Harmonic Generation in Photoexcited Three-Dimensional Dirac Semimetals

High-order harmonic generation (HHG) in condensed matter is highly important for potential applications in various fields, such as materials characterization, all-optical switches, and coherent light source generation. Linking HHG to the properties or dynamic processes of materials is essential for realizing these applications. Here, a bridge has been built between HHG and the transient properties of materials through the engineering of interband polarization in a photoexcited three-dimensional Dirac semimetal (3D-DSM). It has been found that HHG can be efficiently manipulated by the electronic relaxation dynamics of 3D-DSM on an ultrafast time scale of several hundred femtoseconds. Furthermore, time-resolved HHG (tr-HHG) has been demonstrated to be a powerful spectroscopy method for tracking electron relaxation dynamics, enabling the identification of electron thermalization and electron-phonon coupling processes and the quantitative extraction of electron-phonon coupling strength. This demonstration provides insights into the active control of HHG and measurements of the electron dynamics.

Many-body enhancement of high-harmonic generation in monolayer MoS2

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green's function with the GW self energy. We calculate the HHG of monolayer MoS2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.

Manipulating Quantum Interference in Two-Color (ω+3ω) Strong Laser Field Photodissociation Dynamics of D2. J Phys Chem A 2024;128:5021-5027. [PMID: 38885171 DOI: 10.1021/acs.jpca.4c03176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In a strong field regime, exploring the molecular photodissociation process and revealing the underlying reaction mechanism remain challenging tasks due to the dramatic changes of molecular potentials caused by the applied fields. In this paper, we investigate the strong field photodissociation dynamics of D2+ in a synthesized VUV + IR (266 + 800 nm) two-color laser field by solving the three-dimensional time-dependent Schrödinger equation. We show that the Aharonov-Bohm-like quantum interference in the photofragment angular distribution can be controlled by varying the ellipticity of the VUV light. We demonstrate that the interference phenomenon originates from the geometric phase accumulation of the nuclear wave function when it undergoes cyclic evolution on light-induced potential energy surfaces. This work has implications for the control of chemical reactions of a small molecular system through the geometric phase.

Toward Complete All-Optical Intensity Modulation of High-Harmonic Generation from Solids

Optical modulation of high-harmonics generation in solids enables the detection of material properties, such as the band structure, and promising new applications, such as super-resolution imaging in semiconductors. Various recent studies have shown optical modulation of high-harmonics generation in solids, in particular, suppression of high-harmonics generation has been observed by synchronized or delayed multipulse sequences. Here we provide an overview of the underlying mechanisms attributed to this suppression and provide a perspective on the challenges and opportunities regarding these mechanisms. All-optical control of high-harmonic generation allows for femtosecond, and in the future possibly subfemtosecond, switching, which has numerous possible applications: These range from super-resolution microscopy to nanoscale controlled chemistry and highly tunable nonlinear light sources.

Ultrafast Electron-Electron Scattering in Metallic Phase of 2H-NbSe_{2} Probed by High Harmonic Generation

Electron-electron scattering on the order of a few to tens of femtoseconds plays a crucial role in the ultrafast electron dynamics of conventional metals. When mid-infrared light is used for driving and the period of light field is comparable to the scattering time in metals, unique light-driven states and nonlinear optical responses associated with the scattering process are expected to occur. Here, we use high-harmonics spectroscopy to investigate the effect of electron-electron scattering on the electron dynamics in thin film 2H-NbSe_{2} driven by a mid-infrared field. We observed odd-order high harmonics up to 9th order as well as a broadband emission from hot electrons in the energy range from 1.5 to 4.0 eV. The electron-electron scattering time in 2H-NbSe_{2} was estimated from the broadband emission to be almost the same as the period of the mid-infrared light field. A comparison between experimental results and a numerical calculation reveals that competition and cooperation between the driving and scattering enhances the nonperturbative behavior of high harmonics in metals, causing a highly nonequilibrium electronic state corresponding to several thousand Kelvin.

High-Order Harmonic Generation in Solids: The Role of Intraband Transitions in Extreme Nonlinear Optics

High-order harmonic generation (HHG) in gases is frequently used nowadays to produce attosecond pulses and coherent radiation in the visible-to-soft X-ray spectral range. HHG in solids is a natural extension of the idea of HHG in gases, and its first observation about ten years ago opened the door to investigations on attosecond electron dynamics in solids and the development of solid-state attosecond light sources. The common process in both types of HHG is nonlinear photocarrier generation, and thus, transitions between different bands (interband transitions) are always important for HHG. As well, in the case of solids, the transitions within a band (intraband transitions) also need to be considered, because efficient carrier acceleration is possible due to them. This Perspective focuses on experimental findings that show how intraband transitions can be controlled because such an understanding will be essential in the development of unique optoelectronics that can operate at petahertz frequencies.

Third harmonic generation due to free carrier in InSb using a terahertz free electron laser

We report on the third harmonic generation (THG) in InSb semiconductor irradiated by a terahertz (THz) free electron laser (FEL). The conversion of 4 THz (wavelength 70 µm) FEL outputs into its third harmonic 12 THz was observed. We found that by tuning the sample temperature to 360 K, high conversion efficiency up to 1% can be obtained and is the highest in the THz and FIR regions below 10 THz. We also discuss the observed intensity dependence of the THG with the nonlinear order lower than 3 when the pumping intensity was high.

A solid-state high harmonic generation spectrometer with cryogenic cooling

Solid-state high harmonic generation (sHHG) spectroscopy is a promising technique for studying electronic structure, symmetry, and dynamics in condensed matter systems. Here, we report on the implementation of an advanced sHHG spectrometer based on a vacuum chamber and closed-cycle helium cryostat. Using an in situ temperature probe, it is demonstrated that the sample interaction region retains cryogenic temperature during the application of high-intensity femtosecond laser pulses that generate high harmonics. The presented implementation opens the door for temperature-dependent sHHG measurements down to a few Kelvin, which makes sHHG spectroscopy a new tool for studying phases of matter that emerge at low temperatures, which is particularly interesting for highly correlated materials.

Dephasing Dynamics Accessed by High Harmonic Generation: Determination of Electron-Hole Decoherence of Dirac Fermions

We reveal the critical effect of ultrashort dephasing on the polarization of high harmonic generation in Dirac fermions. As the elliptically polarized laser pulse falls in or slightly beyond the multiphoton regime, the elliptically polarized high harmonic generation is produced and exhibits a characteristic polarimetry of the polarization ellipse, which is found to depend on the decoherence time T2. T2 could then be determined to be a few femtoseconds directly from the experimentally observed polarimetry of high harmonics. This shows a sharp contrast with the semimetal regime of higher pump intensity, where the polarimetry is irrelevant to T2. An access to the dephasing dynamics would extend the prospect of high harmonic generation into the metrology of a femtosecond dynamic process in the coherent quantum control.

Twist Phase Matching in Two-Dimensional Materials

Optical phase matching involves establishing a proper phase relationship between the fundamental excitation and generated waves to enable efficient optical parametric processes. It is typically achieved through birefringence or periodic polarization. Here, we report that the interlayer twist angle in two-dimensional (2D) materials creates a nonlinear geometric phase that can compensate for the phase mismatch, and the vertical assembly of the 2D layers with a proper twist sequence generates a nontrivial "twist-phase-matching" (twist-PM) regime. The twist-PM model provides superior flexibility in the design of optical crystals, which can be applied for twisted layers with either periodic or random thickness distributions. The designed crystal from the twisted rhombohedral boron nitride films within a thickness of only 3.2  μm is capable of producing a second-harmonic generation with conversion efficiency of ∼8% and facile polarization controllability that is absent in conventional crystals. Our methodology establishes a platform for the rational design and atomic manufacturing of nonlinear optical crystals based on abundant 2D materials.

Circular dichroism in Floquet Chern insulator via high-order harmonics spectroscopy

High-order harmonics (HOHs) spectroscopy is attracting the attention of the condensed matter community, mostly because the HOHs spectrum encode the material property. Topological materials are of interest for both basic research and advanced technologies because of their robust properties against dissipation and perturbations. Floquet engineering technique have been demonstrated to be a unique tool to manipulate topological phase. In this paper, we apply HOH spectroscopy to characterize the Floquet state via the circular dichroism (CD). We find that the CD of the co-rotating harmonics is sensitive to Floquet topological states.

Nonlinear Optical Properties from Engineered 2D Materials

Two-dimensional (2D) materials with atomic thickness, tunable light-matter interaction, and significant nonlinear susceptibility are emerging as potential candidates for new-generation optoelectronic devices. In this review, we briefly cover the recent research development of typical nonlinear optic (NLO) processes including second harmonic generation (SHG), third harmonic generation (THG), as well as two-photon photoluminescence (2PPL) of 2D materials. Nonlinear light-matter interaction in atomically thin 2D materials is important for both fundamental research and future optoelectronic devices. The NLO performance of 2D materials can be greatly modulated with methods such as carrier injection tuning, strain tuning, artificially stacking, as well as plasmonic resonant enhancement. This review will discuss various nonlinear optical processes and corresponding tuning methods and propose its potential NLO application of 2D materials.

Electrically Tunable Nonlinearity at 3.2 Terahertz in Single-Layer Graphene

Graphene is a nonlinear material in the terahertz (THz) frequency range, with χ(3) ∼ 10-9 m2/V2 ∼ 15 orders of magnitude higher than that of other materials used in the THz range, such as GaAs or lithium niobate. This nonlinear behavior, combined with ultrafast dynamic for excited carriers, proved to be essential for third harmonic generation in the sub-THz and low (<2.5 THz) THz range, using moderate (60 kV/cm) fields and at room temperature. Here, we show that, for monochromatic high peak power (1.8 W) input THz signals, emitted by a quantum cascade laser, the nonlinearity can be controlled using an ionic liquid gate that tunes the graphene Fermi energy up to >1.2 eV. Pump and probe experiments reveal an intense absorption nonlinearity at 3.2 THz, with a dominant 3rd-order contribution at EF > 0.7 eV, hence opening intriguing perspectives per engineering novel architectures for light generation at frequencies > 9 THz.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

Frequency shift of even-order high harmonic generation in monolayer MoS2

Sub-optical-cycle electron dynamics in materials driven by intense laser fields can be investigated by high harmonic generation. We observed frequency shift of high harmonic spectrum near the band gap of monolayer MoS2 experimentally. Through semi-classical quantum trajectory analysis, we demonstrated that the phase of transition dipole moment varies according to the recombination timing and momentum of tunneled electrons. It results in either blue- or red-shift of harmonic frequencies, determined by the modulated energy gap by transition dipole phases (TDPs) and Berry connections. Our finding reveals the effect of TDPs on high harmonic frequency in non-central symmetric materials.

High-harmonic generation from a subwavelength dielectric resonator

Higher-order optical harmonics entered the realm of nanostructured solids being observed recently in optical gratings and metasurfaces with a subwavelength thickness. Structuring materials at the subwavelength scale allows us toresonantly enhance the efficiency of nonlinear processes and reduce the size of high-harmonic sources. We report the observation of up to a seventh harmonic generated from a single subwavelength resonator made of AlGaAs material. This process is enabled by careful engineering of the resonator geometry for supporting an optical mode associated with a quasi-bound state in the continuum in the mid-infrared spectral range at around λ = 3.7 μm pump wavelength. The resonator volume measures ~0.1 λ³. The resonant modes are excited with an azimuthally polarized tightly focused beam. We evaluate the contributions of perturbative and nonperturbative nonlinearities to the harmonic generation process. Our work proves the possibility to miniaturize solid-state sources of high harmonics to the subwavelength volumes.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Polarization-Independent Second Harmonic Generation in 2D Van Der Waals Kagome Nb3 SeI7 Crystals

Second harmonic generation (SHG) of 2D crystals has been of great interest due to its advantages of phase-matching and easy integration into nanophotonic devices. However, the polarization-dependence character of the SHG signal makes it highly troublesome but necessary to match the laser polarization orientation relative to the crystal, thus achieving the maximum polarized SHG intensity. Here, it is demonstrated a polarization-independent SHG, for the first time, in the van der Waals Nb₃ SeI₇ crystals with a breathing Kagome lattice. The Nb₃ triangular clusters and Janus-structure of each Nb₃ SeI₇ layer are confirmed by the STEM. Nb₃ SeI₇ flake shows a strong SHG response due to its noncentrosymmetric crystal structure. More interestingly, the SHG signals of Nb₃ SeI₇ are independent of the polarization of the excitation light owing to the in-plane isotropic arrangement of nonlinear active units. This work provides the first layered nonlinear optical crystal with the polarization-independent SHG effect, providing new possibilities for nonlinear optics.

2D Material Infrared Photonics and Plasmonics

Two-dimensional (2D) materials including graphene, transition metal dichalcogenides, black phosphorus, MXenes, and semimetals have attracted extensive and widespread interest over the past years for their many intriguing properties and phenomena, underlying physics, and great potential for applications. The vast library of 2D materials and their heterostructures provides a diverse range of electrical, photonic, mechanical, and chemical properties with boundless opportunities for photonics and plasmonic devices. The infrared (IR) regime, with wavelengths across 0.78 μm to 1000 μm, has particular technological significance in industrial, military, commercial, and medical settings while facing challenges especially in the limit of materials. Here, we present a comprehensive review of the varied approaches taken to leverage the properties of the 2D materials for IR applications in photodetection and sensing, light emission and modulation, surface plasmon and phonon polaritons, non-linear optics, and Smith-Purcell radiation, among others. The strategies examined include the growth and processing of 2D materials, the use of various 2D materials like semiconductors, semimetals, Weyl-semimetals and 2D heterostructures or mixed-dimensional hybrid structures, and the engineering of light-matter interactions through nanophotonics, metasurfaces, and 2D polaritons. Finally, we give an outlook on the challenges in realizing high-performance and ambient-stable devices and the prospects for future research and large-scale commercial applications.

Effect of stacking configuration on high harmonic generation from bilayer hexagonal boron nitride

High harmonic generation from bilayer h-BN materials with different stacking configurations is theoretically investigated by solving the extended multiband semiconductor Bloch equations in strong laser fields. We find that the harmonic intensity of AA'-stacking bilayer h-BN is one order of magnitude higher than that of AA-stacking bilayer h-BN in high energy region. The theoretical analysis shows that with broken mirror symmetry in AA'-stacking, electrons have much more opportunities to transit between each layer. The enhancement in harmonic efficiency originates from additional transition channels of the carriers. Moreover, the harmonic emission can be dynamically manipulated by controlling the carrier envelope phase of the driving laser and the enhanced harmonics can be utilized to achieve single intense attosecond pulse.

Strong, anisotropic, layer-independent second harmonic generation in multilayer SnS film

Materials based on group IV chalcogenides exhibit extensive technologically important properties. Its unusual chemical bonding and off-centering of in-layer sublattices could cause chemical polarity and weakly broken symmetry, making optical field controlling feasible. Here, we fabricated large-area SnS multilayer films and observed unexpected strong SHG response at 1030 nm. The appreciable SHG intensities were obtained with an independence on layer, which is opposite to the generation principle of overall nonzero dipole moment only in odd-layer material. Taking GaAs for reference, the second-order susceptibility was estimated to be 7.25 pm/V enhanced by mixed-chemical bonding polarity. Further polarization-dependent SHG intensity confirmed the crystalline orientation of SnS films. The results imply surface inversion symmetry broken and nonzero polarization field modified by metavalent bonding should be the origin of SHG responses. Our observations establish multilayer SnS as a promising nonlinear material, and will guide in design of IV chalcogenides with improved optics and photonics properties for the potential applications.

Ferroelectric Domain Control of Nonlinear Light Polarization in MoS2 via PbZr0.2 Ti0.8 O3 Thin Films and Free-Standing Membranes

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) such as MoS₂ exhibit exceptionally strong nonlinear optical responses, while nanoscale control of the amplitude, polar orientation, and phase of the nonlinear light in TMDCs remains challenging. In this work, by interfacing monolayer MoS₂ with epitaxial PbZr_0.2 Ti_0.8 O₃ (PZT) thin films and free-standing PZT membranes, the amplitude and polarization of the second harmonic generation (SHG) signal are modulated via ferroelectric domain patterning, which demonstrates that PZT membranes can lead to in-operando programming of nonlinear light polarization. The interfacial coupling of the MoS₂ polar axis with either the out-of-plane polar domains of PZT or the in-plane polarization of domain walls tailors the SHG light polarization into different patterns with distinct symmetries, which are modeled via nonlinear electromagnetic theory. This study provides a new material platform that enables reconfigurable design of light polarization at the nanoscale, paving the path for developing novel optical information processing, smart light modulators, and integrated photonic circuits.

Near Zero-Threshold Voltage P-N Junction Diodes Based on Super-Semiconducting Nanostructured Ag/Al Arrays

Semiconductor devices are currently one of the most common energy consumption devices. Significantly reducing the energy consumption of semiconductor devices with advanced energy-efficient technologies is highly desirable. The discovery of super-semiconductors (SSCs) based on metallic bi-layer shell arrays provides an opportunity to realize ultra-low-power consumption semiconductor devices. As an example, the achievement of near zero-threshold voltage in p-n junction diodes based on super-semiconducting nanostructured Ag/Al arrays is reported, realizing ultra-low-power p-n junction diodes: ≈3 W per trillion diodes with a working voltage of 1 V or 30 mW per trillion diodes with an operating voltage of 0.1 V. In addition, the p-n junction diodes exhibit a high breakdown field of ≈1.1 × 10⁶  V cm^-1 , similar to that of SiC and GaN, due to a robust built-in field driven by infrared light photons. The SSC p-n diodes with near zero-threshold voltage and high breakdown field allow access to ultra-low-power semiconducting transistors, integrated circuits, chips, etc.

Ultrastrong Optical Harmonic Generations in Layered Platinum Disulfide in the Mid-Infrared

Nonlinear optical activities (e.g., harmonic generations) in two-dimensional (2D) layered materials have attracted much attention due to the great promise in diverse optoelectronic applications such as nonlinear optical modulators, nonreciprocal optical device, and nonlinear optical imaging. Exploration of nonlinear optical response (e.g., frequency conversion) in the infrared, especially the mid-infrared (MIR) region, is highly desirable for ultrafast MIR laser applications ranging from tunable MIR coherent sources, MIR supercontinuum generation, and MIR frequency-comb-based spectroscopy to high harmonic generation. However, nonlinear optical effects in 2D layered materials under MIR pump are rarely reported, mainly due to the lack of suitable 2D layered materials. Van der Waals layered platinum disulfide (PtS₂) with a sizable bandgap from the visible to the infrared region is a promising candidate for realizing MIR nonlinear optical devices. In this work, we investigate the nonlinear optical properties including third-and fifth-harmonic generation (THG and FHG) in thin layered PtS₂ under infrared pump (1550-2510 nm). Strikingly, the ultrastrong third-order nonlinear susceptibility χ⁽³⁾(-3ω;ω,ω,ω) of thin layered PtS₂ in the MIR region was estimated to be over 10^-18 m²/V², which is about one order of that in traditional transition metal chalcogenides. Such excellent performance makes air-stable PtS₂ a potential candidate for developing next-generation MIR nonlinear photonic devices.

Third-Order Optical Nonlinearities of 2D Materials at Telecommunications Wavelengths

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n₂ values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

Trajectory-controlled high-order harmonic generation in ZnO crystals

We experimentally and theoretically study high-order harmonic generation in zinc oxide crystals irradiated by mid-infrared lasers. The trajectories are mapped to the far field spatial distribution of harmonics. The divergence angles of on-axis and off-axis parts exhibit different dependences on the order of the harmonics. This observation can be theoretically reproduced by the coherent interference between the short and long trajectories with dephasing time longer than 0.5 optical cycle. Further, the relative contribution of the short and long trajectories is demonstrated to be accurately controlled by a one-color or two-color laser on the attosecond time scale. This work provides a reliable method to determine the electron dephasing time and demonstrates a versatile control of trajectory interference in the solid high-order harmonic generation.

Atomic-Scale Defects Might Determine the Second Harmonic Generation from Plasmonic Graphene Nanostructures

In this work, we theoretically investigate the impact of the atomic scale lattice imperfections of graphene nanoflakes on their nonlinear response enhanced by the resonance between an incident electromagnetic field and localized plasmon. As a case study, we address the second harmonic generation from graphene plasmonic nanoantennas of different symmetries with missing carbon atom vacancy defects in the honeycomb lattice. Using the many-body time-dependent density matrix approach, we find that one defect in the nanoflake comprising over five thousand carbon atoms can strongly impact the nonlinear hyperpolarizability and override the symmetry constraints. The effect reported here cannot be captured using the relaxation time approximation within the quantum or classical framework. Results obtained in this work have thus important implications for the design of nonlinear graphene devices.

Diabatic and adiabatic transitions between Floquet states imprinted in coherent exciton emission in monolayer WSe2

Floquet engineering is a promising way of controlling quantum system with photon-dressed states on an ultrafast time scale. So far, the energy structure of Floquet states in solids has been intensively investigated. However, the dynamical aspects of the photon-dressed states under ultrashort pulse have not been explored yet. Their dynamics become highly sensitive to the driving field transients, and thus, understanding them is crucial for ultrafast manipulation of a quantum state. Here, we observed the coherent exciton emission in monolayer WSe₂ at room temperature at the appropriate photon energy and the field strength of the driving light pulse using high-harmonic spectroscopy. Together with numerical calculations, our measurements revealed that the coherent exciton emission spectrum reflects the diabatic and adiabatic dynamics of Floquet states of excitons. Our results provide a previosuly unexplored approach to Floquet engineering and lead to control of quantum materials through pulse shaping of the driving field.

High-harmonic generation in polycrystalline CdTe nano-films via macroscopic investigations

Bright high harmonics generation (HHG) in CMOS-compatible nano-films can provide new opportunities for integrated coherent ultra-violet sources and attosecond photonic devices. Up to now, most HHG studies have been limited to single crystals. Polycrystalline materials, which consist of many grains separated by grain boundaries and normally have random crystallographic orientations, have rarely been explored for HHG. Understanding and predicting the HHG properties in polycrystalline nano-films are important owing to its merits of low cost and diversified properties, but challenging due to their complicated electronic structures. Here, we for the first time experimentally discover the correspondence between HHG in polycrystalline matters and macroscopic material parameters, to the best of our knowledge. Pumped by a mid-infrared femtosecond laser centered at 7.1 µm wavelength, bright and long-term stable harmonics extending to 25^th orders (284 nm) are demonstrated in polycrystalline cadmium telluride (CdTe) nano-films. It is found that the HHG strengths in the transmission and the reflection behave differently as a function of the material thickness in the range from 6 nm to 4 µm, which is highly correlated to the measured macroscopic conductivity. The experimental findings agree well with the recent theoretical prediction [Phys. Rev. B103(15), 155426 (2021)10.1103/PhysRevB.103.155426]. This work provides a simple gauge to study and predict HHG in complicated polycrystalline and amorphous nano-systems, and paves the way for novel strong-field nanophotonics based on polycrystalline nano-films.

Optical Control of High-Harmonic Generation at the Atomic Thickness

High-harmonic generation (HHG), an extreme nonlinear optical phenomenon beyond the perturbation regime, is of great significance for various potential applications, such as high-energy ultrashort pulse generation with outstanding spatiotemporal coherence. However, efficient active control of HHG is still challenging due to the weak light-matter interaction displayed by currently known materials. Here, we demonstrate optically controlled HHG in monolayer semiconductors via the engineering of interband polarization. We find that HHG can be efficiently controlled in the excitonic spectral region with modulation depths up to 95% and ultrafast response speeds of several picoseconds. Quantitative time-domain theory of the nonlinear optical susceptibilities in monolayer semiconductors further corroborates these experimental observations. Our demonstration not only offers an in-depth understanding of HHG but also provides an effective approach toward active optical devices for strong-field physics and extreme nonlinear optics.

Ultrafast modulation of a high harmonic generation in a bulk ZnO single crystal

Optical modulation of high harmonic generation (HHG) is of fundamental interest in science and technology, which can facilitate understanding of HHG generation mechanisms and expand the potential optoelectronic applications. However, the current established works have neither shown the advanced modulation performance nor provided a deep understanding of modulation mechanisms. In this work, taking wurtzite zinc oxide (ZnO) single crystal as a prototype, we have demonstrated an all-optical intensity modulation of high-order HHG with a response time of less than 0.2 ps and a depth of more than 95%, based on the pump-probe configuration with two different pumping wavelengths. Besides the achieved excellent modulation performance, we have also revealed that the modulation dynamics in ZnO single crystal highly depend on the excitation conditions. Specifically, the modulation dynamics with the near-bandgap or above-bandgap excitation are attributed to the non-equilibrium interband carrier relaxations, while for mid-gap excitation, the modulation dynamics are dominated by the nonlinear frequency mixing process. This work may enhance the current understanding of the HHG modulation mechanism and enlighten novel device designs.

Gate-tunable quantum pathways of high harmonic generation in graphene

Under strong laser fields, electrons in solids radiate high-harmonic fields by travelling through quantum pathways in Bloch bands in the sub-laser-cycle timescales. Understanding these pathways in the momentum space through the high-harmonic radiation can enable an all-optical ultrafast probe to observe coherent lightwave-driven processes and measure electronic structures as recently demonstrated for semiconductors. However, such demonstration has been largely limited for semimetals because the absence of the bandgap hinders an experimental characterization of the exact pathways. In this study, by combining electrostatic control of chemical potentials with HHG measurement, we resolve quantum pathways of massless Dirac fermions in graphene under strong laser fields. Electrical modulation of HHG reveals quantum interference between the multi-photon interband excitation channels. As the light-matter interaction deviates beyond the perturbative regime, elliptically polarized laser fields efficiently drive massless Dirac fermions via an intricate coupling between the interband and intraband transitions, which is corroborated by our theoretical calculations. Our findings pave the way for strong-laser-field tomography of Dirac electrons in various quantum semimetals and their ultrafast electronics with a gate control.

Under strong laser fields, materials exhibit extreme non-linear optical response, such as high harmonic generation. These higher harmonics provide insights into electron behaviour in materials in sub-laser cycle timescale. Here, Cha et al study higher harmonic generation resulting from the laser driven motion of massless Dirac fermions in graphene.

Polarization spectroscopy of high-order harmonic generation in gallium arsenide

An interesting property of high harmonic generation in solids is its laser polarization dependent nature which in turn provides information about the crystal and band structure of the generation medium. Here we report on the linear polarization dependence of high-order harmonic generation from a gallium arsenide crystal. Interestingly, we observe a significant evolution of the anisotropic response of above bandgap harmonics as a function of the laser intensity. We attribute this change to fundamental microscopic effects of the emission process comprising a competition between intraband and interband dynamics. This intensity dependence of the anisotropic nature of the generation process offers the possibility to drive and control the electron current along preferred directions of the crystal, and could serve as a switching technique in an integrated all-solid-state petahertz optoelectronic device.

Bidirectional residual current in monolayer graphene under few-cycle laser irradiation

By numerically solving the time-dependent Schrödinger equation and semiconductor Bloch equations, the light-induced residual current in monolayer graphene driven by a circularly polarized few-cycle laser is investigated. An evident current direction reversal is disclosed when the amplitude of the driving electric field exceeds a certain threshold value, which is absent in recent investigation [Nature550, 224 (2017)10.1038/nature23900]. Here the internal physical mechanism for the current reversal is inter-optical-cycle interference under a suitable long laser wavelength. Moreover, the reversal-related laser field amplitude depends sensitively on the ratio of ponderomotive energy to photon energy.

Anomalous Temperature Dependence of High-Harmonic Generation in Mott Insulators

We reveal the crucial effect of strong spin-charge coupling on high-harmonic generation (HHG) in Mott insulators. In a system with antiferromagnetic correlations, the HHG signal is drastically enhanced with decreasing temperature, even though the gap increases and the production of charge carriers is suppressed. This anomalous behavior, which has also been observed in recent HHG experiments on Ca_{2}RuO_{4}, originates from a cooperative effect between the spin-charge coupling and the thermal ensemble, as well as the strongly temperature-dependent coherence between charge carriers. We argue that the peculiar temperature dependence of HHG is a generic feature of Mott insulators, which can be controlled via the Coulomb interaction and dimensionality of the system. Our results demonstrate that correlations between different degrees of freedom, which are a characteristic feature of strongly correlated solids, have significant and nontrivial effects on nonlinear optical responses.

High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light-matter hybrids, and application for optical quantum computing.

Self-probed ptychography from semiconductor high-harmonic generation

We demonstrate a method to image an object using a self-probing approach based on semiconductor high-harmonic generation. On the one hand, ptychography enables high-resolution imaging from the coherent light diffracted by an object. On the other hand, high-harmonic generation from crystals is emerging as a new source of extreme-ultraviolet ultrafast coherent light. We combine these two techniques by performing ptychography measurements with nanopatterned crystals serving as the object as well as the generation medium of the harmonics. We demonstrate that this strong field in situ approach can provide structural information about an object. With the future developments of crystal high harmonics as a compact short-wavelength light source, our demonstration can be an innovative approach for nanoscale imaging of photonic and electronic devices in research and industry.

Electronic, transport, magnetic and optical properties of graphene nanoribbons review

Low dimensional materials have attracted great research interest from both theoretical and experimental point of view. These materials exhibit novel physical and chemical properties due to the confinement effect in low dimensions. The experimental observations of graphene open a new platform to study the physical properties of materials restricted to two dimensions. This featured article provides a review on the novel properties of quasi one-dimensional (1D) material known as graphene nanoribbon. Graphene nanoribbons can be obtained by unzipping carbon nanotubes (CNTs) or cutting the graphene sheet. Alternatively, it is also called the finite termination of graphene edges. It gives rise different edge geometries namely zigzag and armchair among others. There are various physical and chemical techniques to realize these materials. Depending on the edge type termination, these are called the zigzag and armchair graphene nanoribbons (ZGNR and AGNR). These edges play an important role in controlling the properties of graphene nanoribbons. The present review article provides an overview of the electronic, transport, optical and magnetic properties of graphene nanoribbons. However, there are different ways to tune these properties for device applications. Here, some of them are highlighted such as external perturbations and chemical modifications. Few applications of graphene nanoribbon have and chemical modifications. Few applications of graphene nanoribbon have also been briefly discussed.

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

High harmonic generation (HHG) has recently been established as a powerful method for probing ultrafast electron dynamics in solids. However, it remains unknown if HHG can be similarly applied for probing lattice distortions such as phonons. Specifically, it is unclear if the extreme nonlinearity of HHG can contribute to enhanced temporal resolution or sensitivity for probing lattice dynamics (compared to other, perturbative, methods). Here, we theoretically explore HHG in solids with active phonons. We present a pump-probe and multidimensional spectroscopy approach that relies on carrier-envelope-phase-sensitivity, in which HHG is highly sensitive for phonon dynamics. Strikingly, the predicted temporal resolution is ∼1 femtosecond, much below the probe pulse duration, owing to the subcycle nature of the approach.

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.

Visualization of the Preacceleration Process for High-Harmonic Generation in Solids

The high-order harmonic generation (HHG) in ZnO is investigated by numerically solving semiconductor Bloch equations (SBEs), which can be explained well by a four-step model. In this model, preacceleration is the first step, in which the electron is accelerated in the valence band until it reaches the point of the minimum band gap. To prove the existence of the preacceleration process, SBE-based k-resolved harmonic spectra and the transient conduction-band population are presented. The results show that the contribution of crystal-momentum channels away from the minimum band gap via preacceleration is non-negligible. Furthermore, the X-shaped distribution in the k-resolved spectra can be described well by the preacceleration process. Based on the above analysis, we can conclude that the preacceleration process plays an important role in HHG.

Dynamic and Active THz Graphene Metamaterial Devices

In recent years, terahertz waves have attracted significant attention for their promising applications. Due to a broadband optical response, an ultra-fast relaxation time, a high nonlinear coefficient of graphene, and the flexible and controllable physical characteristics of its meta-structure, graphene metamaterial has been widely explored in interdisciplinary frontier research, especially in the technologically important terahertz (THz) frequency range. Here, graphene’s linear and nonlinear properties and typical applications of graphene metamaterial are reviewed. Specifically, the discussion focuses on applications in optically and electrically actuated terahertz amplitude, phase, and harmonic generation. The review concludes with a brief examination of potential prospects and trends in graphene metamaterial.

Multiscale numerical tool for studying nonlinear dynamics in solids induced by strong laser pulses

Strong-field phenomena in solids exhibit extreme high-order nonlinear optical effects, which have triggered many theoretical and experimental investigations. However, there is still a lack of highly efficient numerical tools to simulate the relevant phenomena. In this paper, a versatile multiscale numerical tool set is developed for studying high-order nonlinear optical effects in solids, generated by ultrafast strong laser pulses. This tool is based on the tight-binding model approximation of the crystal structure, the related parameters of which are obtained from the density functional theory calculations. And the nonlinear effects are explored by solving the Maxwell equations coupled with the semiconductor Bloch equations. Our numerical tool can provide not only basic electronic structures and optical responses of the crystal, but also the real-time evolution of the macroscopic electromagnetic fields and the current density. The high-performance parallel computing and the interpolation method in our tool make it possible to study the strong-field nonlinear responses and propagation effects on a large spatial and temporal scale. Finally, three theoretical or experimental results published recently are satisfactorily reproduced, showing a good performance of the current toolbox.

Intense Laser Pulse Interaction With Graphene and Graphene Ribbons

In this work we investigate quantum mechanically the interaction of an intense ultrashort laser pulse with the graphene monolayer as well as with the armchair graphene ribbons of different widths. We consider a tight binding (TB) Hamiltonian of the monolayer graphene and give two rules for deriving the dispersion relations of the armchair graphene ribbons of any width, N, from the TB eigenvalues of the monolayer. The band structure of the monolayer and the armchair ribbons of different widths are discussed with illustrations. The time-dependent wavefunctions of the systems and the expectation values of interest are determined by solving the coupled equations of the band amplitudes “exactly” (numerically). First, simulations are made for the population excitation in the conduction band (CB) from the valence band (BV), the VB-CB interband correlation (or “coherence”), the intraband, the interband and the total currents in the monolayer graphene. The graphene currents are compared with the corresponding currents induced in an armchair ribbon (width, N = 3). The change from the 2D monolayer to the 1D ribbon shows a remarkable transition of the dominance of the intraband current that leads to a near steady total current in the monolayer, to a dominance of the interband current in the ribbon that induces an oscillatory current in the ribbon beyond the pulse duration. The difference observed might be a combined effect of the “confinement” in one dimention and a finite band-gap minimum in the case of the ribbon. However, this transition should be further investigated for better clarity. A brief comparison of the radiation spectra emitted from the monolayer and from the ribbon is also made. They show a grossly similar structure and a relative insensitivity with respect to the detailed structure of the targets chosen. This might be due to the dominance of virtual continuum-continuum transitions, to and from the bands states, that lie behind the fundamental quantum process of high harmonic emissions. Lastly, the dependence of the charge currents, induced in a ribbon of unit width (N = 1), on the carrier-envelope-phase (CEP) of the incident laser pulse is investigated. It is seen that the shape of the main part of the current produced in the ribbon can be fully reversed by changing the CEP of the ultrashort laser pulse from 0 to π. More generally, it is suggested that the pulse shape of the charge carriers in the ribbon could be designed by similarly tailoring the form of the vector potential of the incident laser pulse.

Non-classical high harmonic generation in graphene driven by linearly-polarized laser pulses

Recent studies in high-order harmonic generation (HHG) in solid targets reveal new scenarios of extraordinary rich electronic dynamics, in comparison to the atomic and molecular cases. For the later, the main aspects of the process can be described semiclassically in terms of electrons that recombine when the trajectories revisit the parent ion. HHG in solids has been described by an analogous mechanism, in this case involving electron-hole pair recombinations. However, it has been recently reported that a substantial part of the HHG emission corresponds to situations where the electron and hole trajectories do not overlap in space. According to the present knowledge, HHG from this imperfect recollisions reflects the quantum nature of the process, arising in systems with large Berry curvatures or for elliptically polarized driving fields. In this work, we demonstrate that imperfect recollisions are also relevant in the more general case. We show the signature of such recollisions in the HHG spectrum from monolayer graphene -a system with null Berry curvature- irradiated by linearly polarized driving fields. Our calculations also reveal that imperfect multiple-order recollisions contribute to the harmonic emission when electron-hole excursion times exceed one cycle of the driving field. We believe that our work adds a substantial contribution to the full understanding of the sub-femtosecond dynamics of HHG in solid systems.

High-order harmonic generation from the interference of intra-cycle trajectories in the k-space

Considering the crystal momenta of the entire k-space, we demonstrate that constructive intra-cycle interference of electrons enhances the high-order harmonic generation (HHG) of a GaN crystal from dominant interband Bloch oscillations. This results in a higher plateau of the HHG spectrum at a driven yield strength below the Bloch field strength. This phenomenon is confirmed in both the two-band and three-band models. Using two-color laser fields, the constructive or destructive interference of interband Bloch oscillations can be tuned. Our findings reveal the essential impact of intra-cycle interference in the full k-space on the HHG in solids.

High-Order Harmonic Generation and Its Unconventional Scaling Law in the Mott-Insulating Ca_{2}RuO_{4}

Competition and cooperation among orders is at the heart of many-body physics in strongly correlated materials and leads to their rich physical properties. It is crucial to investigate what impact many-body physics has on extreme nonlinear optical phenomena, with the possibility of controlling material properties by light. However, the effect of competing orders and electron-electron correlations on highly nonlinear optical phenomena has not yet been experimentally clarified. Here, we investigated high-order harmonic generation from the Mott-insulating phase of Ca_{2}RuO_{4}. Changing the gap energy in Ca_{2}RuO_{4} as a function of temperature, we observed a strong enhancement of high order harmonic generation at 50 K, increasing up to several hundred times compared to room temperature. We discovered that this enhancement can be well reproduced by an empirical scaling law that depends only on the material gap energy and photon emission energy. Such a scaling law can hardly be explained by the electronic structure change in the single particle model and has not been predicted by previous theoretical studies on HHG in the simple Mott-Hubbard model. Our results suggest that the highly nonlinear optical response of strongly correlated materials is influenced by competition among the multiple degrees of freedom and electron-electron correlations.