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We measured the ellipticity dependence of the harmonic yield of He, Ne, Ar, Kr, and Xe. It is found that the harmonic yield in general decreases monotonically with increasing laser ellipticity but anomalous dependence does occur for each atom for some harmonic orders. Additionally, we found that the degree of anomaly is weakest in helium but is stronger for the heavier atoms. The anomaly also depends on laser intensity. To explain these features, we developed a quantum trajectory Monte Carlo (QTMC) model based on the quantum path integral theory to study high-order harmonic generation (HHG). The model includes the effect of Coulomb potential from the target ion, thus it is capable of calculating near-threshold harmonics quantitatively. This model reveals that the presence of Coulomb potential would generate orbiting trajectories which are responsible for the anomalous ellipticity dependence near the threshold.
Abstract Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials—the Janus transition metal dichalcogenides in the 1 T’ phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T’ MoSSe (e.g., > 50 times higher than 2 H MoS 2 for 18 th order harmonic generation; > 20 times higher than 2 H MoS 2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.
The discovery and development of CMOS-compatible, nonlinear optical materials is essential to produce integrated photonic devices with advanced functionalities. AlN is a strong candidate for on-chip device demonstration due to its intrinsic second-order optical nonlinearities, large bandgap, and well-established fabrication techniques. However, AlN is not easily phase matched for the largest coefficient d 33 ; the coefficients that could potentially be dispersion phase-matched, d 31 and d 15 , have weak nonlinearities. This work investigates ferroelectric Al 1-x B x N (x = 0 to 0.11) for viability as a large bandgap nonlinear optical material with unique suitability towards ultraviolet light generation using second harmonic generation. The linear and nonlinear optical properties are characterized accounting for material anisotropy. With increasing B concentration, a large enhancement from near negligible values to d 31 = 0.9 ± 0.1 pm/V and d 15 = 1.2 ± 0.1 pm/V is observed. This compares favorably to other large bandgap materials like β-Ba(BO 2 ) 2 , where the largest nonlinear coefficient is d 22 ~ 2.3 pm/V at 800 nm. This is accompanied by a change in the bandgap from 6.1 eV to 5.8 eV as B substitution goes from 0 to 11%. A periodically poled, quasi-phase-matched ferroelectric domain pattern with 400 nm domain size and a wall roughness of <16 nm is demonstrated.
Harnessing light waveforms at attosecond time scales provides information of the structure and dynamics of matter on it's natural time scales. For this reason attosecond metrology has been at the forefront of the optical sciences for more than a decade, and it represents the latest time-domain frontier of the quantum world. Attosecond light pulses are commonly generated using higher-order harmonic generation (HHG) , a process capable of generating XUV coherent pulses. In addition to generate attosecond pulses, HHG can be used to study the structure and dynamics of atoms and molecules by analyzing the spectral content of the XUV pulses. This approach is known as HHG spectroscopy and it provides a coherent, time-dependent approach to study structure and dynamics in the quantum world. In this proposal we will generate harmonics from two optical foci produced by a system of a two-dimensional spatial light modulator (SLM) and a lens. In the far eld the train of attosecond pulses will interfere creating harmonic-dependent fringes. The position of such fringes is a direct measurement of the relative phase between the two foci and they also carry information about the quantum state of the target atom or molecule. Therefore, by measuring the amplitude and relative phase of the emitted harmonics we will have access to both, the amplitude and phase of the dipole moments of the studied target. Because the two beams are completely indistinguishable from each other up to a few millimeters from the focus, both driving pulses share the exact beam path. So far we have measured a jitter of 700 zeptoseconds with a 12.5 attosecond resolution in the delay control of the two foci. These two time scales represent some of the best time controls ever achieved to date.
Abstract The spatial resolution of the ps electric field induced second harmonic (EFISH) generation has been enhanced by using non-collinear pump laser beam arrangements. The pump laser beam (1064 nm, nominal pulse duration 150 ps, pulse energy 20–40 mJ) is separated into two coaxial or crossing beams, overlapping only near the focal point. The spatially enhanced EFISH (SEEFISH) signal is generated over a shorter beam overlap region compared to the collinear beam arrangement. Blocking of either of the two beams results in a complete suppression of the signal. The signal is spatially isolated from the ‘conventional’ EFISH signal and measured by a photomultiplier detector. Measurements of a known Laplacian field generated between two parallel cylinder electrodes in ambient air shows that SEEFISH improves the spatial resolution of the measurements by up to a factor of 2, such that the measurement results agree with the Laplacian field distribution. The spatial resolution is improved further by reducing the focal distance of the lens. The magnitude of the SEEFISH signal is significantly lower compared to that of the single-beam EFISH and decreases rapidly as the beam crossing angle is increased, due to the phase mismatch. This approach has a significant potential for measurements of electric field distributions in high-pressure plasmas, with an additional benefit of removing the stray second harmonic signal from the optical access windows.
High-order harmonics generated by a long intense femtosecond laser are known experimentally to create attosecond pulse trains (APTs). In the time domain, an APT consists of a sequence of sharp attosecond bursts that are equally separated by each half optical cycle. Here, in this work, we show that such well-known features can be modified when a longer wavelength driving laser is used. From our simulations, we show that multiple shorter attosecond sub-bursts exist in the femtosecond pulse train within each half optical cycle and the duration of each sub-burst scales approximately as $λ^{–2}_0$ with the driving laser wavelength λ 0 . We show that such sub-bursts can be found using quantitative rescattering model for harmonics generated from a single atom, and their origin is due to the interference of the quantum orbits from first two returns of the recombining electron. We further show that such sub-bursts can be phase matched under proper laser focusing condition and the position of the gas cell, thus, such new features should be observable experimentally.
We study high-order harmonic generation (HHG) with an annularly shaped high-power, high-repetition-rate laser. In this work we investigate how the spatial separation (or divergence) of the incident laser and the generated high-order harmonics depends on the gas pressure when the laser intensity is in the overdriven regime. It is shown that, when the cone size of the incident annular beam is relatively large, the resulting harmonics are highly collimated along the propagation axis and are spatially separated from the incident beam. Under the overdriven condition, dynamic phase matching favors HHG emissions from short-trajectory electrons that are efficiently built up in the second half of the gas medium. We verify that using an annular beam is a simple and effective method for separating the intense incident infrared laser from the generated high harmonics. Such high-flux and low-divergence light pulses are expected to be powerful sources in the laboratory for ultrafast probing of electron dynamics.
Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emission mechanisms play a critical role in shaping the nonlinear response. We show that a time-domain analysis of the harmonic radiation fields identifies the interplay between intra- and interband dynamical processes underlying the nonlinear light generation. With further analysis, we show that changes to the dominant emission regime can occur after only slight changes to the peak driving intensity and central driving wavelength. Furthermore, time-domain analysis of harmonic fields also reveals, for the first time, the possibility of rapid changes in the dominant emission mechanism within the temporal window of the driving pulse envelope. Finally, we examine the experimental viability of performing time-domain analysis of harmonic fields with sub-cycle resolution using realistic parameters.
Attosecond pulses are central to the investigation of valence- and core-electron dynamics on their natural timescales. The reproducible generation and characterization of attosecond waveforms has been demonstrated so far only through the process of high-order harmonic generation. Several methods for shaping attosecond waveforms have been proposed, including the use of metallic filters, multilayer mirrors and manipulation of the driving field. However, none of these approaches allows the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free-electron lasers, by contrast, deliver femtosecond, extreme-ultraviolet and X-ray pulses with energies ranging from tens of microjoules to a few millijoules. Recent experiments have shown that they can generate subfemtosecond spikes, but with temporal characteristics that change shot-to-shot. In this paper we report reproducible generation of high-energy (microjoule level) attosecond waveforms using a seeded free-electron laser. We demonstrate amplitude and phase manipulation of the harmonic components of an attosecond pulse train in combination with an approach for its temporal reconstruction. The results presented here open the way to performing attosecond time-resolved experiments with free-electron lasers.
Efficient nonlinear wave mixing is of paramount importance for a wide range of applications. However, weak optical nonlinearities pose significant challenges for accessing nonlinear light–matter interaction in compact systems. Here, we experimentally study second harmonic generation in deeply subwavelength 3R-MoS 2 metasurfaces (<λ/13 thick). Our measurements, supported by theoretical analysis, reveal a complex interplay and coupling between geometric resonances, optical extinction, and exciton-driven strong nonlinear susceptibility dispersion. We further demonstrate >150-fold enhancement in second harmonic signal at 740 nm mediated by the A exciton resonance. Additionally, our theoretical studies predict an enhancement of more than 10 6 in second harmonic generation in <100 nm thick structures exhibiting bound states in the continuum resonance. These findings provide insight into accessing and harnessing the unprecedented 3R-MoS 2 nonlinearities at a subwavelength scale, paving the way to ultracompact nonlinear photonic devices.
Chiral organic-inorganic hybrid perovskites offer a promising platform for developing non-linear chiro-optical applications and chiral-induced spin selectivity. Here, we show that achiral hybrid perovskites that have highly ordered ferroelectric domains with orthogonal polarization exhibit planar chirality, as manifested by second harmonic generation with strong circular dichroism. Interestingly, the handedness of the second harmonic generation circular dichroism response can be alternatingly switched between orthogonally polarized domains and domain walls. To correlate the origin of planar chirality in these domains, atom-resolved atomic force microscopy is used to reveal distinct arrangements of atomic rows in these ferroelectric crystals that indicate planar symmetry breaking. Remarkably, a large SHG anisotropy factor of 0.41 is measured at the domain wall. Additionally, spatially resolved two-photon photoluminescence excitation measurement provide evidence of larger Rashba spin-splitting in these chiral ferroelectric domains compared to domain-free areas. Our discoveries of domain-dependent planar chirality and spin texture hold great promise for advancement of domain-specific chiro-optical applications.
Composition dependence of second harmonic generation, refractive index, extinction coefficient, and optical bandgap in 20 nm thick crystalline Hf 1– x Zr x O 2 (0 ≤ x ≤ 1) thin films is reported here. The refractive index exhibits a general increase with increasing ZrO 2 content with all values within the range of 1.98–2.14 from 880 nm to 400 nm wavelengths. A composition dependence of the indirect optical bandgap is observed, decreasing from 5.81 eV for HfO 2 to 5.17 eV for Hf 0.4 Zr 0.6 O 2 . The bandgap increases for compositions with x > 0.6, reaching 5.31 eV for Hf 0.1 Zr 0.9 O 2 . Second harmonic signals are measured for 880 nm incident light. The magnitude of the second harmonic signal scales with the magnitude of the remanant polarization in the composition series. Film compositions that display near zero remanent polarizations exhibit minimal second harmonic generation while those with maximum remanent polarization also display the largest second harmonic signal. The results are discussed in the context of ferroelectric phase assemblage in the hafnium zirconium oxide films and demonstrate a path toward a silicon-compatible integrated nonlinear optical material.
Symmetry plays a central role in conventional and topological phases of matter, making the ability to optically drive symmetry changes a critical step in developing future technologies that rely on such control. Topological materials, like topological semimetals, are particularly sensitive to a breaking or restoring of time-reversal and crystalline symmetries, which affect both bulk and surface electronic states. While previous studies have focused on controlling symmetry via coupling to the crystal lattice, we demonstrate here an all-electronic mechanism based on photocurrent generation. Using second harmonic generation spectroscopy as a sensitive probe of symmetry changes, we observe an ultrafast breaking of time-reversal and spatial symmetries following femtosecond optical excitation in the prototypical type-I Weyl semimetal TaAs. Here, our results show that optically driven photocurrents can be tailored to explicitly break electronic symmetry in a generic fashion, opening up the possibility of driving phase transitions between symmetry-protected states on ultrafast timescales.
Attosecond pulses in the soft x-ray (SXR) to water-window energy region offer the tools for creating and studying target-specific localized inner-shell electrons or holes in materials, enabling monitoring or controlling charge and energy flows in a dynamic system on attosecond timescales. Recently, a number of laboratories have reported generation of continuum harmonics in the hundred-electron-volt to kilovolt region with few-cycle long-wavelength mid-infrared lasers. These harmonics have the bandwidth to support pulses with durations of a few to a few-ten attoseconds. But harmonics generated in a gas medium have attochirps that cannot be fully compensated by materials over a broad spectral range; thus, realistically what are the typical shortest attosecond pulses that one can generate? To answer this question, it is essential that the temporal attosecond pulses be accurately characterized. By reanalyzing the soft x-ray attosecond metrology reported in three recent experiments using a newly developed broadband phase retrieval algorithm, we demonstrate here that the generated attosecond pulses in the first two papers have durations of about 60 as, longer than what they have reported. Similarly, the duration from the third experiment is retrieved to be about half of the 322-as upper limit cited in that work. We also introduce the autocorrelation (AC) of the streaking spectrogram. By comparing the ACs from the experiments and from the retrieved SXR pulses, the accuracy of the retrieved results can be directly visualized. Our retrieval method is fast and accurate, and it shall provide a powerful tool for the metrology of the emerging few-ten-attosecond pulses.
Robust atomic-to-meso-scale chirality is now observed in the one-dimensional form of tellurium. This enables a large and counter-intuitive circular-polarization dependent second harmonic generation response above 0.2 which is not present in two-dimensional tellurium. Orientation variations in 1D tellurium nanowires obtained by four-dimensional scanning transmission electron microscopy (4D-STEM) and their correlation with unconventional non-linear optical properties by second harmonic generation circular dichroism (SHG-CD) uncovers an unexpected circular-polarization dependent SHG response from 1D nanowire bundles – an order-of-magnitude higher than in single-crystal two-dimensional tellurium structures – suggesting the atomic- and meso-scale crystalline structure of the 1D material possesses an inherent chirality not present in its 2D form; and which is strong enough to manifest even in the aggregate non-linear optical (NLO) properties of aggregates.
We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of nonperturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (Bi 2 Se 3 ) subjected to intense midinfrared laser fields. We analyze the contributions from the spin-orbit-coupled bulk states and the topological surface bands separately and reveal a major difference in how their harmonic yields depend on the ellipticity of the laser field. Furthermore, bulk harmonics show a monotonic decrease in their yield as the ellipticity increases, in a manner reminiscent of high harmonic generation in gaseous media. However, the surface contribution exhibits a highly nontrivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behavior to (i) the enhanced amplitude and the circular pattern of the interband dipole and the Berry connections in the vicinity of the Dirac point and (ii) the influence of the higher-order, hexagonal warping terms in the Hamiltonian, which are responsible for the hexagonal deformation of the energy surface at higher momenta. The latter are associated directly with spin-orbit-coupling parameters. Our results thus establish the sensitivity of strong-field-driven high harmonic emission to the topology of the band structure as well as to the manifestations of spin-orbit interaction.
Strong coupling between polarization ( P ) and strain (ɛ) in ferroelectric complex oxides offers unique opportunities to dramatically tune their properties. Here colossal strain tuning of ferroelectricity in epitaxial KNbO 3 thin films grown by sub‐oxide molecular beam epitaxy is demonstrated. While bulk KNbO 3 exhibits three ferroelectric transitions and a Curie temperature ( T c ) of ≈676 K, phase‐field modeling predicts that a biaxial strain of as little as −0.6% pushes its T c > 975 K, its decomposition temperature in air, and for −1.4% strain, to T c > 1325 K, its melting point. Furthermore, a strain of −1.5% can stabilize a single phase throughout the entire temperature range of its stability. A combination of temperature‐dependent second harmonic generation measurements, synchrotron‐based X‐ray reciprocal space mapping, ferroelectric measurements, and transmission electron microscopy reveal a single tetragonal phase from 10 K to 975 K, an enhancement of ≈46% in the tetragonal phase remanent polarization ( P r ), and a ≈200% enhancement in its optical second harmonic generation coefficients over bulk values. These properties in a lead‐free system, but with properties comparable or superior to lead‐based systems, make it an attractive candidate for applications ranging from high‐temperature ferroelectric memory to cryogenic temperature quantum computing.