Harmonic Generation Process Research Articles

Strong-field physics in three-dimensional topological insulators

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 non-perturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (Bi$_2$Se$_3$) subjected to intense mid-infrared 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. Bulk harmonics show a monotonous 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 non-trivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behaviour 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.

Laser-induced processes with homonuclear diatomic molecules in orthogonally polarized two-color laser field

Using our theory which is based on the strong-field approximation we analyze high-order above-threshold ionization and high-order harmonic generation processes for the case of the homonuclear diatomic molecules exposed to an orthogonally polarized two-color (OTC) laser field. The OTC field represents a superposition of two linearly polarized fields with mutually orthogonal polarizations and different frequencies. We analyze the photoelectron energy spectra and the harmonic ellipticity as a function of the ratio of the intensities of the OTC laser-field components and the relative phase. Some combinations of the values of these parameters lead to the high-energy electrons, while the harmonic ellipticity depends strongly on the ratio of the intensities of the laser-field components. It is possible to find the value of this ratio for which the ellipticity of the emitted harmonics is large. The signes of ellipticity are opposite for the molecular orientations which are connected through the reflection with respect to the axis along the first OTC field component. This symmetry is explained using the expression which relates the T-matrix element and the harmonic ellipticity.

Electro-optic coefficient measurement of a K(H1-xDx)2PO4 crystal based on χ(2) nonlinear optical technology.

We present a novel method utilizing the χ(2) nonlinear optical technology, which can realize high precision measurement of linear electro-optic (EO) coefficients of nonlinear materials. By applying the linear EO effect to the nonlinear optical process, the theoretical model of this measurement method was established, and the calculation formula of the linear EO coefficient was given. In the proof-of-principle experiment, by introducing an external electric field into the fourth harmonic generation (FHG) process, we comprehensively obtained the linear EO coefficients of K(H1-xDx)2PO4 crystals and revealed the relationship between deuterium content (x) and EO coefficient (γ63): γ63 = -9.789 - 16.53x. Meanwhile, the stability of FHG was greatly improved, and the angular range of efficiency stability was increased to 4.4 times in maximum. This work not only systematically demonstrates the FHG characteristics of KDP-family crystals, which provides a good reference for the deep ultraviolet laser generation, but also offers a new way to measure the basic parameters of nonlinear optical materials.

High-dimensional orbital angular momentum multiplexing nonlinear holography

Nonlinear holography has been identified as a vital platform for optical multiplexing holography because of the appearance of new optical frequencies. However, due to nonlinear wave coupling in nonlinear optical processes, the nonlinear harmonic field is coupled with the input field, laying a fundamental barrier to independent control of the interacting fields for holography. We propose and experimentally demonstrate high-dimensional orbital angular momentum (OAM) multiplexing nonlinear holography to overcome this problem. By dividing the wavefront of the fundamental wave into different orthogonal OAM channels, multiple OAM and polarization-dependent holographic images in both the fundamental wave and second-harmonic wave have been reconstructed independently in the spatial frequency domain through a type-II second harmonic generation process. Moreover, this method can be easily extended to cascaded χ2 nonlinear optical processes for multiplexing in more wavelength channels, leading to potential applications in multicasting in optical communications, multiwavelength display, multidimensional optical storage, anticounterfeiting, and optical encryption.

Structural, mechanical, thermal, optical and antifungal properties of pure and nickel doped ninhydrin non liner single crystals

A conventional method was adopted to prepare pure ninhydrin (NH) and nickel doped ninhydrin (N1NH) single crystals. The present investigation focused on various properties of as grown NH and NINH crystals. Monoclinic crystal structure with P21 space group which is attractive phenomena were noticed in structural mode of grown NH and NINH crystals. Various vibrations of functional groups related to NH and nickel doped NINH crystals were assigned from Fourier-transform infrared peaks of good resolution. Energy-dispersive X-ray spectrum presents the percentage of carbon, oxygen and nickel occurs in the sample. The strength of the samples have deliberated with the help of Vicker’s microhardness tester. The decomposition point of both NH and N1NH crystals has been measured by thermal analysis. The dielectric constant of both NH and N1NH crystals was also determined. Green emission which denotes second harmonic generation (SHG) process for the samples generally confirms the nonlinear optical (NLO) activity of the NH and N1NH crystals and it has been tested successfully based on the technique of Kurtz-Perry. The SHG efficiency values of NH and N1NH samples are comparable with KDP which has been used as reference sample as it is being used commercially. Basically, NH and NINH crystal samples were used for many medical applications. Therefore, the antifungal activity was also focused for investigation against two famous fungi like Aspergillus niger, Aspergillus flavus.

Numerical investigation of relative intensity noise in frequency-doubled multimode fiber lasers

In this paper, we study the intensity noise performance of frequency-doubled lasers. In particular, we investigate how the relative intensity noise (RIN) of multimode fiber lasers is affected by the second harmonic generation process. We first develop an analytical approach and show that, in contrast with a single-mode laser, the low frequency RIN (or excess noise) of a two-mode laser can increase of more than 6 dB after the frequency-doubling operation. This occurs when the intensities of both modes are different and this is explained by a nonlinear coupling between noise and intensity of modes. To deal with more commonly-used multimode fiber lasers, we have extended our study to any number of modes. For this purpose, we have developed a model to numerically simulate the dynamics of a multimode fiber laser. This model includes noise sources and mode competition dynamics due to spatial hole burning. It gives access to the complex amplitude of the electric field of the laser. Using this model, we have confirmed that the excess noise of frequency-doubled multimode fiber lasers can be more than 6 dB higher than the excess noise of the laser before frequency-doubling.

Extreme Ultraviolet Frequency Comb with More than 100 μW Average Power below 100nmSupported by the National Natural Science Foundation of China (Grant Nos. 11674356 and 11527807), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21010400).

Extreme ultraviolet (XUV) frequency comb is a powerful tool in precision measurement. It also brings many new opportunities to the field of strong field physics since high harmonic generation related phenomena can be studied with high repetition rate. We demonstrate the generation of an XUV frequency comb with the aid of intra-cavity high harmonic generation process. The setup is driven by a high power infrared frequency comb, and an average power of 4.5 kW is reached in the femtosecond enhancement cavity. With Xe gas as the working media, harmonics up to the 19th order are observed. Power measurement indicates that as much as 115.9 μW (1.3 mW) are generated at ∼94 nm (∼148 nm). The shortest wavelength we can reach is ∼55 nm. The coherence of the generated light is tested with an optical-heterodyne-based measurement of the third harmonic. The resulted line width is ∼3 Hz. In addition, with this system, we also observe a strong suppression of below threshold harmonics from O2 compared to that from Xe. These results suggest that the current system is ready for precision spectroscopic measurements with few-electron atomic and molecular systems in XUV region as well as the study of strong field physics with an unprecedented 100MHz repetition rate.

High harmonics generation in bilayer graphene at high Fermi energies induced by coherent THz-radiation

The higher-order harmonic generation process in the nonperturbative regime at the interaction of coherent electromagnetic radiation with the AB-stacked bilayer graphene at high Fermi energies is considered. The applied coherent low-frequency radiation field in the high Fermi energy zone of electrons excludes the interband transitions enhancing high harmonic rates. The developed microscopic nonlinear quantum theory for charged carriers interaction with a strong pump wave is valid near the Dirac points of the Brillouin zone. The Liouville–von Neumann equation for the density matrix in the multiphoton excitation regime is solved both analytically and numerically. Based on the numerical solutions, we examine the rates of higher-order harmonics of the pump wave of arbitrary polarization. Obtained results show that bilayer graphene serves as an effective material for the generation of higher-order harmonics from THz to the mid-IR domain of frequencies at moderate pump wave intensities.

Effects of Grain Morphology on Nonlinear Conversion Efficiency of Random Quasi-Phase Matching in Polycrystalline Materials

Monte-Carlo simulations were performed on the efficiency of random quasi-phase matching (RQPM) nonlinear optical frequency conversion in polycrystalline materials to study the detailed effects of the statistical grain morphology. The second harmonic generation (SHG) process was taken for example based on random structures generated by a realistic grain growth model, and the effective nonlinear coefficient was rigorously derived by tensor transformation in randomly rotated coordinates. The effects of average grain size, standard deviation, and sphericity on SHG efficiency were figured out to conclude that the grain-size deviation plays the most important role in RQPM efficiency and the optimal grain size is smaller than the coherence length. The impacts of fundamental wavelength variation were also investigated. These results reveal how the RQPM process is affected by statistical and nonlinear optical laws, which enrich the RQPM theory and provide criteria for polycrystalline material processing in specific nonlinear applications.

Enhancement of nonlinear functionality of step-index silica fibers combining thermal poling and 2D materials deposition.

This work proposes a new route to overcome the limits of the thermal poling technique for the creation of second order nonlinearity in conventional silica optical fibers. We prove that it is possible to enhance the nonlinear behavior of periodically poled fibers merging the effects of poling with the nonlinear intrinsic properties of some materials, such as MoS2, which are deposited inside the cladding holes of a twin-hole silica fiber. The optical waves involved in a second harmonic generation process partially overlap inside the thin film of the nonlinear material and exploit its higher third order susceptibility to produce an enhanced SHG.

High-gain harmonic generation with temporally overlapping seed pulses and application to ultrafast spectroscopy.

Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG) process in a free-electron laser (FEL) is a promising approach to facilitate various coherent nonlinear spectroscopy schemes in the extreme ultraviolet (XUV) spectral range. However, in collinear arrangements using a single nonlinear medium, temporally overlapping seed pulses may introduce nonlinear mixing signals that compromise the experiment at short time delays. Here, we investigate these effects in detail by extending the analysis described in a recent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-order fringe-resolved autocorrelation and wave packet interferometry experiments at photon energies > 23 eV are performed, accompanied by numerical simulations. It turns out that both the autocorrelation and the wave-packet interferometry data are very sensitive to saturation effects and can thus be used to characterize saturation in the HGHG process. Our results further imply that time-resolved spectroscopy experiments are feasible even for time delays smaller than the seed pulse duration.

Frequency-doubling of continuous laser light in the Laguerre–Gaussian modes LG0,0 and LG3,3

For future generations of gravitational wave detectors, it is proposed to use the helical Laguerre-Gaussian LG3,3 mode to reduce thermal noise, which limits the detector sensitivity. At the same time, this requires the efficient generation of squeezed vacuum states in the LG3,3 mode for quantum noise reduction. Since this technique includes the process of second harmonic generation (SHG), we experimentally compare the conversion efficiency and harmonic output field of the LG0,0 and LG3,3 modes in a cavity-enhanced SHG using the same 7% doped MgO:LiNbO3 crystal. Conversion efficiencies of 96% and 45% are achieved, respectively. The influence of mode mismatches and astigmatism is analyzed to estimate the ratio of the pump mode-dependent effective nonlinearities to be d0,0/d3,3∼5. Furthermore, we show that absorption loss in the crystal is more relevant for the LG3,3 mode.

Heuristic model for sum frequency generation in chirped quasi-phase-matching gratings with application to selective, cascaded harmonic generation.

The use of chirped quasi-phase-matching (CQPM) for cascaded harmonic generation (CHG) in a single crystal has gained attraction in recent years. CHG involves multiple stages of second harmonic and sum frequency generation processes, of which their complex dynamics in CQPM structures are not well understood when far from the adiabatic limit. This subsequently poses a challenge to design CQPM structures for the optimization of higher order harmonic generation via cascaded processes. In this paper, we derive a heuristic model with analytical expressions for the approximation of the efficiency, location and length of second harmonic and sum frequency generation processes in CQPM structures in the non-adiabatic, fully nonlinear regime (i.e. with pump depletion). With the developed model, we present a design framework to create cascaded CQPM structures for the generation of any arbitrary harmonic with efficiency close to 100%.

Control of the half-cycle harmonic emission process for generating the intense and ultrashort single attosecond pulses (SAPs)

Abstract In this paper, the half-cycle harmonic generation process has been controlled by using the asymmetric inhomogeneous chirped pulse combined with the ultraviolet (UV) pulse. It is found that by properly optimizing the chirps and chirp delays of the fundamental two-color pulse, the optimal negative and positive half-cycle laser profiles for the harmonic cutoff extension can be obtained. Further, with the introduction of the negative and positive inhomogeneous effect, respectively, the harmonic cutoff from the negative and positive half-cycle laser profiles can be further improved. Next, with the assistance of the UV pulse, the harmonic intensity can be enhanced due to the UV resonance ionization. Moreover, the single and double UV photon resonance ionizations are much better for generating the higher harmonic intensity. As a result, the stronger and broader harmonic plateaus with the larger harmonic cutoff can be obtained, which can support the generation of the high-intensity ultrashort attosecond pulses with the pulse durations of sub-45 as.

Attosecond light science and its application for probing quantum materials

In this paper, we review the development and application of coherent short wavelength light sources implemented using the high harmonic generation (HHG) process. The physics underlying HHG brought quantum physics into the domain of attosecond time-scales for the first time. The observation and manipulation of electron dynamics on such short time-scales—a capability not conceived—of just a few decades ago—is becoming both more-and-more sophisticated and useful as a route to achieve exquisite control over short wavelength light. New experimental techniques are enabling HHG light sources to provide new insights into fundamental quantum interactions in materials, making it possible for the first time to capture the fastest charge, spin, photon and phonon interactions and to achieve diffraction-limited imaging at short wavelengths.

Parametric attosecond pulse amplification far from the ionization threshold from high order harmonic generation in He.

Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schrödinger equation in high-harmonic generation processes from excited states of He+. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He+ ground state and is only produced in a few specific laser cycles in agreement with the experimental measurements. Our simulations show that the amplified photon energy region can be controlled by varying the peak intensity of the laser field. Our results pave the way to the realization of compact attosecond pulse intense XUV lasers with broad applications.

Ultrafast 1 MHz vacuum-ultraviolet source via highly cascaded harmonic generation in negative-curvature hollow-core fibers

Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of∼40meV. In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust∼10Wfiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.

Origin of the multiphoton-regime harmonic-generation plateau structure

A physical interpretation is provided for the formation of the multiphoton-regime plateau feature in the spectra of nonlinear and correlated process of high-order harmonic generation (HHG) of two-active-electron atoms interacting with an intense linearly polarized laser field [Phys. Rev. A 88, 053412 (2013) for beryllium]. While in the strong-field tunneling regime the plateau feature is well known to be due to rescattering effects of the freed electron, its counterpart in the multiphoton regime is due to atomic resonance effects involving both singly excited states and doubly excited states. Here, we propose a strategy to uncover which kind of these states are responsible for this phenomenon. By studying the sensitivity of HHG to the initial state in helium, we show that this multiphoton-regime plateau structure mostly originates from singly excited states.

Time-resolved VUV ARPES at 10.8 eV photon energy and MHz repetition rate

The quest for mapping the femtosecond dynamics of the electronic band structure of complex materials over their full first Brillouin zone is pushing the development of schemes to efficiently generate ultrashort photon pulses in the VUV energy range. At present, the critical aspect in time- and angle-resolved photoelectron spectroscopy (TR-ARPES) is to combine a high photon energy with high photoemission count rates and a narrow pulse-bandwidth, necessary to achieve high energy resolution, while preserving a good time resolution and mitigating space-charge effects. Here we describe a novel approach to produce light pulses at 10.8 eV, combining high repetition rate operation (1–4 MHz), high energy resolution (∼26 meV) and space-charge free operation, with a time-resolution of ∼700 fs. These results have been achieved by generating the ninth harmonic of a Yb fiber laser, through a phase-matched process of third harmonic generation in Xenon of the laser third harmonic. The full up-conversion process is driven by a seed pulse energy as low as 10 μJ, hence is easily scalable to multi-MHz operation. This source opens the way to TR-ARPES experiments for the investigation of the electron dynamics over the full first Brillouin zone of most complex materials, with unprecedented energy and momentum resolutions and high count rates. The performances of the setup are tested by TR-ARPES on the topological insulator Bi2Se3.

On the extreme nonlinear optics of graphene nanoribbons in the strong coherent radiation fields

The generation of high-order harmonics in quasi-one-dimensional graphene nanoribbons (GNRs) initiated by intense coherent radiation is investigated. A microscopic theory describing the extreme nonlinear optical response of GNRs is developed. The closed set of differential equations for the single-particle density matrix at the GNR-strong laser field multiphoton interaction is solved numerically. The obtained solutions indicate the significance of the bandgap width and Fermi energy level on the high-order harmonic generation process in GNRs.