Discriminating between the Role of Phase Matching and that of the Single-Atom Response in Resonance Plasma-Plume High-Order Harmonic Generation

Quantum Electrodynamics in High-Harmonic Generation: Multitrajectory Ehrenfest and Exact Quantum Analysis

High-harmonic generation (HHG) is a nonlinear process in which a material sample is irradiated by intense laser pulses, causing the emission of high harmonics of incident light. HHG has historically been explained by theories employing a classical electromagnetic field, successfully capturing its spectral and temporal characteristics. However, recent research indicates that quantum-optical effects naturally exist or can be artificially induced in HHG, such as entanglement between emitted harmonics. Even though the fundamental equations of motion for quantum electrodynamics (QED) are well-known, a unifying framework for solving them to explore HHG is missing. So far, numerical solutions have employed a wide range of basis-sets, methods, and untested approximations. Based on methods originally developed for cavity polaritonics, here we formulate a numerically accurate QED model consisting of a single active electron and a single quantized photon mode. Our framework can, in principle, be extended to higher electronic dimensions and multiple photon modes to be employed in ab initio codes for realistic physical systems. We employ it as a model of an atom interacting with a photon mode and predict a characteristic minimum structure in the HHG yield vs phase-squeezing. We find that this phenomenon, which can be used for novel ultrafast quantum spectroscopies, is partially captured by a multitrajectory Ehrenfest dynamics approach, with the exact minima position sensitive to the level of theory. On the one hand, this motivates using multitrajectory approaches as an alternative for costly exact calculations. On the other hand, it suggests an inherent limitation of the multitrajectory formalism, indicating the presence of entanglement and true quantum effects (especially prominent for atomic and molecular resonances). Our work creates a roadmap for a universal formalism of QED-HHG that can be employed for benchmarking approximate theories, predicting novel phenomena for advancing quantum applications, and for the measurements of entanglement and entropy.

Harmonic Generation in Molecular Ag2S Plasma

The molecular laser-induced plasma (LIP) produced during the ablation of silver sulfide (Ag2S) was used as a medium for high-order harmonic generation in the extreme ultraviolet range. The role of LIP formation, the plasma components, and the geometry of plasma in the harmonic conversion efficiency was analyzed. We also analyzed the influence of the driving pulses (chirp, single-color pump, two-color pump, and delay between heating and converting pulses) on the harmonic yield in Ag2S LIP. The application of molecular plasma was compared with the application of atomic plasma, which comprised similar metallic elements (Ag) as well as other metal LIPs. The harmonics from the Ag2S LIP were 4 to 10 times stronger than those from the Ag LIP. The harmonics up to the 59th order were achieved under the optimal conditions for the molecular plasma.

Benchmarking Functionals for Strong-Field Light-Matter Interactions in Adiabatic Time-Dependent Density Functional Theory

In recent years, time-dependent density functional theory (TDDFT) has been extensively employed for highly nonlinear optics in molecules and solids, including high harmonic generation (HHG), photoemission, and more. TDDFT exhibits a relatively low numerical cost while still describing both light-matter and electron-electron interactions ab initio, making it highly appealing. However, the majority of implementations of the theory utilize the simplest possible approximations for the exchange-correlation (XC) functional-either the local density or generalized gradient approximations, which are traditionally considered to have rather poor chemical accuracy. We present the first systematic study of the XC functional effect on molecular HHG, testing various levels of theory. Our numerical results suggest justification for using simpler approximations for the XC functional, showing that hybrid and meta functionals (as well as Hartree-Fock) can, at times, lead to poor and unphysical results. The specific source of the failure in more elaborate functionals should be topic of future work, but we hypothesize that its origin might be connected to the adiabatic approximation of TDDFT.

Quasi-phase-matching of resonance-enhanced high-order harmonics in laser plasmas

The resonance-enhanced harmonics in laser-induced arsenic and selenium plasmas are studied at the quasi-phase-matching (QPM) conditions. We demonstrate that the enhancement of these harmonics was significantly smaller than the one of the neighboring harmonics. Though the enhancement factors of the harmonics in the vicinity of resonance-enhanced harmonics were in the range of 5× to 18×, the resonance-enhanced harmonics were almost unenhanced at QPM conditions. The most probable reason for such restriction in the enhancement of specific harmonics at the conditions of QPM was a stronger influence of free electrons on the phase-matching conditions of the resonance-enhanced single harmonic compared to the QPM-enhanced group of harmonics.

High-order harmonics enhancement in laser-induced plasma

The methods of enhancement of the strong high-order harmonics of femtosecond pulses in laser-induced plasma are demonstrated. It comprises the application of the four techniques allowing the enhancement of harmonics in different spectral ranges. Among them are the selection of targets for ablation to create the conditions for resonance enhancement of single harmonic, formation of the quasi-phase-matching of a spectrally tunable group of harmonics, application of the two-color pump of plasma, and the formation of nanoparticles-contained plasmas. The number of generated coherent XUV photons increased in the region of single resonantly enhanced harmonic (62 nm) and the shorter-wavelength region (30-50 nm). The above techniques of harmonics enhancement allowed a significant (up to 50 times) growth in a whole harmonic yield in the case of indium plasma. We discuss the reasons preventing the joint implementation of the four methods of harmonics enhancement in the same spectral region.

Extension of high-order harmonic generation cutoff from laser-ablated tin plasma plumes

The high-order harmonic spectra from laser-ablated tin plasma plumes are investigated experimentally and theoretically at different laser wavelengths. It is found that the harmonic cutoff is extended to ∼84 eV and the harmonic yield is greatly improved by decreasing the driving laser wavelength from 800 nm to 400 nm. Appling the Perelomov-Popov-Terent'ev theory with the semiclassical cutoff law and one-dimensional time-dependent Schrödinger equation, the contribution of the Sn³⁺ ion to harmonic generation accounts for the cutoff extension at 400 nm. With the qualitative analysis of the phase mismatching effect, we reveal the phase matching caused by the dispersion of free electrons is greatly optimized in the 400 nm driving field relative to the 800 nm driving field. The high-order harmonic generated from laser-ablated tin plasma plumes driven by the short laser wavelength provides a promising way to extend cutoff energy and generate intensely coherent extreme ultraviolet radiation.

High-Order Harmonics Generation in MoS2 Transition Metal Dichalcogenides: Effect of Nickel and Carbon Nanotube Dopants

The transition metal dichalcogenides have instigated a lot of interest as harmonic generators due to their exceptional nonlinear optical properties. Here, the molybdenum disulfide (MoS2) molecular structures with dopants being in a plasma state are used to demonstrate the generation of intense high-order harmonics. The MoS2 nanoflakes and nickel-doped MoS2 nanoflakes produced stronger harmonics with higher cut-offs compared with Mo bulk and MoS2 bulk. Conversely, the MoS2 with nickel nanoparticles and carbon nanotubes (MoS2-NiCNT) produced weaker coherent XUV emissions than other materials, which is attributed to the influence of phase mismatch. The influence of heating and driving pulse intensities on the harmonic yield and cut-off energies are investigated in MoS2 molecular structures. The enhanced coherent extreme ultraviolet emission at ~32 nm (38 eV) due to the 4p-4d resonant transitions is obtained from all aforementioned molecular structures, except for MoS2-NiCNT.

Comparative study of medium length-dependent high-harmonic generation from metal ions

We present an experimental study on the high-harmonic yields from the ions in the laser-ablated plumes of various metal targets (W, Mo, Cr, Cu, Ni, Fe, Ag and Mg) with the purpose of comparing their ion density and single-atom response. The harmonic yields as a function of medium length are measured and the results are fitted against a theoretical model to extract the coherence length, absorption length and strength single-atom response (in arbitrary units) of different harmonic orders for each target. It is found that the coherence lengths decrease monotonically as a function of harmonic order for all targets. Ion density of the generation media are estimated by the trend of the coherence length as a function of harmonic order. Qualitatively, targets with lower melting temperatures seem to produce laser-ablated plumes of higher ion density, vice versa. Also, the strength of the single-atom response of the metal ion species with only one electron in the outermost subshell are weak compared with the other targets considered in this study.

Harmonics Generation in the Laser-Induced Plasmas of Metal and Semiconductor Carbide Nanoparticles

Carbon-containing plasma is an attractive medium for generation of harmonics of laser pulses in the extreme ultraviolet range. We ablate two metal carbide (B₄C and Cr₃C₂) nanoparticles and silicon carbide (SiC) nanoparticles and generate harmonics after propagation of 35 fs pulses through the laser-induced plasmas. We analyze the spectra, spectral shifts, and splitting of harmonics from nanoparticles-contained plasmas, which demonstrate the chirp-related harmonic cut-off scaling. In addition, we present the simplified two-color pump model calculations of HHG based on the strong field approximation.

High-order harmonics generation in nanosecond-pulses-induced plasma containing Ni-doped CsPbBr3perovskite nanocrystals using chirp-free and chirped femtosecond pulses

We demonstrate high-order harmonic generation in Ni-doped CsPbBr₃perovskite nanocrystals ablated by nanosecond pulses using chirp-free 35 fs, and chirped 135 fs pulses in the case of single-color pump (800 nm) and a two-color pump (800 and 400 nm). We analyzed the spectral shift, cut-off, and intensity distribution of harmonics in the case of chirped drving pulses compared to chirp-free pulses. It is shown that the presence of Ni dopants and CsPbBr₃plasma components improves the harmonics emission. Also, we measured the third-order nonlinear optical (NLO) properties of these nanocrystals using 800 nm, 60 fs, 1 kHz pulses. The variations of measured NLO parameters of CsPbBr₃perovskite nanocrystals containing different concentrations of nickel correlate with variations of generated high-order harmonics from laser induced plasmas of studied nanocrystals in terms of harmonics intensity, cut-off, and spectral shift (in case of chirped driving pulses). The spectral shift of the harmonics generated from the Ni-doped CsPbBr₃perovskite nanocrystals can be used to form tunable extreme ultraviolet sources.

Laser-Induced Molecular Plasma: A Medium for High-Order Harmonics Generation of Ultrashort Pulses

I present a study of laser-induced plasmas (LIPs) produced on the surfaces of molecular targets to create optimal conditions for high-order harmonics generation during the propagation of femtosecond pulses through the LIP. The resonance enhancement of a harmonic, two-color pump of plasma, quasi-phase-matching and nanoparticle-induced growth of the harmonic yield are analyzed, which allows for the formation of sources of coherent extreme ultraviolet radiation based on molecular plasma formation.

Investigation of high-harmonic cutoff of metal ions driven by near-infrared laser

The cutoff-energies of high-harmonic generation in the laser-ablated plumes of various metal targets (Ca, Mg, Fe, Zn, Ta, Mo, Al, W, In, Cu, Au, Ti, Ag) driven by near-infrared (0.8-µm) femtosecond laser are investigated and compared. Due to the low ionization potentials of metal atoms, it is believed that the observed high-harmonic cutoffs are contributed by the singly charged or even doubly charged ions. Ionization calculations using Perelomov-Popov-Terent'ev theory are performed to estimate the laser intensities at which saturation of ionization occur for different ions. Treating the calculated values as the effective driving laser intensities, the observed cutoffs from most of the targets are in reasonable agreement with the predictions of the semi-classical cutoff law.

High-order harmonics generation in the laser-induced lead-free perovskites-containing plasmas

High-order harmonics generation in the laser-induced plasmas produced on the surfaces of lead-free perovskites is studied. We analyze the harmonics generation in (CH₃NH₃)₂CuCl₄ and (CH₃NH₃)₂CuBr₄ plasmas during their ablation by the femtosecond, picosecond, and nanosecond pulses. The modifications of the high-order harmonics spectra are studied using the -color pump scheme (800 nm and 400 nm, 40 fs pulses). The influence of the variations of laser chirp and pulse duration on the dynamics of high-order harmonics generation is examined. The spectral shift, chirp-related harmonic cutoff scaling, and the role of the pulse duration of converting and heating laser radiation are examined at different conditions of plasma formation and harmonic generation. The dependencies of the pulse duration and the fluence of heating pulses on the harmonic’s blue shift are found. The effect of harmonics broadening and splitting on the two red- and blue-shifted components is demonstrated.

Application of vector beams for enhanced high-order harmonics generation in laser-induced plasmas

High-order harmonics driven by phase- and polarization-structured femtosecond pulses are unique sources of the extreme ultraviolet vortex and vector beams, which have various applications. Here, we report the generation of intense high-order harmonics during propagation of the polarization-structured vector beams (radially polarized beam, azimuthally polarized beam, and their superposition) through the laser-induced plasmas (In, C, CdS, Zns, Ag₂S). Low-order harmonics became stronger with radially polarized and azimuthally polarized driving beams compared with the linearly polarized beams, which is explained on the basis of phase matching and specific properties of vector beams. Contrary to that, the resonance-enhanced harmonic generated in the indium plasma in the case of radially polarized and azimuthally polarized beams was twice weaker compared with the harmonic generated by the LP beam due to modification in the resonant transition selection rules leading to a decrease of the oscillator strength of ionic transitions. Harmonic cut-off and intensity in the case of superposition of the radially and azimuthally polarized beams were lesser compared with the cases of the individual (radially polarized and azimuthally polarized) beams.

Analysis of laser plasma dynamics using the time resolved nonlinear optical response of ablated carbon nanocomposites mixed with epoxy resin

Nonlinear optical properties of carbon nanostructures attract attention due to the unique response of these materials during interactions with ultrashort laser pulses. Here we probe the carbon nanocomposites mixed with epoxy resin in laser-induced plasmas using the high-order harmonics generation (HHG) method. We analyze the nanosecond pulses induced plasmas containing three carbon nanostructures (fullerenes, multiwalled carbon nanotubes and diamond nanoparticles) using 40 fs pulses propagating through these plasmas. HHG efficiencies in ablated graphite and nanocomposites are compared. We utilize two digitally synchronized (nanosecond and femtosecond) laser sources allowing for the HHG-based analysis of the evolution of different plasma plumes up to 10 µs delay from the beginning of ablation. The role of different carbon-containing nanocomposites is analyzed and the evidence for the presence of various nanomaterials in laser-induced plasma at the moment of propagation of the driving femtosecond pulses is demonstrated.

Resonance-enhanced high harmonic in metal ions driven by elliptically polarized laser pulses

Resonance enhancement of a single order harmonic has been a main attractive feature in high-harmonic generation from laser ablated plumes of metals. Although it has been extensively investigated experimentally and theoretically, studies so far have focused only on linearly polarized driving fields. In this Letter, we study the dependence of the resonant harmonic yield in tin ions on the driving laser ellipticity. We find that the resonance leads to a less rapid decay of the harmonic yield as a function of driving ellipticity, and it is qualitatively reproduced by quantum mechanical simulations. To the best of our knowledge, our findings provide a new type of evidence for supporting previously proposed mechanisms for enhancement.

Revealing Molecular Strong Field Autoionization Dynamics

The novel strong field autoionization (SFAI) dynamics is identified and investigated by channel-resolved angular streaking measurements of two electrons and two ions for the double-ionized CO. Comparing with the laser-assisted autoionization calculations, we demonstrate the electrons from SFAI are generated from the field-induced decay of the autoionizing state with a following acceleration in the laser fields. The energy-dependent photoelectron angular distributions further reveal that the subcycle ac-Stark effect modulates the lifetime of the autoionizing state and controls the emission of SFAI electrons in molecular frame. Our results pave the way to control the emission of resonant high-harmonic generation and trace the electron-electron correlation and electron-nuclear coupling by strong laser fields. The lifetime modulation of quantum systems in the strong laser field has great potential for quantum manipulation of chemical reactions and beyond.

Reexamining Different Factors of the Resonance-Enhanced High-Order Harmonic Generation in Atomic and Nanoparticle Laser-Induced Tin Plasmas

We reexamine the resonance enhancement of a single harmonic emission during the propagation of ultrafast pulses through atomic and nanoparticle tin-containing laser-induced plasma (LIP). We compare the single atomic Sn and Sn nanoparticle plasmas to demonstrate a distinction in the enhancement factor of the single harmonic in the case of fixed and tunable near-infrared pulses. The analysis of the dynamics of Sn LIP shows the range of optimal delays between heating and driving pulses (130–180 ns), at which the maximal harmonic yield can be achieved. The enhancements of the 17th and 18th harmonics of 806 nm pulses were analyzed in the case of single-color and two-color pumps of LIP, showing up to a 12-fold enhancement of even harmonics in the two-color pump case. We show the enhancement of a single harmonic in the vicinity of the 4d105s25p2P3/2→4d95s25p2 transitions of Sn II ions and demonstrate how this process depends on the constituency of the plasma components at different conditions of target ablation. The application of tunable (1280–1440 nm) radiation allows for demonstrating the variations of single harmonic enhancement using a two-color pump of Sn-containing LIP.

High-Order Harmonics Generation in Atomic and Molecular Zinc Plasmas

We demonstrate the variations of single harmonic resonance enhancement during high-order harmonics generation in zinc-containing atomic and molecular species at the conditions of single-color and two-color pumps of laser-induced plasmas by applying different laser sources. We show how selenides of this metal notably modify the enhancement of single (9th, 15th or 16th) harmonic compared with purely atomic zinc plasmas. The variations of single harmonic enhancement are demonstrated using fixed (806 nm) and tunable (1280–1440 nm) radiation.

Investigation of Resonance-Enhanced High-Order Harmonics by Two-Component Laser-Produced Plasmas

Resonance-enhanced harmonics from laser-produced plasma plumes are an interesting phenomenon, whose underlying mechanism is still under debate. In particular, it is unclear whether the macroscopic dispersion properties of the plasma are the key factors for the formation of the enhancement. To shed light on this problem, we perform experiments with two-component plasmas, in which one of the components (tin) is known to be able to generate enhanced harmonics and the other component (lead) is known for altering the overall dispersion properties of the plasma medium. We compare the harmonics spectra from the plasma of pure tin and the plasma of tin/lead alloy. Depending on the driving wavelength, we observe enhanced harmonics at around 47 or 44 nm in both types of plasmas. The two enhanced regions could be attributed to resonances in singly-charged and doubly-charged tin ions, respectively. Our results indicate that the co-existence of lead plasma does not destroy the presence of the enhanced harmonics of tin plasma, and it seems to suggest that the macroscopic properties of the plasma are not the origin of the resonance-enhanced harmonics in tin.

High-Order Harmonic Generation in Au Nanoparticle-Contained Plasmas

Gold nanoparticles (NPs) have a wide range of applications in various fields. Here, we present high-order nonlinear optical studies of the plasmas produced from ablation of Au bulk targets and Au NP films deposited on paper and glass substrates. Experimentally, we analyze high-order harmonic generation (HHG) from gold NPs-containing plasmas. The HHG is produced by 35-fs pulses at 800 and 400 nm, while the plasmas are produced by femtosecond (35 fs, 800 nm), picosecond (200 ps, 800 nm), and nanosecond (5 ns, 1064 nm) pulses, respectively. High-order harmonics produced from ablated Au NPs on paper were 40 times stronger than the HHG from that ablated from the Au bulk targets. Through molecular dynamic simulations, we investigate the formation of gold NPs during laser ablation of a metal surface under different conditions.

Harmonic Generation from Neutral Manganese Atoms in the Vicinity of the Giant Autoionization Resonance

High harmonics from laser-ablated plumes are mostly generated from ionic species. We demonstrate that with ultrashort infrared (∼1.82  μm) driving lasers, high harmonics from laser-ablated manganese are predominantly generated from neutral atoms, a transition metal atom with an ionization potential of 7.4 eV. Our results open the possibility to advance laser-ablation technique to study the dynamics of neutral atoms of low ionization potential. Moreover, as manganese contains giant autoionizing resonance, intense and broadband high harmonics have been demonstrated from this resonance at energies from 49 to 53 eV. This opens the possibility to generate intense attosecond pulses directly from the giant resonances, as well as to study these resonances using high-harmonic spectroscopy.

Control of quasi-phase-matching of high-harmonics in a spatially structured plasma

High-harmonic generation is widely used for providing extreme ultraviolet radiation in attosecond science. Such experiments include photoelectron spectroscopy, diffractive imaging, or the investigation of spin dynamics. Many applications are restricted by a low photon flux which originates from the low efficiency of the generation process. In this article an effective method based on the quasi-phase-matched generation of high harmonics in spatially structured, laser ablated plasma is demonstrated. Through a proper dimensioning of the plasma structure, the harmonic yield is optimized for a controllable range of harmonic orders. By using four coherent zones, the intensity of a single harmonic is increased to a maximal possible value of 16 compared to using a single zone. The Gouy phase shift of the fundamental field is identified as the primary effect responsible for constructive interference of the harmonic fields generated in the individual plasma jets of the plasma structure.

High-order harmonic generation from the dressed autoionizing states

In high-order harmonic generation, resonant harmonics (RH) are sources of intense, coherent extreme-ultraviolet radiation. However, intensity enhancement of RH only occurs for a single harmonic order, making it challenging to generate short attosecond pulses. Moreover, the mechanism involved behind such RH was circumstantial, because of the lack of direct experimental proofs. Here, we demonstrate the exact quantum paths that electron follows for RH generation using tin, showing that it involves not only the autoionizing state, but also a harmonic generation from dressed-AIS that appears as two coherent satellite harmonics at frequencies ±2Ω from the RH (Ω represents laser frequency). Our observations of harmonic emission from dressed states open the possibilities of generating intense and broadband attosecond pulses, thus contributing to future applications in attosecond science, as well as the perspective of studying the femtosecond and attosecond dynamics of autoionizing states.

High-energy photons in XUV range and attosecond pulses are generated from infrared laser pulses through high harmonic generation in gases and solids. Here, the authors demonstrate the microscopic origin of resonant harmonic generation involving the autoionizing states of Sn in plasma plumes.