One of the specialized spectroscopic techniques used to analyze the interaction of a light field with a target atom or molecule is nonlinear four-wave mixing in the extreme ultraviolet (XUV) region. In this paper, we investigate the fundamental interaction of atomic argon and molecular nitrogen gases with a light field in the perturbative nonlinear regime by cascading high-order harmonic generation (HHG) radiation with a multi-color laser. We optimize the phase-matching of collinear, multiple-cycle laser pulses with incommensurate frequencies (800 nm, 1400 nm and 560 nm) in third-order nonlinear wave-mixing with HHG-XUV radiation. Using a single-gas-cell interaction chamber, we reveal the electron wave packet dynamics in atomic and molecular systems by examining the time-dependent spectral features of the wave-mixing field, including intensity and frequency modulation patterns. This simple experimental setup presents a novel spectroscopy technique that can provide deeper insights into target systems, and potentially more complex molecular gases, involving multi-electron interaction regimes.

We present a two-dimensional (2D) nonlinear four-wave mixing scheme in the extreme ultraviolet (XUV) to investigate ultrafast electronic wave-packets dynamics of multi-electron states in the above-threshold ionization region, using atomic argon and molecular nitrogen as examples. Coherent light sources in the range between 24 and 45 eV is generated by phase-matched cascaded four-wave mixing processes with a collinear configuration of two femtosecond laser fields 800 nm and 1400 nm. Motion of the electrons involving the excited states 3s3p6np (1 ) of argon gas, the state and the predissociation state of molecular nitrogen ion are unravelled through the ‘on-axis’ and ‘off-axis’ features of the two-dimensional spectra. Interpretation of the experimental data is supported by a theoretical dipole control model. Hence, results of this study may be promising for studies of dynamics of electrons in more complex systems.

We conducted a study on high-harmonic generation (HHG) in mixed gases, specifically Ar–Ne or Ar–Kr, with the aim of investigating the impact of ionization rate and neutral dispersion on the HHG process. Our focus was on understanding how these factors influence the HHG process when using gases with low and high ionization potentials. Based on phase-matched high-order harmonic generation in pure Ar gas, our investigation shows that the influence of plasma dispersion and neutral dispersion can be varied independently in mixed gas while the laser intensity is kept constant. Our results reveal that the addition of low ionization potential gases, such as Kr, to the Ar gas leads to a more rapid reduction in phase matching, due to the strong effects of ionization. The observed experimental outcomes align well with our theoretical calculations. This study provides valuable insights into the interplay of ionization rate and neutral dispersion in high-harmonic generation and the special requirement of the controlling of laser intensity for phase-matched harmonic generation. The findings contribute to a deeper understanding of the underlying dynamics and offer practical considerations for optimizing HHG properties.

In this study, we explore high harmonic generation (HHG) in pure argon (Ar) gas and a mixture of argon and helium (He). We investigate phase-matching conditions and interference effects in both single and mixed-gas systems. By varying the gas pressure in the Ar-He mixture, we optimize the harmonic spectrum, achieving a broad range from H17 to H43, corresponding to photon energies of 25 eV to 75 eV. We attribute the spectrum broadening to a cascaded HHG process: argon-generated extreme ultraviolet photons excite helium's outer electrons, which are then driven by the fundamental laser field to contribute to HHG. This finding aligns with previous studies, showing that mixing gases with low and high ionization potentials can enhance HHG. The results offer a broad HHG spectrum ideal for ultra-fast spectroscopy and high-resolution imaging applications.

We studied the γ-ray emission from laser interactions with structured targets of Al and Au. Bremsstrahlung and Non-linear Compton Scattering (NCS) emission are considered for the γ-ray emission using the open source 2-D PIC code EPOCH. Different shapes of the target generated additional hot electrons, which helps to enhance the photon energy in individual cases. The enhancement of photon energy is due to the target's shape and the hot electrons. Hot electron generation and their dynamics, like refluxing behavior, are crucial phenomena in thin targets. This study uses four different shapes of Al and Au targets. The relative strength of emissions from both bremsstrahlung and NCS are compared. The shape of the target enhances the γ-ray energy, electron energy, and emitted photon number and improves the electron beam divergence. The effect of each target shape on hot electrons' refluxing behavior and the role of the electric and magnetic fields are discussed in detail.

"In this study, we experimentally investigate the variation of the phase matching condition of the high harmonic generation (HHG) process with pure argon gas and an argon-neon gas mixture. Phase-matched HHG is generated around the absorption edge of argon gas and then neon gas is added to the original argon gas. The pressure-dependent intensity of the harmonics produced by pure argon gas and the gas mixture is examined. We show that as more neon gas is added to the mixture, the phase matching of the higher order harmonics is less favourable than that of the lower order harmonics. Finally, the total phase mismatch at various gas mixture pressures is discussed. Our experimental results are in agreement with the theoretical calculation."

We describe a thorough study of the wave-mixing procedure in the extreme ultraviolet (XUV) region involving three laser fields (800 nm, 1400 nm and 1860 nm). In addition to the phase matched HHG spectrum generated by an 800-nm laser (driving field), non-integer order wave-mixing spectra are produced when the driving field and the control field (1400 nm or 1860 nm) are collinearly focused into krypton gas. In addition, the simultaneous presence of three laser fields generates resolvable four-wave mixing (FWM) frequencies that clearly indicate the contribution of each control field. We also discuss an application of the FWM scheme to extend the HHG cutoff region and generate the XUV quasi-continuum spectrum.

We discuss the generation of cascaded extreme ultraviolet four-wave mixing fields with a single-gas-cell configuration and use them to study the dynamics of free electron wave packets of the noble gases. The temporal evolution of atomic dipoles in the vicinity of one-electron excitation Rydberg states 3s3p6np of argon and 4s4p6n′p of krypton is reflected in the intensity profiles of the four-wave mixing spectra. Different interference pathways for these dipole-allowed transitions are revealed in the time-delay-dependent phase shift of the four-wave mixing fields. The results of this study may be promising for studies of more complex systems.

Studies of the generation and propagation of light fields in the extreme ultraviolet (XUV) can provide insights into the fundamental interaction of atoms in highly excited levels and ionized atoms. In this paper, we present experimental results of nonlinear four-wave mixing (FWM) processes using a combination of XUV radiation and optical pulses in argon gas. The XUV pulses are produced by phase-matched high-order harmonic generation (HHG). Optimized phase-matching of collinear multiple-cycle laser pulses with incommensurate frequencies (800 nm, 1400 nm, and 560 nm) is used to indicate the different pathways of the third-order and fifth-order nonlinear responses in the mixing process in a single gas cell configuration. A perturbative nonlinear optics approach can be used to explain our cascaded wave-mixing patterns. Our results reveal that the time-dependent spectral features of the mixing fields are associated with auto-ionization processes. Overall, the intensity and frequency modulation of the wave-mixing fields provides a new technique to investigate the dynamical evolution of electron wave-packets in atomic and molecular gases.

Gold atoms are stripped of 72 of their electrons to form nitrogen-like Au72+ ions inside extremely hot plasmas by irradiating gold foils and nanowires with highly relativistic femtosecond laser pulses.

We demonstrate that a two-colour three-pulsenonlinear spectroscopy can be used to study the dynamics of excited carriers inSi quantum dot structures embedded in SiN. Decays of the transverse optical phonon population and the transverse acoustic phonon population are measured and discussed. A simple theoretical modelis also used to support interpretation of our experimental observations.

Using two multiple-cycle optical pulses with incommensurate frequencies (e.g., at wavelengths 1400 nm and 800 nm) in a collinear configuration, a cascaded background-free four-wave mixing EUV field can be realized because the EUV pulse produced by phase-matched high order harmonic generation in combination with the other two optical pulses creates a third-order nonlinear polarisation which drives a phase-matched four-wave mixing process along the propagating direction. The four-wave mixing emission can be manipulated by varying the delay of the second optical pulse. The phase-matching of the four-wave mixing process together with the relatively long interaction path combine to produce a strong output signal which leads to an enhanced signal-noise ratio of the Fourier-transformed signal used to obtain the two-dimensional cross correlation spectrum. Some key features of this two-dimensional spectroscopy, such as the on-axis and off-axis peaks, can lead to the determination of interaction pathways of real dipole-allowed transitions and virtual transitions in the EUV.

We demonstrate generation of phase-matched four-wave mixing frequencies in XUV region by using a driving field and two control fields. Our findings are promising to produce an XUV quasi-continuum for attosecond pulses synthesis. © 2019 The Author(s)

We report here experimental results of perturbative nonlinear optical wave-mixing processes in the extreme ultraviolet region by using two-color and three-color laser fields. Besides the usual odd-harmonic spectrum of high harmonic generation, new spectral components are observed when multiple incommensurate lasers (one driving plus one or two control field) interact with neutral krypton gas. To demonstrate the wave-mixing process underlying such an observation, we first couple the driving field with either the signal or the idler field of an optical parametric amplifier in the gaseous ensemble to generate certain mixing frequencies. The two control fields are then simultaneously combined with the driving field to produce broad and distinguishable mixing peaks that clearly reveal the contribution of each control laser. Finally, the variation of the intensity of the mixing waves with the intensity of each control field, the gas density, and the relative focus position is examined for signatures of phase-matched generation of the mixing fields in this spectral region.

We use a delayed weak laser beam to control the spectral features of extreme ultraviolet (XUV) pulses generated by a strong femtosecond laser beam through phase-matched high harmonic generation (HHG) in an atomic medium, e.g. krypton. The variation of the HHG spectrum reveals the influence of the free electrons on the propagation of the XUV field in the medium. In addition, a signature of the autoionization process is visible. Our findings provide a promising technique to study ultrafast dynamics of atomic and molecular gases.

We apply a cascaded four-wave mixing process in the extreme ultraviolet (XUV) region using two collinear multiple-cycle laser pulses with incommensurate frequencies (wavelengths 1400 and 800 nm) to construct a two-dimensional cross-correlation spectrum. We show that the two-dimensional spectrum can be used to extract the amplitude and phase modifications of the atomic dipole moments of the coupled states in atomic krypton interacting with the intense pulsed laser light. The experimental configuration and a simple model for qualitative interpretation allow us to demonstrate the validity and power of the 2D spectroscopy method in the XUV region.

We report here a detailed study of the four-wave mixing process in the extreme ultraviolet (XUV) region around 30 nm by using two collinear incommensurate frequency laser pulses. The experimental results reveal evidence of the coherent accumulation of the wave-mixing fields and low-order (third-order and fifth-order) nonlinear response of an argon medium. The dependence of the intensities of the mixing fields on the intensity of a weak control field, on the argon pressure and on the interaction length is analyzed to show that the four-wave mixing fields in this spectral range are generated under the phase-matched condition.

Coherent diffractive imaging (CDI) is a lensless microscopy technique in which the structure of a specimen of interest is probed using a coherent short-wavelength light source. CDI has been widely used in nanotechnology and structural biology to capture high resolution images of non-crystalline objects. In this paper, we review the theoretical and experimental aspects of coherent diffractive imaging using a focused narrow-bandwidth table-top high harmonic source. The review begins with an outline of generation and characterization of the high harmonic source. Theoretical description of coherent diffractive imaging technique is then summarized. The review concludes with our recent results in imaging using a single harmonic beam selected by employing XUV focusing mirrors. These achievements provide a promising technique for the non-crystallographic structural determination of membrane proteins using a table-top extreme ultraviolet source.

We report here evidence of phase-matched optical wave mixing in the extreme ultraviolet (XUV) region. This process has been studied with a collinear two-colour high-order harmonic generation scheme. An 800 nm, 30 fs driving field is used to produce a small bandwidth comb of odd harmonic orders (wavelength around 30 nm) in a long cell filled with argon gas. Mixing frequencies in this spectral range are produced by applying a second weak control-field of 1,400 nm, 40 fs. Low order (third-and fifth-order) nonlinear optical wave mixing is observed to be a phase-matched process. The dependence of the intensity of the harmonic orders and the mixing frequencies on different control-field intensities, gas pressure, and interaction length is analysed to verify the phase matching process.

We present a detailed study of the wave-mixing process in the extreme ultraviolet (XUV) region (around 30 nm) by using two collinear multiple-cycle laser pulses with incommensurate frequencies (wavelengths 1400 and 800 nm). The experimental data provide evidence for the coherent accumulation of wave-mixing fields and a high third-order response of the medium in this spectral range. We show that the time evolution of the mixing fields can be used to study the coherence dynamics of the free-electron wave packet with a lifetime of 200-750 fs.