We consider the process of high-order harmonics generation (HHG) in the xenon atom enhanced by the inter-shell correlation between the valence 5p and inner 4d shells. We derive the HHG spectrum from a numerical solution of the one-electron time-dependent Schrödinger equation multiplied by the enhancement factor taken as the photoionization cross-sections ratio calculated with and without the inter-shell correlation. Such a simplified approach is adequate to describe the experimental HHG spectrum reported by Shiner et al [Nat. Phys. 7, 464 (2011)] generated by a single color IR laser. Similarly, we find good agreement when applied to the two-color driven HHG spectra reported by Facciala et al [Phys. Rev. Lett. 117, 093902 (2016)].
Solving the one-dimensional time-dependent Schrödinger equation for simple model potentials, we investigate resonance-enhanced high-order harmonic generation, with emphasis on the physical mechanism of the enhancement. By truncating a long-range potential, we investigate the significance of the long-range tail, the Rydberg series, and the existence of highly excited states for the enhancements in question. We conclude that the channel closings typical of a short-range or zero-range potential are capable of generating essentially the same effects.
We resolve an open question about the origin of the giant enhancement in the high-harmonic generation (HHG) spectrum of atomic xenon around 100 eV. By solving the many-body time-dependent Schrödinger equation with all orbitals in the 4d, 5s, and 5p shells active, we demonstrate the enhancement results truly from collective many-body excitation induced by the returning photoelectron via two-body interchannel interactions. Without the many-body interactions, which promote a 4d electron into the 5p vacancy created by strong-field ionization, no collective excitation and no enhancement in the HHG …
We present a method to tune the resonantly enhanced harmonic emission from engineered potentials, which would be experimentally feasible in the purview of the recent advances in atomic and condensed matter physics. The recombination of the electron from the potential dependent excited state to the ground state causes the emission of photons with a specific energy. The energy of the emitted photons can be controlled by appropriately tweaking the potential parameters. The resonant enhancement in high-harmonic generation enables the emission of very intense extreme ultra-violet or soft x-ray radi…
We present theoretical studies of high-order harmonic generation (HHG) in rare gases driven by plasmonic field enhancement. This kind of fields appears when plasmonic nanostructures are illuminated by an intense few-cycle laser and have a particular spatial dependency, depending on the geometrical shape of the nanostructure. We demonstrate that the strong nonhomogeneous character of the laser enhanced field plays an important role in the HHG process and significantly extends the harmonic cutoff. Our models are based on numerical solution of the time dependent Schroedinger equation (TDSE) and s…
Using a high-frequency field superposed to a linearly polarized bichromatic laser field composed by a wave with frequency $ω$ and a wave with frequency $2ω$, we show it is possible to enhance the intensity of a group of high harmonics in orders of magnitude. These harmonics have frequencies about 30% higher than the monochromatic-cutoff frequency, and, within the three-step-model framework, correspond to a set of electron trajectories for which tunneling ionization is strongly suppressed. Particular features in the observed enhancement suggest that the high-frequency field provides an addition…
We perform a detailed analysis of high-order harmonic generation (HHG) in atoms within the strong field approximation (SFA) by considering spatially inhomogeneous monochromatic laser fields. We investigate how the individual pairs of quantum orbits contribute to the harmonic spectra. We show that in the case of inhomogeneous fields, the electron tunnels with two different canonical momenta. One of them leads to a higher cutoff and the other one develops a lower cutoff. Furthermore, we demonstrate that the quantum orbits have a very different behavior in comparison to the homogeneous field. We …
At the core of attosecond science lies the ability to generate laser pulses of sub-femtosecond duration. In tabletop devices the process relies on high-harmonic generation, where a major challenge is to obtain high yields and high cutoff energies required for the generation of attosecond pulses. We develop a computational method that can simultaneously resolve these issues by optimizing the driving pulses using quantum optimal control theory. Our target functional, an integral over the harmonic yield over a desired energy range, leads to a remarkable cutoff extension and yield enhancement for …
Resonant enhancement of high harmonic generation can be obtained in plasmas containing ions with strong radiative transitions resonant with harmonic orders. The mechanism for this enhancement is still debated. We perform the first temporal characterization of the attosecond emission from a tin plasma under near-resonant conditions for two different resonance detunings. We show that the resonance considerably changes the relative phase of neighbouring harmonics. For very small detunings, their phase locking may even be lost, evidencing strong phase distortions in the emission process and a modi…
We present a theoretical study of the influence of resonant enhancement on quantum path dynamics in the generation of harmonics above and below the ionization threshold in helium. By varying the wavelength and intensity of the driving field from 425 nm to 500 nm and from 30 TW/cm${^2}$ to 140 TW/cm${^2}$, respectively, we identify enhancements of harmonics 7, 9, and 11 that correspond to multiphoton resonances between the ground state and the Stark shifted $1s2p$, $1s3p$, and $1s4p$ excited states. A time-frequency analysis of the emission shows that both the short and long quantum path contri…
The sub-cycle dynamics of electrons driven by strong laser fields is central to the emerging field of attosecond science. We demonstrate how the dynamics can be probed through high-order harmonic generation, where different trajectories leading to the same harmonic order are initiated at different times, thereby probing different field strengths. We find large differences between the trajectories with respect to both their sensitivity to driving field ellipticity and resonant enhancement. To accurately describe the ellipticity dependence of the long trajectory harmonics we must include a sub-c…
We consider harmonics generation and wave-mixing by two-color multi photon resonant excitation of three-level atoms/molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atom and homonuclear diatomic molecular ion show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appr…
We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths ($\approx 2 μ$m), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.
Using a quantum mechanical three-step model we present numerical calculations on the high-harmonic generation from four polyatomic molecules. Ethylene (C$_2$H$_4$) serves as an example where orbital symmetry directly affects the harmonic yield. We treat the case of methane (CH$_4$) to address the high-harmonic generation resulting from a molecule with degenerate orbitals. To this end we illustrate how the single orbital contributions show up in the total high-harmonic signal. This example illustrates the importance of adding coherently amplitude contributions from the individual degenerate orb…
We present a high harmonic generation theory which generalizes the strong-field approximation to the resonant case, when the harmonic frequency is close to that of the transition from the ground to an autoionizing state of the generating system. We show that the line shape of the resonant harmonic is a product of the Fano-like factor and the harmonic line which would be emitted in the absence of the resonance. The theory predicts rapid variation of the harmonic phase in the vicinity of the resonance. The calculated resonant harmonic phase is in reasonable agreement with recent measurements. Pr…
We produce oriented rotational wave packets in CO and measure their characteristics via high harmonic generation. The wavepacket is created using an intense, femtosecond laser pulse and its second harmonic. A delayed 800 nm pulse probes the wave packet, generating even-order high harmonics that arise from the broken symmetry induced by the orientation dynamics. The even-order harmonic radiation that we measure appears on a zero background, enabling us to accurately follow the temporal evolution of the wave packet. Our measurements reveal that, for the conditions optimum for harmonic generation…
In strong field laser physics it is a common practice to use the high-order harmonic cutoff to estimate the laser intensity of the pulse that generates the harmonic radiation. Based on the semiclassical arguments it is possible to find a direct relationship between the maximum value of the photon energy and the laser intensity. This approach is only valid if the electric field driving HHG is spatially homogenous. In laser-matter processes driven by plasmonics fields, the enhanced fields present a spatial dependence that strongly modifies the electron motion and consequently the laser driven ph…
Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by beyond mean-field electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized quiver motion of the electrons. The finite-latti…
Intrinsic to the process of high-order harmonic generation is the creation of plasma and the resulting spatiotemporal distortions of the driving laser pulse. Inside a high finesse cavity where the driver pulse and gas medium are reused, this can lead to optical bistability of the cavity-plasma system, accumulated self-phase modulation of the intracavity pulse, and coupling to higher order cavity modes. We present an experimental and theoretical study of these effects and discuss their implications for power scaling of intracavity high-order harmonic generation and extreme ultraviolet frequency…
The high-order harmonic spectrum generated in two-color intense laser field under certain conditions has a pronounced maximum caused by the so called spectral caustic. Using a numerical solution of the 3D time-dependent Schrödinger equation we study the width of the maximum and the degree of the generation enhancement due to the caustic as a function of the fundamental intensity, wavelength, and atomic ionization potential. It is shown that the degree of this enhancement can be well quantitatively characterized by a single parameter: the ratio of the radius of the free electronic oscillation i…
High-order harmonic generation (HHG) from molecular ion HeH$^{2+}$ in two initial states of $1sσ$ (ground state) and $2pσ$ (first excited state) is investigated theoretically, in homogeneous and plasmonic-enhanced laser fields. The electron ionization and the enhancement of HHG yield in ground and first excited states, as the initial states, is studied and a strong orientation effect for ionization of electron in $2pσ$ state is discovered, that it can be used to reach a longer lifetime for the electron in the first excited state, which is responsible for the enhancement in HHG yield, during th…
High harmonic generation (HHG) provides a flexible framework for the development of coherent light sources in the extreme-ultraviolet and soft x-ray regimes. However it suffers from low conversion efficiencies as the control of the HHG spectral and temporal characteristics requires manipulating electron trajectories on attosecond time scale. The phase matching mechanism has been employed to selectively enhance specific quantum paths leading to HHG. A few important fundamental questions remain open, among those how much of the enhancement can be achieved by the single-emitter and what is the ro…
We investigate the effect on high-order harmonic generation of the distortion of molecular orbitals by the driving laser field. Calculations for high-order harmonic generation including orbital distortion are performed for N2. Our results allow us to suggest that field-distortion is the reason why the two-center interference minimum has never been observed experimentally in N2. We propose experimental parameters which should allow an observation of the two-center interference minimum.
We present a new theory that the molecular high order harmonic generation in an intense laser field is determined by molecular internal symmetry and momentum distribution of the tunneling-ionized electron. The molecular internal symmetry determines the quantum interference form of the returning electron inside the molecule. The electron momentum distribution determines the relative interference strength of each individual electron de Broglie wave. All individual electron de Broglie wave interferences add together to collectively modulate the molecular high harmonic generation. We specifically …
The strong-field approximation for high-harmonic generation in near-infrared and infrared laser pulses is formulated in the accelerated Kramers-Henneberger frame. The accompanying physical picture is discussed and the nature of the leading-order term is contrasted with that of the three-step model following the strong-field-approximation formulation in the length or velocity gauges. The theory is illustrated by high-harmonic generation spectra for atomic hydrogen.
We studied the high-harmonic generation by the interaction of sub-cycle laser pulses with the He atom. The sub-cycle pulses are modeled using the complex source vector beam model, which is an exact solution to Maxwell's equations and accurately models the sub-cycle field profiles. We observed that the harmonic cutoff could be extended with the variation of the sub-cycle pulse duration, mainly because of the inherent blueshift associated with shorter pulses. The scaling laws for the harmonic yield and harmonic cutoff energy with pulse duration and fundamental driver wavelengths are also deduced…
We report the generation of five phase-locked harmonics, f_1: 2403 nm, f_2: 1201 nm, f_3: 801 nm, f_4: 600 nm, and f_5: 480 nm with an exact frequency ratio of 1 : 2 : 3 : 4 : 5 by implementing a divide-by-three optical-frequency divider in the high harmonic generation process. All five harmonics are generated coaxially with high phase coherence in time and space, which are applicable for various practical uses.
We study high-order harmonic generation (HHG) driven by seeded plasmonic-enhanced fields. On one hand, plasmonic-enhanced fields have shown a great potential to extend the HHG cutoff, an instrumental pre-requisite for the generation of attosecond pulses. On another hand, the use of XUV seeds appears to have a considerable potential to improve the HHG conversion efficiency, which is typically modest when a unique fundamental laser pulse is employed. By mixing these two sources, we show it is possible to, simultaneously, boost the HHG cutoff and to increase the harmonic photon flux. The combinat…
