High-order Harmonic Generation Process Research Articles

Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses

High-energy isolated attosecond pulses required for the most intriguing nonlinear attosecond experiments as well as for attosecond-pump/attosecond-probe spectroscopy are still lacking at present. Here we propose and demonstrate a robust generation method of intense isolated attosecond pulses, which enable us to perform a nonlinear attosecond optics experiment. By combining a two-colour field synthesis and an energy-scaling method of high-order harmonic generation, the maximum pulse energy of the isolated attosecond pulse reaches as high as 1.3 μJ. The generated pulse with a duration of 500 as, as characterized by a nonlinear autocorrelation measurement, is the shortest and highest-energy pulse ever with the ability to induce nonlinear phenomena. The peak power of our tabletop light source reaches 2.6 GW, which even surpasses that of an extreme-ultraviolet free-electron laser.

High-harmonic generation from a coherent superposition of electronic states: Controlling interference patterns via short and long quantum orbits

Laser pump-probe schemes are explored numerically from a molecular time-dependent Schr\"odinger equation for monitoring attosecond electron motion by high-order-harmonic generation (HHG) from a coherent superposition of electronic states. Varying the time delay between the probe and pump pulse on an attosecond time scale alters the HHG signal, leading to universal interference patterns. By using an extended three-step recollision model, we show that various regular interference patterns in the HHG spectra, including continuous harmonic frequency redshifts as a function of pump-probe delay, are related to interference between specific pairs of short or long quantum orbits. For small excited-state population (regime A), interferences are controlled by electron-tunneling times, whereas for equal populations (regime B), recollision time control dominates thus allowing for control of the HHG process by the pump-probe delay time and by electron-state populations. We show that each specific pattern is closely related to the interference between pairs of specific (short or long) quantum orbits originating from a specific electron bound state. One can generate a specific pattern by varying the populations in the coherent superposition, the laser intensity, wavelength, and ionization potential of the electronic states.

High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles

We present theoretical investigations of high-order harmonic generation (HHG) resulting from the interaction of noble gases with localized surface plasmons. These plasmonic fields are produced when a metal nanoparticle is subject to a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic structure, has a strong spatial dependency. We demonstrate that the strong non-homogeneity of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic cut-off energy. In order to understand and characterize this new feature, we include the functional form of the laser electric field obtained from recent attosecond streaking experiments [F. S{\"u}{\ss}mann and M. F. Kling, Proc. of SPIE, {\bf Vol. 8096}, 80961C (2011)] in the time dependent Schr\"odinger equation (TDSE). By performing classical simulations of the HHG process we show consistency between them and the quantum mechanical predictions. These allow us to understand the origin of the extended harmonic spectra as a selection of particular trajectory sets. The use of metal nanoparticles shall pave a completely new way of generating coherent XUV light with a laser field which characteristics can be synthesized locally.

Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses

We theoretically investigate the quantum paths of the high-order harmonic generation (HHG) by using a left and a right circularly polarized Gaussian laser pulse with a proper time delay. When the carrier phase of the two pulses is ${\ensuremath{\varphi}}_{1}=0$, ${\ensuremath{\varphi}}_{2}=0.5\ensuremath{\pi}$, the ``gating'' structure of the combined laser field disappears. The numerical results indicate that no ``gating''-structure-combined laser pulse can control the quantum path. The HHG process is investigated by the semiclassical three-step model that makes use of a finite initial transverse velocity in the elliptically polarized field. For the case of ${\ensuremath{\lambda}}_{1}=800$ nm, ${\ensuremath{\lambda}}_{2}=1600$ nm, only a short quantum path contributes to the HHG, and an isolated attosecond pulse would be obtained. For the case of ${\ensuremath{\lambda}}_{2}=1600$, ${\ensuremath{\varphi}}_{2}=0.5\ensuremath{\pi}$, a supercontinuum spectrum plateau from 180 to 570 eV which includes the water window region is obtained, and attosecond pulses with the duration of about 75 as and a tunable central wavelength could be generated by superposing a bandwidth of 50 eV in the plateau area.

Efficient high-order harmonic generation boosted by below-threshold harmonics

High-order harmonic generation (HHG) in gases has been established as an important technique for the generation of coherent extreme ultraviolet (XUV) pulses at ultrashort time scales. Its main drawback, however, is the low conversion efficiency, setting limits for many applications, such as ultrafast coherent imaging, nonlinear processes in the XUV range, or seeded free electron lasers. Here we introduce a novel scheme based on using below-threshold harmonics, generated in a “seeding cell”, to boost the HHG process in a “generation cell”, placed further downstream in the focused laser beam. By modifying the fundamental driving field, these low-order harmonics alter the ionization step of the nonlinear HHG process. Our dual-cell scheme enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources.

Influence of large permanent dipoles on molecular orbital tomography

The influence of large permanent dipoles on molecular orbital tomography via high-order harmonic generation (HHG) is investigated in this work. It is found that, owing to the modification of the angle-dependent ionization rate resulting from the Stark shift, the one-side-recollision condition for the tomographic imaging can not be satisfied even with the few-cycle driving pulses. To overcome this problem, we employ a tailored driving pulse by adding a weak low-frequency pulse to the few-cycle laser pulse to control the HHG process and the recollision of the continuum electrons are effectively restricted to only one side of the core. Then we carried out the orbital reconstruction in both the length and velocity forms. The results show that, the orbital structure can only be successfully reproduced by using the dipole matrix elements projected perpendicular to the permanent dipole in both forms.

High-Power Tunable Terahertz Radiation by High-Order Harmonic Generation

We propose a new type of terahertz (THz) radiation source based on the electron beam-wave interaction. A high-order harmonic-generation process was introduced to a traveling-wave tube (TWT)-like device-the high-harmonic TWT or HHTWT. The scheme is configured as a frequency multiplier and amplifier with W-band (millimeter wave) input signals and THz output power. Simulations show that operation at the seventh harmonic is possible and other order harmonic waves were suppressed. The output frequency can be tuned continuously over a 30-GHz bandwidth with more than 20-dBm output power. The peak output power is about 30 dBm at 707 GHz. The output frequency is insensitive to beam voltage jitter.

Generation of EUV radiation by plasmonic field enhancement using nano‐structured bowties and funnel‐waveguides

Recent experimental data of high‐order harmonic generation (HHG), obtained by use of the plasmonic field enhancement of nanostructure bowties and funnel‐waveguides, are presented. Emphasis is laid on reproduction of previous experimental results and also elucidation of the fundamental limitations associated with the nanostructure thermal damage, small laser‐gas interaction volume, and atomic line emission in the plasmon‐driven HHG process. In addition, the dominance of coherent harmonics is quantitatively verified by implementing a two‐beam interference experiment using a pair of funnel‐waveguides. This study proves that funnel‐waveguides are a superior plasmonic device capable of providing not only high thermal immunity but also sufficient atom emitters to produce practically usable extreme‐ultraviolet (EUV) radiation in a reproducible manner.

High order harmonic generation in noble gases using plasmonic field enhancement

Theoretical studies of high‐order harmonic generation (HHG) in rare gases driven by plasmonic field enhancement are presented. 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. It is demonstrated that the strong nonhomogeneous character of the laser enhanced field plays an important role in the HHG process and significantly extends the harmonic cutoff. The models are based on numerical solution of the time dependent Schrödinger equation (TDSE) and supported by classical and semiclassical calculations.

Theory of High Harmonic Generation for Probing Time-Resolved Large-Amplitude Molecular Vibrations with Ultrashort Intense Lasers

We present a theory that incorporates the vibrational degrees of freedom in a high-order harmonic generation (HHG) process with ultrashort intense laser pulses. In this model, laser-induced time-dependent transition dipoles for each fixed molecular geometry are added coherently, weighted by the laser-driven time-dependent nuclear wave packet distribution. We show that the nuclear distribution can be strongly modified by the HHG driving laser. The validity of this model is first checked against results from the numerical solution of the time-dependent Schrödinger equation for a simple model system. We show that in combination with the established quantitative rescattering theory this model is able to reproduce the time-resolved pump-probe HHG spectra of N(2)O(4) reported by Li et al. [Science 322, 1207 (2008)].

Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures

We study high-order harmonic generation (HHG) resulting from the illumination of plasmonic nanostructures with a short laser pulse of long wavelength. We demonstrate that both the confinement of the electron motion and the inhomogeneous character of the laser electric field play an important role in the HHG process and lead to a significant increase of the harmonic cutoff. In particular, in bow-tie nanostructures with small gaps, electron trajectories with large excursion amplitudes experience significant confinement and their contribution is essentially suppressed. In order to understand and characterize this feature, we combine the numerical solution of the time-dependent Schrödinger equation (TDSE) with the electric fields obtained from 3D finite element simulations. We employ time-frequency analysis to extract more detailed information from the TDSE results and classical tools to explain the extended harmonic spectra. The spatial inhomogeneity of the laser electric field modifies substantially the electron trajectories and contributes also to cutoff increase.

High-order-harmonic generation from inhomogeneous fields

We present theoretical studies of high-order-harmonic generation (HHG) produced by nonhomogeneous fields resulting from the illumination of plasmonic nanostructures with a short laser pulse. We show that both the inhomogeneity of the local fields and the confinement of the electron movement play an important role in the HHG process and lead to the generation of even harmonics and a significantly increased cutoff, more pronounced for the longer-wavelength cases studied. In order to understand and characterize the new HHG features, we employ two different approaches: the numerical solution of the time-dependent Schr\"odinger equation and the semiclassical approach known as the strong-field approximation (SFA). Both approaches predict comparable results and show the new features, but by using the semiclassical arguments behind the SFA and time-frequency analysis tools, we are able to fully understand the reasons for the cutoff extension.

Nonadiabatic quantum path analysis of the high-order harmonic generation in a highly ionized medium

The nonadiabatic saddle-point method is used to investigate the process of high-order harmonic generation in a gas, driven by few-optical-cycle pulses with above-saturation intensity and controlled electric field. The peculiar effects produced on the generation process by temporal reshaping of the driving field, induced by propagation in a highly ionized gas cell, can be used to control the electron quantum paths, which contribute to the harmonic generation process. It is shown that complete spectral tunability of the harmonic peak position over the entire extreme-ultraviolet spectrum, obtained by changing the carrier-envelope phase of the driving pulses, can be understood by considering the effects of driving pulse distortions on the phase of the relevant electron quantum paths.

Generation of 40-as few-cycle pulse through chirp manipulation

We discuss theoretically how supercontinuum spectra produced from high-order harmonic generation processes in a synthesized same-color laser field is optimized by adjusting the chirp parameter of the controlling pulse. Furthermore, a 40-attosecond isolated pulse with an effective bandwidth of 121 orders is obtained from He+ ion when the chirp rate ratio of pulses has a small value. The numerical results show that the efficiency of single as pulse generation is enhanced, and the quantum paths are controlled successfully. Our simulation shows that the produced pulses with high signal-to-noise ratio are obtained straightforwardly without any phase compensation. These results are explained using the classical approach.

High field physics and extreme nonlinear optics

Despite the fact that high order harmonic generation (HHG) aims at serving as a table-top light source for imaging applications with extremely high spatial resolution, a general lack of accurate conversion efficiency measurements exists in the field. Here, we present such a measurement for a HHG setup with a semi-infinite gas cell. By combining measurements with a calibrated photodiode sensitive in the extreme ultra-violet (XUV) and spatially resolved spectral measurements of HHG spectra, we are able to determine conversion efficiencies of the HHG process as well as brilliance values for individual harmonics. The method is explained in detail and applicable to any target geometry.

Extreme Nonlinear Optics in a Femtosecond Enhancement Cavity

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 combs.

Valley in the efficiency of the high-order harmonic yield at ultra-high laser intensities

We study the process of high-order harmonic generation using laser pulses with non-adiabatic turn-on and intensities well above saturation. As a main point, we report the existence of a valley structure in the efficiency of single-atom high-order harmonic generation with increasing laser intensities. Consequently, after an initial decrease, the high-frequency radiation yield is shown to increase for higher intensities, returning to a level similar to the case below saturation. Such behavior contradicts the general belief of a progressive degradation of the harmonic emission at ultrahigh intensities, based on the experience with pulses with smoother turn-on. We shall show that this behavior corresponds to the emergence of a new pathway for high-order harmonic generation, which takes place during the pulse turn-on. Our study combines trajectory analysis, wavelet techniques and the numerical integration of 3-Dimensional Time Dependent Schrödinger Equation. The increase in efficiency raises the possibility of employing ultrahigh intensities to generate high-frequency radiation beyond the water window.

High-order harmonic generation from coherently excited molecules

High-order harmonic generation (HHG) from electronically excited molecules exposed to single-cycle laser pulses is investigated. H+2 ions are used as an example under the condition that they are prepared in a coherent superposition of the two lowest lying states. We show that the populated excited state can be used to gate the ionization and the HHG processes. The HHG yields are found dependent on the coherent phase and the carrier-envelope phase of the laser pulse, providing the possibility of monitoring electron localization dynamics. We further demonstrate that the presence of multi-path recombinations leads to interference in harmonic yields enabling the determination of harmonic chirp.

Attosecond pulse generation by applying a weak static electric field to a few-cycle pulse

The high-order harmonic generation process under the combination of a few-cycle pulse and a static electric field was investigated in this work. A linear harmonic cutoff extension was observed with its dependence on the relative strength ratio of the static electric field with respect to a single-color, 2.5 optical cycle (oc), 800 nm, 1.4×1015 W cm−2 few-cycle pulse as the fundamental driving field. Exploiting the relative strength ratio tuning from 0 to 0.1, a linear continuum width extending on the XUV spectrum up to 191 eV, which supports the creation of an 18 attosecond isolated attosecond pulse, was generated. Moreover, classical trajectory calculation and time–frequency analyses for explaining the mechanism are also presented.

High-order harmonic generation enhanced by XUV light

The combination of high-order harmonic generation (HHG) with resonant XUV excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process is investigated theoretically. In this setup, the first electron performs a HHG three-step process, whereas the second electron Rabi flops between the core and the valence vacancy. The modified HHG spectrum due to recombination with the valence and the core is determined and analyzed for krypton on the 3d→4p resonance in the ion. We assume an 800 nm laser with an intensity of about 10(14) W/cm2 and XUV radiation from the Free Electron Laser in Hamburg (FLASH) with an intensity in the range 10(13)-10(16)W cm2. Our prediction opens perspectives for nonlinear XUV physics, attosecond x rays, and HHG-based spectroscopy involving core orbitals.